Daily Papers

Lara is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of Lara's expressive ability reports that it can represent relational algebra and most linear algebra operations. However, several essential computations, such as matrix inversion and determinant, cannot be expressed in Lara. Lara cannot represent global and iterative computation, either. This article proposes IterLara, extending Lara with iterative operators, to provide an algebraic model that unifies operations in general-purpose computing, like big data, AI, scientific computing, and database. We study the expressive ability of Lara and IterLara and prove that IterLara with aggregation functions can represent matrix inversion, determinant. Besides, we demonstrate that IterLara with no limitation of function utility is Turing complete. We also propose the Operation Count (OP) as a metric of computation amount for IterLara and ensure that the OP metric is in accordance with the existing computation metrics.

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al., 2017) and the Neural GPU (Kaiser & Sutskever, 2016). We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete. Our study also reveals some minimal sets of elements needed to obtain these completeness results.

Since the success of GPT, large language models (LLMs) have been revolutionizing machine learning and have initiated the so-called LLM prompting paradigm. In the era of LLMs, people train a single general-purpose LLM and provide the LLM with different prompts to perform different tasks. However, such empirical success largely lacks theoretical understanding. Here, we present the first theoretical study on the LLM prompting paradigm to the best of our knowledge. In this work, we show that prompting is in fact Turing-complete: there exists a finite-size Transformer such that for any computable function, there exists a corresponding prompt following which the Transformer computes the function. Furthermore, we show that even though we use only a single finite-size Transformer, it can still achieve nearly the same complexity bounds as that of the class of all unbounded-size Transformers. Overall, our result reveals that prompting can enable a single finite-size Transformer to be efficiently universal, which establishes a theoretical underpinning for prompt engineering in practice.

Large language models have transformed natural language processing, yet supervised fine-tuning (SFT) remains computationally intensive. This paper formally proves that capabilities acquired through SFT can be approximated by a base transformer model using inference-time techniques, specifically in-context learning (ICL), without altering model parameters, under idealized assumptions including unbounded computational resources and access to the fine-tuning dataset. We extend these results to practical scenarios with finite context lengths and partial dataset access. For text generation tasks with fixed output length l, datasets of size Oleft( m V{varepsilon^2} log m{delta} right) or, with bounded context, Oleft( l log V{varepsilon^2} log 1{delta} right) suffice to approximate fine-tuned behavior across m contexts within error varepsilon, where V is the vocabulary size and delta is the failure probability. For linear classification, datasets of size Oleft( d{varepsilon} right) or, with fixed context, Oleft( 1{varepsilon^2} log 1{delta} right) are sufficient, where d is the input dimension. Grounded in the Turing completeness of transformers, these results provide a theoretical foundation for resource-efficient deployment of large language models, with practical techniques like retrieval-augmented generation bridging theory to real-world applications.

Researchers are investing substantial effort in developing powerful general-purpose agents, wherein Foundation Models are used as modules within agentic systems (e.g. Chain-of-Thought, Self-Reflection, Toolformer). However, the history of machine learning teaches us that hand-designed solutions are eventually replaced by learned solutions. We formulate a new research area, Automated Design of Agentic Systems (ADAS), which aims to automatically create powerful agentic system designs, including inventing novel building blocks and/or combining them in new ways. We further demonstrate that there is an unexplored yet promising approach within ADAS where agents can be defined in code and new agents can be automatically discovered by a meta agent programming ever better ones in code. Given that programming languages are Turing Complete, this approach theoretically enables the learning of any possible agentic system: including novel prompts, tool use, control flows, and combinations thereof. We present a simple yet effective algorithm named Meta Agent Search to demonstrate this idea, where a meta agent iteratively programs interesting new agents based on an ever-growing archive of previous discoveries. Through extensive experiments across multiple domains including coding, science, and math, we show that our algorithm can progressively invent agents with novel designs that greatly outperform state-of-the-art hand-designed agents. Importantly, we consistently observe the surprising result that agents invented by Meta Agent Search maintain superior performance even when transferred across domains and models, demonstrating their robustness and generality. Provided we develop it safely, our work illustrates the potential of an exciting new research direction toward automatically designing ever-more powerful agentic systems to benefit humanity.

Can Transformers predict new syllogisms by composing established ones? More generally, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity, but this does not address the learnability objective. This paper puts forward the notion of 'globality degree' of a target distribution to capture when weak learning is efficiently achievable by regular Transformers, where the latter measures the least number of tokens required in addition to the tokens histogram to correlate nontrivially with the target. As shown experimentally and theoretically under additional assumptions, distributions with high globality cannot be learned efficiently. In particular, syllogisms cannot be composed on long chains. Furthermore, we show that (i) an agnostic scratchpad cannot help to break the globality barrier, (ii) an educated scratchpad can help if it breaks the globality at each step, however not all such scratchpads can generalize to out-of-distribution (OOD) samples, (iii) a notion of 'inductive scratchpad', that composes the prior information more efficiently, can both break the globality barrier and improve the OOD generalization. In particular, some inductive scratchpads can achieve length generalizations of up to 6x for some arithmetic tasks depending on the input formatting.

Communicating state machines provide a formal foundation for distributed computation. Unfortunately, they are Turing-complete and, thus, challenging to analyse. In this paper, we classify restrictions on channels which have been proposed to work around the undecidability of verification questions. We compare half-duplex communication, existential B-boundedness, and k-synchronisability. These restrictions do not prevent the communication channels from growing arbitrarily large but still restrict the power of the model. Each restriction gives rise to a set of languages so, for every pair of restrictions, we check whether one subsumes the other or if they are incomparable. We investigate their relationship in two different contexts: first, the one of communicating state machines, and, second, the one of communication protocol specifications using high-level message sequence charts. Surprisingly, these two contexts yield different conclusions. In addition, we integrate multiparty session types, another approach to specify communication protocols, into our classification. We show that multiparty session type languages are half-duplex, existentially 1-bounded, and 1-synchronisable. To~show this result, we provide the first formal embedding of multiparty session types into high-level message sequence charts.

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with relational data. In this work, we study the ability of transformer networks to simulate algorithms on graphs from a theoretical perspective. The architecture that we utilize is a looped transformer with extra attention heads that interact with the graph. We prove by construction that this architecture can simulate algorithms such as Dijkstra's shortest path algorithm, Breadth- and Depth-First Search, and Kosaraju's strongly connected components algorithm. The width of the network does not increase with the size of the input graph, which implies that the network can simulate the above algorithms for any graph. Despite this property, we show that there is a limit to simulation in our solution due to finite precision. Finally, we show a Turing Completeness result with constant width when the extra attention heads are utilized.

In this article we prove that the general transformer neural model undergirding modern large language models (LLMs) is Turing complete under reasonable assumptions. This is the first work to directly address the Turing completeness of the underlying technology employed in GPT-x as past work has focused on the more expressive, full auto-encoder transformer architecture. From this theoretical analysis, we show that the sparsity/compressibility of the word embedding is an important consideration for Turing completeness to hold. We also show that Transformers are are a variant of B machines studied by Hao Wang.

Understanding and accurately following instructions is critical for large language models (LLMs) to be effective across diverse tasks. In this work, we rigorously examine the key factors that enable models to generalize to unseen instructions, providing insights to guide the collection of data for instruction-tuning. Through controlled experiments, inspired by the Turing-complete Markov algorithm, we demonstrate that such generalization only emerges when training data is diversified enough across semantic domains. Our findings also reveal that merely diversifying within limited domains fails to ensure robust generalization. In contrast, cross-domain data diversification, even under constrained data budgets, significantly enhances a model's adaptability. We further extend our analysis to real-world scenarios, including fine-tuning of $textbf{specialist} and textbf{generalist}$ models. In both cases, we demonstrate that 1) better performance can be achieved by increasing the diversity of an established dataset while keeping the data size constant, and 2) when scaling up the data, diversifying the semantics of instructions is more effective than simply increasing the quantity of similar data. Our research provides important insights for dataset collation, particularly when optimizing model performance by expanding training data for both specialist and generalist scenarios. We show that careful consideration of data diversification is key: training specialist models with data extending beyond their core domain leads to significant performance improvements, while generalist models benefit from diverse data mixtures that enhance their overall instruction-following capabilities across a wide range of applications. Our results highlight the critical role of strategic diversification and offer clear guidelines for improving data quality.

Transformers-based models, such as BERT, have been one of the most successful deep learning models for NLP. Unfortunately, one of their core limitations is the quadratic dependency (mainly in terms of memory) on the sequence length due to their full attention mechanism. To remedy this, we propose, BigBird, a sparse attention mechanism that reduces this quadratic dependency to linear. We show that BigBird is a universal approximator of sequence functions and is Turing complete, thereby preserving these properties of the quadratic, full attention model. Along the way, our theoretical analysis reveals some of the benefits of having O(1) global tokens (such as CLS), that attend to the entire sequence as part of the sparse attention mechanism. The proposed sparse attention can handle sequences of length up to 8x of what was previously possible using similar hardware. As a consequence of the capability to handle longer context, BigBird drastically improves performance on various NLP tasks such as question answering and summarization. We also propose novel applications to genomics data.

Human intelligence emerged through the process of natural selection and evolution on Earth. We investigate what it would take to re-create this process in silico. While past work has often focused on low-level processes (such as simulating physics or chemistry), we instead take a more targeted approach, aiming to evolve agents that can accumulate open-ended culture and technologies across generations. Towards this, we present JaxLife: an artificial life simulator in which embodied agents, parameterized by deep neural networks, must learn to survive in an expressive world containing programmable systems. First, we describe the environment and show that it can facilitate meaningful Turing-complete computation. We then analyze the evolved emergent agents' behavior, such as rudimentary communication protocols, agriculture, and tool use. Finally, we investigate how complexity scales with the amount of compute used. We believe JaxLife takes a step towards studying evolved behavior in more open-ended simulations. Our code is available at https://github.com/luchris429/JaxLife

Instruction tuning -- tuning large language models on instruction-output pairs -- is a promising technique for making models better adapted to the real world. Yet, the key factors driving the model's capability to understand and follow instructions not seen during training remain under-explored. Our investigation begins with a series of synthetic experiments within the theoretical framework of a Turing-complete algorithm called Markov algorithm, which allows fine-grained control over the instruction-tuning data. Generalization and robustness with respect to the training distribution emerge once a diverse enough set of tasks is provided, even though very few examples are provided for each task. We extend these initial results to a real-world application scenario of code generation and find that a more diverse instruction set, extending beyond code-related tasks, improves the performance of code generation. Our observations suggest that a more diverse semantic space for instruction-tuning sets greatly improves the model's ability to follow instructions and perform tasks.

The Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior without explicit knowledge of the system's underlying topology presents a significant challenge, motivating the development of algorithms that can generalize across various grid configurations and boundary conditions. We develop a decoder-only generative pretrained transformer model to solve this problem, showing that our model can simulate Life on a toroidal grid with no prior knowledge on the size of the grid, or its periodic boundary conditions (LifeGPT). LifeGPT is topology-agnostic with respect to its training data and our results show that a GPT model is capable of capturing the deterministic rules of a Turing-complete system with near-perfect accuracy, given sufficiently diverse training data. We also introduce the idea of an `autoregressive autoregressor' to recursively implement Life using LifeGPT. Our results pave the path towards true universal computation within a large language model (LLM) framework, synthesizing of mathematical analysis with natural language processing, and probing AI systems for situational awareness about the evolution of such algorithms without ever having to compute them. Similar GPTs could potentially solve inverse problems in multicellular self-assembly by extracting CA-compatible rulesets from real-world biological systems to create new predictive models, which would have significant consequences for the fields of bioinspired materials, tissue engineering, and architected materials design.

Instruction tuning -- fine-tuning a large language model (LLM) on pairs of instructions and desired outcomes -- is an approach that enables pre-trained language models to perform real-world tasks and follow human instructions. Its practical success depends on the model learning a broader set of instructions than those it was trained on. Yet the factors that determine model generalization to such unseen tasks are not well understood. %To understand the driving factors of generalization, In this paper, we experiment with string rewrites, a symbolic task that serves as a building block for Turing complete Markov algorithms while allowing experimental control of "inputs" and "instructions". We investigate the trade-off between the number of instructions the model is trained on and the number of training samples provided for each instruction and observe that the diversity of the instruction set determines generalization. Generalization emerges once a diverse enough set of tasks is provided, even though very few examples are provided for each task. Instruction diversity also ensures robustness with respect to non-uniform distributions of instructions in the training set.

In the burgeoning field of artificial intelligence (AI), the unprecedented progress of large language models (LLMs) in natural language processing (NLP) offers an opportunity to revisit the entire approach of traditional metrics of machine intelligence, both in form and content. As the realm of machine cognitive evaluation has already reached Imitation, the next step is an efficient Language Acquisition and Understanding. Our paper proposes a paradigm shift from the established Turing Test towards an all-embracing framework that hinges on language acquisition, taking inspiration from the recent advancements in LLMs. The present contribution is deeply tributary of the excellent work from various disciplines, point out the need to keep interdisciplinary bridges open, and delineates a more robust and sustainable approach.

We present a paper abstract writing system based on an attentive neural sequence-to-sequence model that can take a title as input and automatically generate an abstract. We design a novel Writing-editing Network that can attend to both the title and the previously generated abstract drafts and then iteratively revise and polish the abstract. With two series of Turing tests, where the human judges are asked to distinguish the system-generated abstracts from human-written ones, our system passes Turing tests by junior domain experts at a rate up to 30% and by non-expert at a rate up to 80%.

We evaluated 3 systems (ELIZA, GPT-3.5 and GPT-4) in a randomized, controlled, and preregistered Turing test. Human participants had a 5 minute conversation with either a human or an AI, and judged whether or not they thought their interlocutor was human. GPT-4 was judged to be a human 54% of the time, outperforming ELIZA (22%) but lagging behind actual humans (67%). The results provide the first robust empirical demonstration that any artificial system passes an interactive 2-player Turing test. The results have implications for debates around machine intelligence and, more urgently, suggest that deception by current AI systems may go undetected. Analysis of participants' strategies and reasoning suggests that stylistic and socio-emotional factors play a larger role in passing the Turing test than traditional notions of intelligence.

We present a PaperRobot who performs as an automatic research assistant by (1) conducting deep understanding of a large collection of human-written papers in a target domain and constructing comprehensive background knowledge graphs (KGs); (2) creating new ideas by predicting links from the background KGs, by combining graph attention and contextual text attention; (3) incrementally writing some key elements of a new paper based on memory-attention networks: from the input title along with predicted related entities to generate a paper abstract, from the abstract to generate conclusion and future work, and finally from future work to generate a title for a follow-on paper. Turing Tests, where a biomedical domain expert is asked to compare a system output and a human-authored string, show PaperRobot generated abstracts, conclusion and future work sections, and new titles are chosen over human-written ones up to 30%, 24% and 12% of the time, respectively.

We propose Token Turing Machines (TTM), a sequential, autoregressive Transformer model with memory for real-world sequential visual understanding. Our model is inspired by the seminal Neural Turing Machine, and has an external memory consisting of a set of tokens which summarise the previous history (i.e., frames). This memory is efficiently addressed, read and written using a Transformer as the processing unit/controller at each step. The model's memory module ensures that a new observation will only be processed with the contents of the memory (and not the entire history), meaning that it can efficiently process long sequences with a bounded computational cost at each step. We show that TTM outperforms other alternatives, such as other Transformer models designed for long sequences and recurrent neural networks, on two real-world sequential visual understanding tasks: online temporal activity detection from videos and vision-based robot action policy learning. Code is publicly available at: https://github.com/google-research/scenic/tree/main/scenic/projects/token_turing

Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to achieve length generalization, these proposals typically apply to a limited set of tasks. Building on prior scratchpad and Chain-of-Thought (CoT) techniques, we propose Turing Programs, a novel CoT strategy that decomposes an algorithmic task into steps mimicking the computation of a Turing Machine. This framework is both universal, as it can accommodate any algorithmic task, and simple, requiring only copying text from the context with small modifications. We show that by using Turing Programs, we obtain robust length generalization on a range of algorithmic tasks: addition, multiplication and in-context SGD. We then demonstrate that transformers achieve length generalization on random Turing Programs, suggesting that length generalization is possible for any algorithmic task. Finally, we theoretically prove that transformers can implement Turing Programs, constructing a simple RASP (Weiss et al.) program that simulates an arbitrary Turing machine.

We evaluated 4 systems (ELIZA, GPT-4o, LLaMa-3.1-405B, and GPT-4.5) in two randomised, controlled, and pre-registered Turing tests on independent populations. Participants had 5 minute conversations simultaneously with another human participant and one of these systems before judging which conversational partner they thought was human. When prompted to adopt a humanlike persona, GPT-4.5 was judged to be the human 73% of the time: significantly more often than interrogators selected the real human participant. LLaMa-3.1, with the same prompt, was judged to be the human 56% of the time -- not significantly more or less often than the humans they were being compared to -- while baseline models (ELIZA and GPT-4o) achieved win rates significantly below chance (23% and 21% respectively). The results constitute the first empirical evidence that any artificial system passes a standard three-party Turing test. The results have implications for debates about what kind of intelligence is exhibited by Large Language Models (LLMs), and the social and economic impacts these systems are likely to have.

Transformer-based language models for automatic code completion have shown great promise so far, yet the evaluation of these models rarely uses real data. This study provides both quantitative and qualitative assessments of three public code language models when completing real-world code. We first developed an open-source IDE extension, Code4Me, for the online evaluation of the models. We collected real auto-completion usage data for over a year from more than 1200 users, resulting in over 600K valid completions. These models were then evaluated using six standard metrics across twelve programming languages. Next, we conducted a qualitative study of 1690 real-world completion requests to identify the reasons behind the poor model performance. A comparative analysis of the models' performance in online and offline settings was also performed, using benchmark synthetic datasets and two masking strategies. Our findings suggest that while developers utilize code completion across various languages, the best results are achieved for mainstream languages such as Python and Java. InCoder outperformed the other models across all programming languages, highlighting the significance of training data and objectives. Our study also revealed that offline evaluations do not accurately reflect real-world scenarios. Upon qualitative analysis of the model's predictions, we found that 66.3% of failures were due to the models' limitations, 24.4% occurred due to inappropriate model usage in a development context, and 9.3% were valid requests that developers overwrote. Given these findings, we propose several strategies to overcome the current limitations. These include refining training objectives, improving resilience to typographical errors, adopting hybrid approaches, and enhancing implementations and usability.

Token-level code completion is one of the most critical features in modern Integrated Development Environments (IDEs). It assists developers by suggesting relevant identifiers and APIs during coding. While completions are typically derived from static analysis, their usefulness depends heavily on how they are ranked, as correct predictions buried deep in the list are rarely seen by users. Most current systems rely on hand-crafted heuristics or lightweight machine learning models trained on user logs, which can be further improved to capture context information and generalize across projects and coding styles. In this work, we propose a new scoring approach to ranking static completions using language models in a lightweight and model-agnostic way. Our method organizes all valid completions into a prefix tree and performs a single greedy decoding pass to collect token-level scores across the tree. This enables a precise token-aware ranking without needing beam search, prompt engineering, or model adaptations. The approach is fast, architecture-agnostic, and compatible with already deployed models for code completion. These findings highlight a practical and effective pathway for integrating language models into already existing tools within IDEs, and ultimately providing smarter and more responsive developer assistance.

We show that transformer-based large language models are computationally universal when augmented with an external memory. Any deterministic language model that conditions on strings of bounded length is equivalent to a finite automaton, hence computationally limited. However, augmenting such models with a read-write memory creates the possibility of processing arbitrarily large inputs and, potentially, simulating any algorithm. We establish that an existing large language model, Flan-U-PaLM 540B, can be combined with an associative read-write memory to exactly simulate the execution of a universal Turing machine, U_{15,2}. A key aspect of the finding is that it does not require any modification of the language model weights. Instead, the construction relies solely on designing a form of stored instruction computer that can subsequently be programmed with a specific set of prompts.

Code completion is an essential feature of IDEs, yet current autocompleters are restricted to either grammar-based or NLP-based single token completions. Both approaches have significant drawbacks: grammar-based autocompletion is restricted in dynamically-typed language environments, whereas NLP-based autocompleters struggle to understand the semantics of the programming language and the developer's code context. In this work, we present CodeFill, a language model for autocompletion that combines learned structure and naming information. Using a parallel Transformer architecture and multi-task learning, CodeFill consumes sequences of source code token names and their equivalent AST token types. Uniquely, CodeFill is trained both for single-token and multi-token (statement) prediction, which enables it to learn long-range dependencies among grammatical and naming elements. We train CodeFill on two datasets, consisting of 29M and 425M lines of code, respectively. To make the evaluation more realistic, we develop a method to automatically infer points in the source code at which completion matters. We compare CodeFill against four baselines and two state-of-the-art models, GPT-C and TravTrans+.CodeFill surpasses all baselines in single token prediction (MRR: 70.9% vs. 66.2% and 67.8%) and outperforms the state of the art for multi-token prediction (ROUGE-L: 63.7% vs. 52.4% and 59.2%, for n=4 tokens). We publicly release our source code and datasets.

With the rapid development and widespread application of Large Language Models (LLMs), rigorous evaluation has become particularly crucial. This research adopts a novel perspective, focusing on evaluating the core computational reasoning ability of LLMs, defined as the capacity of model to accurately understand rules, and execute logically computing operations. This capability assesses the reliability of LLMs as precise executors, and is critical to advanced tasks such as complex code generation and multi-step problem-solving. We propose an evaluation framework based on Universal Turing Machine (UTM) simulation. This framework requires LLMs to strictly follow instructions and track dynamic states, such as tape content and read/write head position, during multi-step computations. To enable standardized evaluation, we developed TMBench, a benchmark for systematically studying the computational reasoning capabilities of LLMs. TMBench provides several key advantages, including knowledge-agnostic evaluation, adjustable difficulty, foundational coverage through Turing machine encoding, and unlimited capacity for instance generation, ensuring scalability as models continue to evolve. We find that model performance on TMBench correlates strongly with performance on other recognized reasoning benchmarks (Pearson correlation coefficient is 0.73), clearly demonstrating that computational reasoning is a significant dimension for measuring the deep capabilities of LLMs. Code and data are available at https://github.com/HaitaoWuTJU/Turing-Machine-Bench.

Code completion, a key downstream task in code generation, is one of the most frequent and impactful methods for enhancing developer productivity in software development. As intelligent completion tools evolve, we need a robust evaluation benchmark that enables meaningful comparisons between products and guides future advancements. However, existing benchmarks focus more on coarse-grained tasks without industrial analysis resembling general code generation rather than the real-world scenarios developers encounter. Moreover, these benchmarks often rely on costly and time-consuming human annotation, and the standalone test cases fail to leverage minimal tests for maximum repository-level understanding and code coverage. To address these limitations, we first analyze business data from an industrial code completion tool and redefine the evaluation criteria to better align with the developer's intent and desired completion behavior throughout the coding process. Based on these insights, we introduce Codev-Agent, an agent-based system that automates repository crawling, constructs execution environments, extracts dynamic calling chains from existing unit tests, and generates new test samples to avoid data leakage, ensuring fair and effective comparisons. Using Codev-Agent, we present the Code-Development Benchmark (Codev-Bench), a fine-grained, real-world, repository-level, and developer-centric evaluation framework. Codev-Bench assesses whether a code completion tool can capture a developer's immediate intent and suggest appropriate code across diverse contexts, providing a more realistic benchmark for code completion in modern software development.

Large pre-trained language models have become popular for many applications and form an important backbone of many downstream tasks in natural language processing (NLP). Applying 'explainable artificial intelligence' (XAI) techniques to enrich such models' outputs is considered crucial for assuring their quality and shedding light on their inner workings. However, large language models are trained on a plethora of data containing a variety of biases, such as gender biases, affecting model weights and, potentially, behavior. Currently, it is unclear to what extent such biases also impact model explanations in possibly unfavorable ways. We create a gender-controlled text dataset, GECO, in which otherwise identical sentences appear in male and female forms. This gives rise to ground-truth 'world explanations' for gender classification tasks, enabling the objective evaluation of the correctness of XAI methods. We also provide GECOBench, a rigorous quantitative evaluation framework benchmarking popular XAI methods, applying them to pre-trained language models fine-tuned to different degrees. This allows us to investigate how pre-training induces undesirable bias in model explanations and to what extent fine-tuning can mitigate such explanation bias. We show a clear dependency between explanation performance and the number of fine-tuned layers, where XAI methods are observed to particularly benefit from fine-tuning or complete retraining of embedding layers. Remarkably, this relationship holds for models achieving similar classification performance on the same task. With that, we highlight the utility of the proposed gender-controlled dataset and novel benchmarking approach for research and development of novel XAI methods. All code including dataset generation, model training, evaluation and visualization is available at: https://github.com/braindatalab/gecobench

We propose an alternative to the Turing test that removes the inherent asymmetry between humans and machines in Turing's original imitation game. In this new test, both humans and machines judge each other. We argue that this makes the test more robust against simple deceptions. We also propose a small number of refinements to improve further the test. These refinements could be applied also to Turing's original imitation game.

With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to be no. A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer. Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element. The concept that this is solely a quantum effect and does not work for a classical case is also discussed.

We evaluated GPT-4 in a public online Turing Test. The best-performing GPT-4 prompt passed in 41% of games, outperforming baselines set by ELIZA (27%) and GPT-3.5 (14%), but falling short of chance and the baseline set by human participants (63%). Participants' decisions were based mainly on linguistic style (35%) and socio-emotional traits (27%), supporting the idea that intelligence is not sufficient to pass the Turing Test. Participants' demographics, including education and familiarity with LLMs, did not predict detection rate, suggesting that even those who understand systems deeply and interact with them frequently may be susceptible to deception. Despite known limitations as a test of intelligence, we argue that the Turing Test continues to be relevant as an assessment of naturalistic communication and deception. AI models with the ability to masquerade as humans could have widespread societal consequences, and we analyse the effectiveness of different strategies and criteria for judging humanlikeness.

Planning remains one of the last standing bastions for large language models (LLMs), which now turn their attention to search. Most of the literature uses the language models as world models to define the search space, forgoing soundness for the sake of flexibility. A recent work, Thought of Search (ToS), proposed defining the search space with code, having the language models produce that code. ToS requires a human in the loop, collaboratively producing a sound successor function and goal test. The result, however, is worth the effort: all the tested datasets were solved with 100% accuracy. At the same time LLMs have demonstrated significant progress in code generation and refinement for complex reasoning tasks. In this work, we automate ToS (AutoToS), completely taking the human out of the loop of solving planning problems. AutoToS guides the language model step by step towards the generation of sound and complete search components, through feedback from both generic and domain specific unit tests. We achieve 100% accuracy, with minimal feedback iterations, using LLMs of various sizes on all evaluated domains.

Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than computability in philosophical and AI problems. Second, to rephrase the notion of computability in terms of solvability, i.e. treating computability as non-sufficient for establishing intelligence. The Church-Turing thesis is therefore revisited and rephrased in order to capture the ontological background of spatial and temporal complexity. Third, to emphasize ontological differences between different time complexities, which seem to provide a solid base towards better understanding of artificial intelligence in general.

We introduce Psi-Turing Machines (Psi-TM): classical Turing machines equipped with a constant-depth introspection interface iota and an explicit per-step information budget B(d,n)=c,dlog_2 n . With the interface frozen, we develop an information-theoretic lower-bound toolkit: Budget counting, Psi -Fooling, and Psi -Fano, with worked examples L_k and L_k^{phase} . We prove an oracle-relative separation P^{Psi} neq NP^{Psi} and a strict depth hierarchy, reinforced by an Anti-Simulation Hook that rules out polynomial emulation of iota_k using many calls to iota_{k-1} under the budget regime. We also present two independent platforms (Psi-decision trees and interface-constrained circuits IC-AC^{0}/IC-NC^{1}) and bridges that transfer bounds among machine, tree, and circuit with explicit poly/log losses. The model preserves classical computational power outside iota yet enables precise oracle-aware statements about barriers (relativization; partial/conditional progress on natural proofs and proof complexity). The aim is a standardized minimal introspection interface with clearly accounted information budgets.

Length generalization, the ability to solve problems of longer sequences than those observed during training, poses a core challenge of Transformer-based large language models (LLM). Although existing studies have predominantly focused on data-driven approaches for arithmetic operations and symbolic manipulation tasks, these approaches tend to be task-specific with limited overall performance. To pursue a more general solution, this paper focuses on a broader case of reasoning problems that are computable, i.e., problems that algorithms can solve, thus can be solved by the Turing Machine. From this perspective, this paper proposes Turing MAchine Imitation Learning (TAIL) to improve the length generalization ability of LLMs. TAIL synthesizes chain-of-thoughts (CoT) data that imitate the execution process of a Turing Machine by computer programs, which linearly expands the reasoning steps into atomic states to alleviate shortcut learning and explicit memory fetch mechanism to reduce the difficulties of dynamic and long-range data access in elementary operations. To validate the reliability and universality of TAIL, we construct a challenging synthetic dataset covering 8 classes of algorithms and 18 tasks. Without bells and whistles, TAIL significantly improves the length generalization ability as well as the performance of Qwen2.5-7B on various tasks using only synthetic data, surpassing previous methods and DeepSeek-R1. The experimental results reveal that the key concepts in the Turing Machine, instead of the thinking styles, are indispensable for TAIL for length generalization, through which the model exhibits read-and-write behaviors consistent with the properties of the Turing Machine in their attention layers. This work provides a promising direction for future research in the learning of LLM reasoning from synthetic data.

We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a language model can process arbitrarily long inputs using a bounded context. For this purpose, we consider a generalization of autoregressive decoding where, given a long input, emitted tokens are appended to the end of the sequence as the context window advances. We first show that the resulting system corresponds to a classical model of computation, a Lag system, that has long been known to be computationally universal. By leveraging a new proof, we show that a universal Turing machine can be simulated by a Lag system with 2027 production rules. We then investigate whether an existing large language model can simulate the behaviour of such a universal Lag system. We give an affirmative answer by showing that a single system-prompt can be developed for gemini-1.5-pro-001 that drives the model, under deterministic (greedy) decoding, to correctly apply each of the 2027 production rules. We conclude that, by the Church-Turing thesis, prompted gemini-1.5-pro-001 with extended autoregressive (greedy) decoding is a general purpose computer.

Fill-in-the-Middle (FIM) models play a vital role in code completion tasks, leveraging both prefix and suffix context to provide more accurate and contextually relevant suggestions. This paper presents approaches to improve FIM code completion while addressing the challenge of maintaining low latency for real-time coding assistance. We enhance FIM code completion by incorporating context and curriculum examples in the training process. We identify patterns where completion suggestions fail more frequently, revealing complexities that smaller language models struggle with. To address these challenges, we develop a curriculum dataset by extracting hard-to-complete patterns from code repositories and generate context examples using semantic and static analysis tools (e.g. TSC compiler). We fine-tune various sized models, including StarCoder and DeepSeek, on this enhanced dataset. Our evaluation encompasses three key dimensions: the Santa Coder FIM task, the Amazon CCEval benchmark, and a new Multi-Line Infilling evaluation benchmark derived from SWE-bench. Comprehensive ablation studies across multiple model sizes reveal that while all fine-tuned models show improvements, the performance gains are more pronounced for smaller parameter models and incorporating difficult-to-complete examples, as part of curriculum learning, improves the code completion performance. This finding is particularly significant given the latency constraints of code completion tasks. While larger models like GPT and Claude perform well in multi-line completions but are prohibitively challenging to use given high latency, and our fine-tuned models achieve a balance between performance and latency. Finally, we validate our approach through online A/B testing, demonstrating tangible improvements in Completion Acceptance Rate (CAR) and Completion Persistence Rate (CPR), with zero latency impact.

In this work, we propose an approach for collecting completion usage logs from the users in an IDE and using them to train a machine learning based model for ranking completion candidates. We developed a set of features that describe completion candidates and their context, and deployed their anonymized collection in the Early Access Program of IntelliJ-based IDEs. We used the logs to collect a dataset of code completions from users, and employed it to train a ranking CatBoost model. Then, we evaluated it in two settings: on a held-out set of the collected completions and in a separate A/B test on two different groups of users in the IDE. Our evaluation shows that using a simple ranking model trained on the past user behavior logs significantly improved code completion experience. Compared to the default heuristics-based ranking, our model demonstrated a decrease in the number of typing actions necessary to perform the completion in the IDE from 2.073 to 1.832. The approach adheres to privacy requirements and legal constraints, since it does not require collecting personal information, performing all the necessary anonymization on the client's side. Importantly, it can be improved continuously: implementing new features, collecting new data, and evaluating new models - this way, we have been using it in production since the end of 2020.

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where algorithmic definitions enable automated generation of arbitrarily many challenging theorem-proof pairs. We demonstrate this approach on two TCS domains: Busy Beaver problems, which involve proving bounds on Turing machine halting behavior, and Mixed Boolean Arithmetic problems, which combine logical and arithmetic reasoning. Our framework automatically synthesizes problems with parallel formal (Lean4) and informal (Markdown) specifications, creating a scalable pipeline for generating verified proof challenges. Evaluation on frontier models reveals substantial gaps in automated theorem proving: while DeepSeekProver-V2-671B achieves 57.5\% success on Busy Beaver problems, it manages only 12\% on Mixed Boolean Arithmetic problems. These results highlight the difficulty of long-form proof generation even for problems that are computationally easy to verify, demonstrating the value of TCS domains for advancing automated reasoning research.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

Transformer-based language models are highly effective for code completion, with much research dedicated to enhancing the content of these completions. Despite their effectiveness, these models come with high operational costs and can be intrusive, especially when they suggest too often and interrupt developers who are concentrating on their work. Current research largely overlooks how these models interact with developers in practice and neglects to address when a developer should receive completion suggestions. To tackle this issue, we developed a machine learning model that can accurately predict when to invoke a code completion tool given the code context and available telemetry data. To do so, we collect a dataset of 200k developer interactions with our cross-IDE code completion plugin and train several invocation filtering models. Our results indicate that our small-scale transformer model significantly outperforms the baseline while maintaining low enough latency. We further explore the search space for integrating additional telemetry data into a pre-trained transformer directly and obtain promising results. To further demonstrate our approach's practical potential, we deployed the model in an online environment with 34 developers and provided real-world insights based on 74k actual invocations.

We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.

Leveraging recent advancements in large language models, modern neural code completion models have demonstrated the capability to generate highly accurate code suggestions. However, their massive size poses challenges in terms of computational costs and environmental impact, hindering their widespread adoption in practical scenarios. Dynamic inference emerges as a promising solution, as it allocates minimal computation during inference while maintaining the model's performance. In this research, we explore dynamic inference within the context of code completion. Initially, we conducted an empirical investigation on GPT-2, focusing on the inference capabilities of intermediate layers for code completion. We found that 54.4% of tokens can be accurately generated using just the first layer, signifying significant computational savings potential. Moreover, despite using all layers, the model still fails to predict 14.5% of tokens correctly, and the subsequent completions continued from them are rarely considered helpful, with only a 4.2% Acceptance Rate. These findings motivate our exploration of dynamic inference in code completion and inspire us to enhance it with a decision-making mechanism that stops the generation of incorrect code. We thus propose a novel dynamic inference method specifically tailored for code completion models. This method aims not only to produce correct predictions with largely reduced computation but also to prevent incorrect predictions proactively. Our extensive evaluation shows that it can averagely skip 1.7 layers out of 16 layers in the models, leading to an 11.2% speedup with only a marginal 1.1% reduction in ROUGE-L.

In today's software world with its cornucopia of reusable software libraries, when a programmer is faced with a programming task that they suspect can be completed through the use of a library, they often look for code examples using a search engine and then manually adapt found examples to their specific context of use. We put forward a vision based on a new breed of developer tools that have the potential to largely automate this process. The key idea is to adapt code autocompletion tools such that they take into account not only the developer's already-written code but also the intent of the task the developer is trying to achieve next, formulated in plain natural language. We call this practice of enriching the code with natural language intent to facilitate its completion natural language-guided programming. To show that this idea is feasible we design, implement and benchmark a tool that solves this problem in the context of a specific domain (data science) and a specific programming language (Python). Central to the tool is the use of language models trained on a large corpus of documented code. Our initial experiments confirm the feasibility of the idea but also make it clear that we have only scratched the surface of what may become possible in the future. We end the paper with a comprehensive research agenda to stimulate additional research in the budding area of natural language-guided programming.

Code completion has become an essential tool for daily software development. Existing evaluation benchmarks often employ static methods that do not fully capture the dynamic nature of real-world coding environments and face significant challenges, including limited context length, reliance on superficial evaluation metrics, and potential overfitting to training datasets. In this work, we introduce a novel framework for enhancing code completion in software development through the creation of a repository-level benchmark ExecRepoBench and the instruction corpora Repo-Instruct, aim at improving the functionality of open-source large language models (LLMs) in real-world coding scenarios that involve complex interdependencies across multiple files. ExecRepoBench includes 1.2K samples from active Python repositories. Plus, we present a multi-level grammar-based completion methodology conditioned on the abstract syntax tree to mask code fragments at various logical units (e.g. statements, expressions, and functions). Then, we fine-tune the open-source LLM with 7B parameters on Repo-Instruct to produce a strong code completion baseline model Qwen2.5-Coder-Instruct-C based on the open-source model. Qwen2.5-Coder-Instruct-C is rigorously evaluated against existing benchmarks, including MultiPL-E and ExecRepoBench, which consistently outperforms prior baselines across all programming languages. The deployment of can be used as a high-performance, local service for programming development\url{https://execrepobench.github.io/}.

Code completion aims to help improve developers' productivity by suggesting the next code tokens from a given context. Various approaches have been proposed to incorporate abstract syntax tree (AST) information for model training, ensuring that code completion is aware of the syntax of the programming languages. However, existing syntax-aware code completion approaches are not on-the-fly, as we found that for every two-thirds of characters that developers type, AST fails to be extracted because it requires the syntactically correct source code, limiting its practicality in real-world scenarios. On the other hand, existing on-the-fly code completion does not consider syntactic information yet. In this paper, we propose PyCoder to leverage token types, a kind of lightweight syntactic information, which is readily available and aligns with the natural order of source code. Our PyCoder is trained in a multi-task training manner so that by learning the supporting task of predicting token types during the training phase, the models achieve better performance on predicting tokens and lines of code without the need for token types in the inference phase. Comprehensive experiments show that PyCoder achieves the first rank on the CodeXGLUE leaderboard with an accuracy of 77.12% for the token-level predictions, which is 0.43%-24.25% more accurate than baselines. In addition, PyCoder achieves an exact match of 43.37% for the line-level predictions, which is 3.63%-84.73% more accurate than baselines. These results lead us to conclude that token type information (an alternative to syntactic information) that is rarely used in the past can greatly improve the performance of code completion approaches, without requiring the syntactically correct source code like AST-based approaches do. Our PyCoder is publicly available on HuggingFace.

We introduce a new type of test, called a Turing Experiment (TE), for evaluating how well a language model, such as GPT-3, can simulate different aspects of human behavior. Unlike the Turing Test, which involves simulating a single arbitrary individual, a TE requires simulating a representative sample of participants in human subject research. We give TEs that attempt to replicate well-established findings in prior studies. We design a methodology for simulating TEs and illustrate its use to compare how well different language models are able to reproduce classic economic, psycholinguistic, and social psychology experiments: Ultimatum Game, Garden Path Sentences, Milgram Shock Experiment, and Wisdom of Crowds. In the first three TEs, the existing findings were replicated using recent models, while the last TE reveals a "hyper-accuracy distortion" present in some language models.

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has not received enough attention, though. This study presents the ICPC benchmark, which consists of 254 international collegiate programming contest (ICPC) tasks. Each problem includes official analysis, reference code, and sample, high-quality unit, and hidden tests. We are able to develop and evaluate a variety of LM inference techniques for competitive programming with these resources. With zero-shot chain-of-thought prompting, we find that o1 only achieves a 19.1\% pass@1 solve rate. With our best inference technique, which combines multi-turn self-judge with reflection and retrieval over episodic information, raises this to 42.2\%. Furthermore, we conduct a new human-in-the-loop investigation to gain a deeper understanding of the remaining difficulties. Surprisingly, we discover that o1 can solve 17 out of 18 problems that were previously unsolvable by any model or technique with just a few specific instructions. A footstep toward LMs with grounded, imaginative, and algorithmic thinking is provided by our quantitative findings and qualitative research. We open-source our code and data at https://github.com/kraritt/zolve.

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

We present "Human or Not?", an online game inspired by the Turing test, that measures the capability of AI chatbots to mimic humans in dialog, and of humans to tell bots from other humans. Over the course of a month, the game was played by over 1.5 million users who engaged in anonymous two-minute chat sessions with either another human or an AI language model which was prompted to behave like humans. The task of the players was to correctly guess whether they spoke to a person or to an AI. This largest scale Turing-style test conducted to date revealed some interesting facts. For example, overall users guessed the identity of their partners correctly in only 68% of the games. In the subset of the games in which users faced an AI bot, users had even lower correct guess rates of 60% (that is, not much higher than chance). This white paper details the development, deployment, and results of this unique experiment. While this experiment calls for many extensions and refinements, these findings already begin to shed light on the inevitable near future which will commingle humans and AI.

We introduce {rm C{small LEVER}}, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, {rm C{small LEVER}} avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use {rm C{small LEVER}} to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).

Writing tests is a time-consuming yet essential task during software development. We propose to leverage recent advances in deep learning for text and code generation to assist developers in writing tests. We formalize the novel task of test completion to automatically complete the next statement in a test method based on the context of prior statements and the code under test. We develop TeCo -- a deep learning model using code semantics for test completion. The key insight underlying TeCo is that predicting the next statement in a test method requires reasoning about code execution, which is hard to do with only syntax-level data that existing code completion models use. TeCo extracts and uses six kinds of code semantics data, including the execution result of prior statements and the execution context of the test method. To provide a testbed for this new task, as well as to evaluate TeCo, we collect a corpus of 130,934 test methods from 1,270 open-source Java projects. Our results show that TeCo achieves an exact-match accuracy of 18, which is 29% higher than the best baseline using syntax-level data only. When measuring functional correctness of generated next statement, TeCo can generate runnable code in 29% of the cases compared to 18% obtained by the best baseline. Moreover, TeCo is significantly better than prior work on test oracle generation.

Large Language Models are powerful tools for program synthesis and advanced auto-completion, but come with no guarantee that their output code is syntactically correct. This paper contributes an incremental parser that allows early rejection of syntactically incorrect code, as well as efficient detection of complete programs for fill-in-the-middle (FIM) tasks. We extend the Earley parsing algorithm to allow for left and right quotients of context-free grammars, and develop methods to handle quotienting of several context-sensitive features present in the grammars of many common programming languages. The result of these contributions is an efficient, general, and well-grounded method for left and right quotient parsing. To validate our theoretical contributions -- and the effectiveness of certain design decisions -- we evaluate our method on the particularly difficult case of FIM completion for Python 3, with syntax-correctness constraints. Our results demonstrate that constrained generation can significantly reduce the incidence of syntax errors in recommended code.

The recent success of Large Language Models (LLMs) signifies an impressive stride towards artificial general intelligence. They have shown a promising prospect in automatically completing tasks upon user instructions, functioning as brain-like coordinators. The associated risks will be revealed as we delegate an increasing number of tasks to machines for automated completion. A big question emerges: how can we make machines behave responsibly when helping humans automate tasks as personal copilots? In this paper, we explore this question in depth from the perspectives of feasibility, completeness and security. In specific, we present Responsible Task Automation (ResponsibleTA) as a fundamental framework to facilitate responsible collaboration between LLM-based coordinators and executors for task automation with three empowered capabilities: 1) predicting the feasibility of the commands for executors; 2) verifying the completeness of executors; 3) enhancing the security (e.g., the protection of users' privacy). We further propose and compare two paradigms for implementing the first two capabilities. One is to leverage the generic knowledge of LLMs themselves via prompt engineering while the other is to adopt domain-specific learnable models. Moreover, we introduce a local memory mechanism for achieving the third capability. We evaluate our proposed ResponsibleTA on UI task automation and hope it could bring more attentions to ensuring LLMs more responsible in diverse scenarios. The research project homepage is at https://task-automation-research.github.io/responsible_task_automation.

Researchers have made significant progress in automating the software development process in the past decades. Recent progress in Large Language Models (LLMs) has significantly impacted the development process, where developers can use LLM-based programming assistants to achieve automated coding. Nevertheless, software engineering involves the process of program improvement apart from coding, specifically to enable software maintenance (e.g. bug fixing) and software evolution (e.g. feature additions). In this paper, we propose an automated approach for solving GitHub issues to autonomously achieve program improvement. In our approach called AutoCodeRover, LLMs are combined with sophisticated code search capabilities, ultimately leading to a program modification or patch. In contrast to recent LLM agent approaches from AI researchers and practitioners, our outlook is more software engineering oriented. We work on a program representation (abstract syntax tree) as opposed to viewing a software project as a mere collection of files. Our code search exploits the program structure in the form of classes/methods to enhance LLM's understanding of the issue's root cause, and effectively retrieve a context via iterative search. The use of spectrum-based fault localization using tests, further sharpens the context, as long as a test-suite is available. Experiments on SWE-bench-lite (300 real-life GitHub issues) show increased efficacy in solving GitHub issues (19% on SWE-bench-lite), which is higher than the efficacy of the recently reported SWE-agent. In addition, AutoCodeRover achieved this efficacy with significantly lower cost (on average, $0.43 USD), compared to other baselines. We posit that our workflow enables autonomous software engineering, where, in future, auto-generated code from LLMs can be autonomously improved.

AI-supported programming has arrived, as shown by the introduction and successes of large language models for code, such as Copilot/Codex (Github/OpenAI) and AlphaCode (DeepMind). Above human average performance on programming challenges is now possible. However, software engineering is much more than solving programming contests. Moving beyond code completion to AI-supported software engineering will require an AI system that can, among other things, understand how to avoid code smells, to follow language idioms, and eventually (maybe!) propose rational software designs. In this study, we explore the current limitations of AI-supported code completion tools like Copilot and offer a simple taxonomy for understanding the classification of AI-supported code completion tools in this space. We first perform an exploratory study on Copilot's code suggestions for language idioms and code smells. Copilot does not follow language idioms and avoid code smells in most of our test scenarios. We then conduct additional investigation to determine the current boundaries of AI-supported code completion tools like Copilot by introducing a taxonomy of software abstraction hierarchies where 'basic programming functionality' such as code compilation and syntax checking is at the least abstract level, software architecture analysis and design are at the most abstract level. We conclude by providing a discussion on challenges for future development of AI-supported code completion tools to reach the design level of abstraction in our taxonomy.

Code completion is a prominent application of Large Language Models (LLMs) in software engineering. Due to the near real-time response requirements of this task, base models with small to medium-sized parameters are typically employed, supplemented by various optimization and post-training techniques. However, these optimization methods often have trade-offs, leading to a seesaw effect where performance improvements on certain datasets or metrics are accompanied by degradations on others -- sometimes even falling below the baseline model's performance. This paper proposes SynthCoder, a model that integrates leading industry practices to achieve state-of-the-art performance on the Fill-in-the-Middle (FIM) code completion task. In specific, we first construct a diverse dataset by combining Abstract Syntax Tree (AST) node extraction with heuristics that simulate developer behavior. Then we enrich our training corpus with cross-file contextual information using the BM25 algorithm and call graphs, enhancing the model's ability to perform code completion in both file-level and repository-level scenarios. As the last step, we employ a two-stage training process using the Seed-Coder-8B-Base as the base model. First, we fine-tune the model using Curriculum Learning technology. Following this, we perform alignment using Direct Preference Optimization (DPO) with preference pairs generated through Rejection Sampling. Experimental results demonstrate that our final model excels on mainstream repository-level code completion benchmarks, including aiXcoder, ExecRepoBench, CrossCodeEval, and CoLT. Furthermore, our carefully curated training set effectively mitigates the model's tendency to just repeat existing code, a common issue existing in various code completion models.

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When dealing with arithmetic tasks, LLMs often memorize specific examples rather than learning the underlying computational logic, limiting their ability to generalize to new problems. In this paper, we propose a Composable Arithmetic Execution Framework (CAEF) that enables LLMs to learn to execute step-by-step computations by emulating Turing Machines, thereby gaining a genuine understanding of computational logic. Moreover, the proposed framework is highly scalable, allowing composing learned operators to significantly reduce the difficulty of learning complex operators. In our evaluation, CAEF achieves nearly 100% accuracy across seven common mathematical operations on the LLaMA 3.1-8B model, effectively supporting computations involving operands with up to 100 digits, a level where GPT-4o falls short noticeably in some settings.

The adoption of AI-powered code completion tools in software development has increased substantially, yet the user interaction data produced by these systems remain proprietary within large corporations. This creates a barrier for the academic community, as researchers must often develop dedicated platforms to conduct studies on human--AI interaction, making reproducible research and large-scale data analysis impractical. In this work, we introduce Code4MeV2, a research-oriented, open-source code completion plugin for JetBrains IDEs, as a solution to this limitation. Code4MeV2 is designed using a client--server architecture and features inline code completion and a context-aware chat assistant. Its core contribution is a modular and transparent data collection framework that gives researchers fine-grained control over telemetry and context gathering. Code4MeV2 achieves industry-comparable performance in terms of code completion, with an average latency of 200~ms. We assess our tool through a combination of an expert evaluation and a user study with eight participants. Feedback from both researchers and daily users highlights its informativeness and usefulness. We invite the community to adopt and contribute to this tool. More information about the tool can be found at https://app.code4me.me.

Artificial Intelligence (AI) has made incredible progress recently. On the one hand, advanced foundation models like ChatGPT can offer powerful conversation, in-context learning and code generation abilities on a broad range of open-domain tasks. They can also generate high-level solution outlines for domain-specific tasks based on the common sense knowledge they have acquired. However, they still face difficulties with some specialized tasks because they lack enough domain-specific data during pre-training or they often have errors in their neural network computations on those tasks that need accurate executions. On the other hand, there are also many existing models and systems (symbolic-based or neural-based) that can do some domain-specific tasks very well. However, due to the different implementation or working mechanisms, they are not easily accessible or compatible with foundation models. Therefore, there is a clear and pressing need for a mechanism that can leverage foundation models to propose task solution outlines and then automatically match some of the sub-tasks in the outlines to the off-the-shelf models and systems with special functionalities to complete them. Inspired by this, we introduce TaskMatrix.AI as a new AI ecosystem that connects foundation models with millions of APIs for task completion. Unlike most previous work that aimed to improve a single AI model, TaskMatrix.AI focuses more on using existing foundation models (as a brain-like central system) and APIs of other AI models and systems (as sub-task solvers) to achieve diversified tasks in both digital and physical domains. As a position paper, we will present our vision of how to build such an ecosystem, explain each key component, and use study cases to illustrate both the feasibility of this vision and the main challenges we need to address next.

Pretrained code language models have enabled great progress towards program synthesis. However, common approaches only consider in-file local context and thus miss information and constraints imposed by other parts of the codebase and its external dependencies. Existing code completion benchmarks also lack such context. To resolve these restrictions we curate a new dataset of permissively licensed Python packages that includes full projects and their dependencies and provide tools to extract non-local information with the help of program analyzers. We then focus on the task of function call argument completion which requires predicting the arguments to function calls. We show that existing code completion models do not yield good results on our completion task. To better solve this task, we query a program analyzer for information relevant to a given function call, and consider ways to provide the analyzer results to different code completion models during inference and training. Our experiments show that providing access to the function implementation and function usages greatly improves the argument completion performance. Our ablation study provides further insights on how different types of information available from the program analyzer and different ways of incorporating the information affect the model performance.

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

Large Language Models (LLMs) have shown remarkable abilities in structured reasoning and symbolic tasks, with coding emerging as a particular area of strength. This success has sparked growing interest in applying LLMs to mathematics, both in informal problem-solving and formal theorem proving. However, progress in formal mathematics has proven to be significantly more difficult, despite surface-level similarities between programming and proof construction. This discrepancy raises important questions about how LLMs ``reason'', how they are supervised, and whether they internally track a notion of computational or deductive state. In this article, we address the state-of-the-art of the discipline, focusing on recent models and benchmarks, and explore three central issues at the intersection of machine learning and mathematical cognition: (i) the trade-offs between formal and informal mathematics as training domains; (ii) the deeper reasons why proof generation remains more brittle than code synthesis; (iii) and the question of whether LLMs represent, or merely mimic, a notion of evolving logical state. Our goal is not to draw hard boundaries, but to identify where the current limits lie, and how they might be extended.

Code completion, which aims to predict the following code token(s) according to the code context, can improve the productivity of software development. Recent work has proved that statistical language modeling with transformers can greatly improve the performance in the code completion task via learning from large-scale source code datasets. However, current approaches focus only on code context within the file or project, i.e. internal context. Our distinction is utilizing "external" context, inspired by human behaviors of copying from the related code snippets when writing code. Specifically, we propose a retrieval-augmented code completion framework, leveraging both lexical copying and referring to code with similar semantics by retrieval. We adopt a stage-wise training approach that combines a source code retriever and an auto-regressive language model for programming language. We evaluate our approach in the code completion task in Python and Java programming languages, achieving a state-of-the-art performance on CodeXGLUE benchmark.

Programming is a powerful and ubiquitous problem-solving tool. Developing systems that can assist programmers or even generate programs independently could make programming more productive and accessible, yet so far incorporating innovations in AI has proven challenging. Recent large-scale language models have demonstrated an impressive ability to generate code, and are now able to complete simple programming tasks. However, these models still perform poorly when evaluated on more complex, unseen problems that require problem-solving skills beyond simply translating instructions into code. For example, competitive programming problems which require an understanding of algorithms and complex natural language remain extremely challenging. To address this gap, we introduce AlphaCode, a system for code generation that can create novel solutions to these problems that require deeper reasoning. In simulated evaluations on recent programming competitions on the Codeforces platform, AlphaCode achieved on average a ranking of top 54.3% in competitions with more than 5,000 participants. We found that three key components were critical to achieve good and reliable performance: (1) an extensive and clean competitive programming dataset for training and evaluation, (2) large and efficient-to-sample transformer-based architectures, and (3) large-scale model sampling to explore the search space, followed by filtering based on program behavior to a small set of submissions.

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence, capable of processing and understanding extensive human knowledge to enhance problem-solving across various domains. This paper explores the potential of LLMs to drive the discovery of symbolic solutions within scientific and engineering disciplines, where such solutions are crucial for advancing theoretical and practical applications. We propose a novel framework that utilizes LLMs in an evolutionary search methodology, augmented by a dynamic knowledge library that integrates and refines insights in an open-ended manner. This approach aims to tackle the dual challenges of efficiently navigating complex symbolic representation spaces and leveraging both existing and newly generated knowledge to foster open-ended innovation. By enabling LLMs to interact with and expand upon a knowledge library, we facilitate the continuous generation of novel solutions in diverse forms such as language, code, and mathematical expressions. Our experimental results demonstrate that this method not only enhances the efficiency of searching for symbolic solutions but also supports the ongoing discovery process, akin to human scientific endeavors. This study represents a first effort in conceptualizing the search for symbolic solutions as a lifelong, iterative process, marking a significant step towards harnessing AI in the perpetual pursuit of scientific and engineering breakthroughs. We have open-sourced our code and data, please visit https://github.com/pgg3/CoEvo for more information.

We present MBXP, an execution-based code completion benchmark in 10+ programming languages. This collection of datasets is generated by our conversion framework that translates prompts and test cases from the original MBPP dataset to the corresponding data in a target language. Based on this benchmark, we are able to evaluate code generation models in a multi-lingual fashion, and in particular discover generalization ability of language models on out-of-domain languages, advantages of large multi-lingual models over mono-lingual, benefits of few-shot prompting, and zero-shot translation abilities. In addition, we use our code generation model to perform large-scale bootstrapping to obtain synthetic canonical solutions in several languages. These solutions can be used for other code-related evaluations such as insertion-based, summarization, or code translation tasks where we demonstrate results and release as part of our benchmark.

Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarce, often perceived as an act of mathematical genius by great mathematicians such as Ramanujan, Euler, and Gauss. Recent efforts to automate the discovery of formulas for mathematical constants, such as the Ramanujan Machine project, relied on exhaustive search. Despite several successful discoveries, exhaustive search remains limited by the space of options that can be covered and by the need for vast amounts of computational resources. Here we propose a fundamentally different method to search for conjectures on mathematical constants: through analysis of integer sequences. We introduce the Enumerated Signed-continued-fraction Massey Approve (ESMA) algorithm, which builds on the Berlekamp-Massey algorithm to identify patterns in integer sequences that represent mathematical constants. The ESMA algorithm found various known formulas for e, e^2, tan(1), and ratios of values of Bessel functions. The algorithm further discovered a large number of new conjectures for these constants, some providing simpler representations and some providing faster numerical convergence than the corresponding simple continued fractions. Along with the algorithm, we present mathematical tools for manipulating continued fractions. These connections enable us to characterize what space of constants can be found by ESMA and quantify its algorithmic advantage in certain scenarios. Altogether, this work continues in the development of augmenting mathematical intuition by computer algorithms, to help reveal mathematical structures and accelerate mathematical research.

Code completion aims at speeding up code writing by recommending to developers the next tokens they are likely to type. Deep Learning (DL) models pushed the boundaries of code completion by redefining what these coding assistants can do: We moved from predicting few code tokens to automatically generating entire functions. One important factor impacting the performance of DL-based code completion techniques is the context provided as input. With "context" we refer to what the model knows about the code to complete. In a simple scenario, the DL model might be fed with a partially implemented function to complete. In this case, the context is represented by the incomplete function and, based on it, the model must generate a prediction. It is however possible to expand such a context to include additional information, like the whole source code file containing the function to complete, which could be useful to boost the prediction performance. In this work, we present an empirical study investigating how the performance of a DL-based code completion technique is affected by different contexts. We experiment with 8 types of contexts and their combinations. These contexts include: (i) coding contexts, featuring information extracted from the code base in which the code completion is invoked (e.g., code components structurally related to the one to "complete"); (ii) process context, with information aimed at depicting the current status of the project in which a code completion task is triggered (e.g., a textual representation of open issues relevant for the code to complete); and (iii) developer contexts, capturing information about the developer invoking the code completion (e.g., the APIs frequently used). Our results show that additional contextual information can benefit the performance of DL-based code completion, with relative improvements up to +22% in terms of correct predictions.

In software development through integrated development environments (IDEs), code completion is one of the most widely used features. Nevertheless, majority of integrated development environments only support completion of methods and APIs, or arguments. In this paper, we introduce IntelliCode Compose - a general-purpose multilingual code completion tool which is capable of predicting sequences of code tokens of arbitrary types, generating up to entire lines of syntactically correct code. It leverages state-of-the-art generative transformer model trained on 1.2 billion lines of source code in Python, C#, JavaScript and TypeScript programming languages. IntelliCode Compose is deployed as a cloud-based web service. It makes use of client-side tree-based caching, efficient parallel implementation of the beam search decoder, and compute graph optimizations to meet edit-time completion suggestion requirements in the Visual Studio Code IDE and Azure Notebook. Our best model yields an average edit similarity of 86.7% and a perplexity of 1.82 for Python programming language.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

Recent progress in large-scale language models has enabled breakthroughs in previously intractable computer programming tasks. Prior work in meta-learning and neural architecture search has led to substantial successes across various task domains, spawning myriad approaches for algorithmically optimizing the design and learning dynamics of deep learning models. At the intersection of these research areas, we implement a code-generating language model with the ability to modify its own source code. Self-programming AI algorithms have been of interest since the dawn of AI itself. Although various theoretical formulations of generalized self-programming AI have been posed, no such system has been successfully implemented to date under real-world computational constraints. Applying AI-based code generation to AI itself, we develop and experimentally validate the first practical implementation of a self-programming AI system. We empirically show that a self-programming AI implemented using a code generation model can successfully modify its own source code to improve performance and program sub-models to perform auxiliary tasks. Our model can self-modify various properties including model architecture, computational capacity, and learning dynamics.

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate language models (LMs). In this paper, we introduce the USACO benchmark with 307 problems from the USA Computing Olympiad, along with high-quality unit tests, reference code, and official analyses for each problem. These resources enable us to construct and test a range of LM inference methods for competitive programming for the first time. We find GPT-4 only achieves a 8.7% pass@1 accuracy with zero-shot chain-of-thought prompting, and our best inference method improves it to 20.2% using a combination of self-reflection and retrieval over episodic knowledge. However, this is far from solving the benchmark. To better understand the remaining challenges, we design a novel human-in-the-loop study and surprisingly find that a small number of targeted hints enable GPT-4 to solve 13 out of 15 problems previously unsolvable by any model and method. Our benchmark, baseline methods, quantitative results, and qualitative analysis serve as an initial step toward LMs with grounded, creative, and algorithmic reasoning.

We introduce Goedel-Prover, an open-source large language model (LLM) that achieves the state-of-the-art (SOTA) performance in automated formal proof generation for mathematical problems. The key challenge in this field is the scarcity of formalized math statements and proofs, which we tackle in the following ways. We train statement formalizers to translate the natural language math problems from Numina into formal language (Lean 4), creating a dataset of 1.64 million formal statements. LLMs are used to check that the formal statements accurately preserve the content of the original natural language problems. We then iteratively build a large dataset of formal proofs by training a series of provers. Each prover succeeds in proving many statements that the previous ones could not, and these new proofs are added to the training set for the next prover. The final prover outperforms all existing open-source models in whole-proof generation. On the miniF2F benchmark, it achieves a 57.6% success rate (Pass@32), exceeding the previous best open-source model by 7.6%. On PutnamBench, Goedel-Prover successfully solves 7 problems (Pass@512), ranking first on the leaderboard. Furthermore, it generates 29.7K formal proofs for Lean Workbook problems, nearly doubling the 15.7K produced by earlier works.

Artificial intelligence (AI) has made significant strides in recent years, yet it continues to struggle with a fundamental aspect of cognition present in all animals: common sense. Current AI systems, including those designed for complex tasks like autonomous driving, problem-solving challenges such as the Abstraction and Reasoning Corpus (ARC), and conversational benchmarks like the Turing Test, often lack the ability to adapt to new situations without extensive prior knowledge. This manuscript argues that integrating common sense into AI systems is essential for achieving true autonomy and unlocking the full societal and commercial value of AI. We propose a shift in the order of knowledge acquisition emphasizing the importance of developing AI systems that start from minimal prior knowledge and are capable of contextual learning, adaptive reasoning, and embodiment -- even within abstract domains. Additionally, we highlight the need to rethink the AI software stack to address this foundational challenge. Without common sense, AI systems may never reach true autonomy, instead exhibiting asymptotic performance that approaches theoretical ideals like AIXI but remains unattainable in practice due to infinite resource and computation requirements. While scaling AI models and passing benchmarks like the Turing Test have brought significant advancements in applications that do not require autonomy, these approaches alone are insufficient to achieve autonomous AI with common sense. By redefining existing benchmarks and challenges to enforce constraints that require genuine common sense, and by broadening our understanding of embodiment to include both physical and abstract domains, we can encourage the development of AI systems better equipped to handle the complexities of real-world and abstract environments.

Code generation is a core capability of large language models (LLMs), yet mainstream benchmarks (e.g., APPs and LiveCodeBench) contain questions with medium-level difficulty and pose no challenge to advanced LLMs. To better reflected the advanced reasoning and code generation ability, We introduce Humanity's Last Code Exam (HLCE), comprising 235 most challenging problems from the International Collegiate Programming Contest (ICPC World Finals) and the International Olympiad in Informatics (IOI) spanning 2010 - 2024. As part of HLCE, we design a harmonized online-offline sandbox that guarantees fully reproducible evaluation. Through our comprehensive evaluation, we observe that even the strongest reasoning LLMs: o4-mini(high) and Gemini-2.5 Pro, achieve pass@1 rates of only 15.9% and 11.4%, respectively. Meanwhile, we propose a novel "self-recognition" task to measure LLMs' awareness of their own capabilities. Results indicate that LLMs' self-recognition abilities are not proportionally correlated with their code generation performance. Finally, our empirical validation of test-time scaling laws reveals that current advanced LLMs have substantial room for improvement on complex programming tasks. We expect HLCE to become a milestone challenge for code generation and to catalyze advances in high-performance reasoning and human-AI collaborative programming. Our code and dataset are also public available(https://github.com/Humanity-s-Last-Code-Exam/HLCE).

The advent of automation in particular Software Engineering (SE) tasks has transitioned from theory to reality. Numerous scholarly articles have documented the successful application of Artificial Intelligence to address issues in areas such as project management, modeling, testing, and development. A recent innovation is the introduction of ChatGPT, an ML-infused chatbot, touted as a resource proficient in generating programming codes and formulating software testing strategies for developers and testers respectively. Although there is speculation that AI-based computation can increase productivity and even substitute software engineers in software development, there is currently a lack of empirical evidence to verify this. Moreover, despite the primary focus on enhancing the accuracy of AI systems, non-functional requirements including energy efficiency, vulnerability, fairness (i.e., human bias), and safety frequently receive insufficient attention. This paper posits that a comprehensive comparison of software engineers and AI-based solutions, considering various evaluation criteria, is pivotal in fostering human-machine collaboration, enhancing the reliability of AI-based methods, and understanding task suitability for humans or AI. Furthermore, it facilitates the effective implementation of cooperative work structures and human-in-the-loop processes. This paper conducts an empirical investigation, contrasting the performance of software engineers and AI systems, like ChatGPT, across different evaluation metrics. The empirical study includes a case of assessing ChatGPT-generated code versus code produced by developers and uploaded in Leetcode.

Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to automate proofs in languages such as F*. Seeking to spur research on using AI to automate the construction of proof-oriented programs, we curate a dataset of 600K lines of open-source F* programs and proofs, including software used in production systems ranging from Windows and Linux, to Python and Firefox. Our dataset includes around 32K top-level F* definitions, each representing a type-directed program and proof synthesis problem -- producing a definition given a formal specification expressed as an F* type. We provide a program-fragment checker that queries F* to check the correctness of candidate solutions. We believe this is the largest corpus of SMT-assisted program proofs coupled with a reproducible program-fragment checker. Grounded in this dataset, we investigate the use of AI to synthesize programs and their proofs in F*, with promising results. Our main finding in that the performance of fine-tuned smaller language models (such as Phi-2 or StarCoder) compare favorably with large language models (such as GPT-4), at a much lower computational cost. We also identify various type-based retrieval augmentation techniques and find that they boost performance significantly. With detailed error analysis and case studies, we identify potential strengths and weaknesses of models and techniques and suggest directions for future improvements.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Recent progress in large language models (LLMs) has shown promise in formal theorem proving, yet existing benchmarks remain limited to isolated, static proof tasks, failing to capture the iterative, engineering-intensive workflows of real-world formal mathematics libraries. Motivated by analogous advances in software engineering, we introduce the paradigm of Automated Proof Engineering (APE), which aims to automate proof engineering tasks such as feature addition, proof refactoring, and bug fixing using LLMs. To facilitate research in this direction, we present APE-Bench I, the first realistic benchmark built from real-world commit histories of Mathlib4, featuring diverse file-level tasks described in natural language and verified via a hybrid approach combining the Lean compiler and LLM-as-a-Judge. We further develop Eleanstic, a scalable parallel verification infrastructure optimized for proof checking across multiple versions of Mathlib. Empirical results on state-of-the-art LLMs demonstrate strong performance on localized edits but substantial degradation on handling complex proof engineering. This work lays the foundation for developing agentic workflows in proof engineering, with future benchmarks targeting multi-file coordination, project-scale verification, and autonomous agents capable of planning, editing, and repairing formal libraries.

Computer Science (CS) stands as a testament to the intricacies of human intelligence, profoundly advancing the development of artificial intelligence and modern society. However, the current community of large language models (LLMs) overly focuses on benchmarks for analyzing specific foundational skills (e.g. mathematics and code generation), neglecting an all-round evaluation of the computer science field. To bridge this gap, we introduce CS-Bench, the first bilingual (Chinese-English) benchmark dedicated to evaluating the performance of LLMs in computer science. CS-Bench comprises approximately 5K meticulously curated test samples, covering 26 subfields across 4 key areas of computer science, encompassing various task forms and divisions of knowledge and reasoning. Utilizing CS-Bench, we conduct a comprehensive evaluation of over 30 mainstream LLMs, revealing the relationship between CS performance and model scales. We also quantitatively analyze the reasons for failures in existing LLMs and highlight directions for improvements, including knowledge supplementation and CS-specific reasoning. Further cross-capability experiments show a high correlation between LLMs' capabilities in computer science and their abilities in mathematics and coding. Moreover, expert LLMs specialized in mathematics and coding also demonstrate strong performances in several CS subfields. Looking ahead, we envision CS-Bench serving as a cornerstone for LLM applications in the CS field and paving new avenues in assessing LLMs' diverse reasoning capabilities. The CS-Bench data and evaluation code are available at https://github.com/csbench/csbench.

The class of tree-adjoining languages can be characterized by various two-level formalisms, consisting of a context-free grammar (CFG) or pushdown automaton (PDA) controlling another CFG or PDA. These four formalisms are equivalent to tree-adjoining grammars (TAG), linear indexed grammars (LIG), pushdown-adjoining automata (PAA), and embedded pushdown automata (EPDA). We define semiring-weighted versions of the above two-level formalisms, and we design new algorithms for computing their stringsums (the weight of all derivations of a string) and allsums (the weight of all derivations). From these, we also immediately obtain stringsum and allsum algorithms for TAG, LIG, PAA, and EPDA. For LIG, our algorithm is more time-efficient by a factor of O(n|N|) (where n is the string length and |N| is the size of the nonterminal set) and more space-efficient by a factor of O(|Gamma|) (where |Gamma| is the size of the stack alphabet) than the algorithm of Vijay-Shanker and Weir (1989). For EPDA, our algorithm is both more space-efficient and time-efficient than the algorithm of Alonso et al. (2001) by factors of O(|Gamma|^2) and O(|Gamma|^3), respectively. Finally, we give the first PAA stringsum and allsum algorithms.

The standard paradigm for solving coding tasks via large language models (LLMs) is to generate-then-rank programs, where the latter step uses a verifier in the ranking process. The growing consensus is that a comprehensive verifier (e.g., a full test suite) should be prioritized over an outcome reward model (ORM) whenever possible, with little consideration given to the trade-offs involved. We aim to challenge this assumption by systematically exploring the tradeoff between speed and accuracy. We find that ORMs play a crucial role in scaling verification through trading accuracy for speed, even when a comprehensive verifier is available. Their value becomes especially apparent when used in a generate-prune-then-rank approach, where a faster but less accurate verifier removes incorrect solutions prior to ranking -- leading to a system that is 11.65x faster while only being 8.33% less accurate than the full test suite. We analyze the generate-prune-then-rank approach and show that it works by filtering out incorrect but highly ranked solutions. These findings enable the design of scalable and accurate program ranking systems.

This paper describes our submission for the End-to-end Multi-domain Task Completion Dialog shared task at the 9th Dialog System Technology Challenge (DSTC-9). Participants in the shared task build an end-to-end task completion dialog system which is evaluated by human evaluation and a user simulator based automatic evaluation. Different from traditional pipelined approaches where modules are optimized individually and suffer from cascading failure, we propose an end-to-end dialog system that 1) uses Generative Pretraining 2 (GPT-2) as the backbone to jointly solve Natural Language Understanding, Dialog State Tracking, and Natural Language Generation tasks, 2) adopts Domain and Task Adaptive Pretraining to tailor GPT-2 to the dialog domain before finetuning, 3) utilizes heuristic pre/post-processing rules that greatly simplify the prediction tasks and improve generalizability, and 4) equips a fault tolerance module to correct errors and inappropriate responses. Our proposed method significantly outperforms baselines and ties for first place in the official evaluation. We make our source code publicly available.

AI for software engineering has made remarkable progress recently, becoming a notable success within generative AI. Despite this, there are still many challenges that need to be addressed before automated software engineering reaches its full potential. It should be possible to reach high levels of automation where humans can focus on the critical decisions of what to build and how to balance difficult tradeoffs while most routine development effort is automated away. Reaching this level of automation will require substantial research and engineering efforts across academia and industry. In this paper, we aim to discuss progress towards this in a threefold manner. First, we provide a structured taxonomy of concrete tasks in AI for software engineering, emphasizing the many other tasks in software engineering beyond code generation and completion. Second, we outline several key bottlenecks that limit current approaches. Finally, we provide an opinionated list of promising research directions toward making progress on these bottlenecks, hoping to inspire future research in this rapidly maturing field.

Automated software engineering has been greatly empowered by the recent advances in Large Language Models (LLMs) for programming. While current benchmarks have shown that LLMs can perform various software engineering tasks like human developers, the majority of their evaluations are limited to short and self-contained algorithmic tasks. Solving challenging and practical programming tasks requires the capability of utilizing diverse function calls as tools to efficiently implement functionalities like data analysis and web development. In addition, using multiple tools to solve a task needs compositional reasoning by accurately understanding complex instructions. Fulfilling both of these characteristics can pose a great challenge for LLMs. To assess how well LLMs can solve challenging and practical programming tasks, we introduce Bench, a benchmark that challenges LLMs to invoke multiple function calls as tools from 139 libraries and 7 domains for 1,140 fine-grained programming tasks. To evaluate LLMs rigorously, each programming task encompasses 5.6 test cases with an average branch coverage of 99%. In addition, we propose a natural-language-oriented variant of Bench, Benchi, that automatically transforms the original docstrings into short instructions only with essential information. Our extensive evaluation of 60 LLMs shows that LLMs are not yet capable of following complex instructions to use function calls precisely, with scores up to 60%, significantly lower than the human performance of 97%. The results underscore the need for further advancements in this area.

Today's AI systems have human-designed, fixed architectures and cannot autonomously and continuously improve themselves. The advance of AI could itself be automated. If done safely, that would accelerate AI development and allow us to reap its benefits much sooner. Meta-learning can automate the discovery of novel algorithms, but is limited by first-order improvements and the human design of a suitable search space. The G\"odel machine proposed a theoretical alternative: a self-improving AI that repeatedly modifies itself in a provably beneficial manner. Unfortunately, proving that most changes are net beneficial is impossible in practice. We introduce the Darwin G\"odel Machine (DGM), a self-improving system that iteratively modifies its own code (thereby also improving its ability to modify its own codebase) and empirically validates each change using coding benchmarks. Inspired by Darwinian evolution and open-endedness research, the DGM maintains an archive of generated coding agents. It grows the archive by sampling an agent from it and using a foundation model to create a new, interesting, version of the sampled agent. This open-ended exploration forms a growing tree of diverse, high-quality agents and allows the parallel exploration of many different paths through the search space. Empirically, the DGM automatically improves its coding capabilities (e.g., better code editing tools, long-context window management, peer-review mechanisms), increasing performance on SWE-bench from 20.0% to 50.0%, and on Polyglot from 14.2% to 30.7%. Furthermore, the DGM significantly outperforms baselines without self-improvement or open-ended exploration. All experiments were done with safety precautions (e.g., sandboxing, human oversight). The DGM is a significant step toward self-improving AI, capable of gathering its own stepping stones along paths that unfold into endless innovation.

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-k sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-k sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education.

In this paper we argue that key, often sensational and misleading, claims regarding linguistic capabilities of Large Language Models (LLMs) are based on at least two unfounded assumptions; the assumption of language completeness and the assumption of data completeness. Language completeness assumes that a distinct and complete thing such as `a natural language' exists, the essential characteristics of which can be effectively and comprehensively modelled by an LLM. The assumption of data completeness relies on the belief that a language can be quantified and wholly captured by data. Work within the enactive approach to cognitive science makes clear that, rather than a distinct and complete thing, language is a means or way of acting. Languaging is not the kind of thing that can admit of a complete or comprehensive modelling. From an enactive perspective we identify three key characteristics of enacted language; embodiment, participation, and precariousness, that are absent in LLMs, and likely incompatible in principle with current architectures. We argue that these absences imply that LLMs are not now and cannot in their present form be linguistic agents the way humans are. We illustrate the point in particular through the phenomenon of `algospeak', a recently described pattern of high stakes human language activity in heavily controlled online environments. On the basis of these points, we conclude that sensational and misleading claims about LLM agency and capabilities emerge from a deep misconception of both what human language is and what LLMs are.

In this technical report, we present TeleChat, a collection of large language models (LLMs) with parameters of 3 billion, 7 billion and 12 billion. It includes pretrained language models as well as fine-tuned chat models that is aligned with human preferences. TeleChat is initially pretrained on an extensive corpus containing a diverse collection of texts from both English and Chinese languages, including trillions of tokens. Subsequently, the model undergoes fine-tuning to align with human preferences, following a detailed methodology that we describe. We evaluate the performance of TeleChat on various tasks, including language understanding, mathematics, reasoning, code generation, and knowledge-based question answering. Our findings indicate that TeleChat achieves comparable performance to other open-source models of similar size across a wide range of public benchmarks. To support future research and applications utilizing LLMs, we release the fine-tuned model checkpoints of TeleChat's 7B and 12B variant, along with code and a portion of our pretraining data, to the public community.

Repository-level code completion has drawn great attention in software engineering, and several benchmark datasets have been introduced. However, existing repository-level code completion benchmarks usually focus on a limited number of languages (<5), which cannot evaluate the general code intelligence abilities across different languages for existing code Large Language Models (LLMs). Besides, the existing benchmarks usually report overall average scores of different languages, where the fine-grained abilities in different completion scenarios are ignored. Therefore, to facilitate the research of code LLMs in multilingual scenarios, we propose a massively multilingual repository-level code completion benchmark covering 18 programming languages (called M2RC-EVAL), and two types of fine-grained annotations (i.e., bucket-level and semantic-level) on different completion scenarios are provided, where we obtain these annotations based on the parsed abstract syntax tree. Moreover, we also curate a massively multilingual instruction corpora M2RC- INSTRUCT dataset to improve the repository-level code completion abilities of existing code LLMs. Comprehensive experimental results demonstrate the effectiveness of our M2RC-EVAL and M2RC-INSTRUCT.

We present PutnamBench, a new multilingual benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1697 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the theorems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. Proving the theorems requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.

In this paper, we aim to do code completion based on implementing a Neural Network from Li et. al.. Our contribution is that we use an encoding that is in-between character and word encoding called Byte Pair Encoding (BPE). We use this on the source code files treating them as natural text without first going through the abstract syntax tree (AST). We have implemented two models: an attention-enhanced LSTM and a pointer network, where the pointer network was originally introduced to solve out of vocabulary problems. We are interested to see if BPE can replace the need for the pointer network for code completion.

With the growing reliance on automated code completion tools in software development, the need for robust evaluation benchmarks has become critical. However, existing benchmarks focus more on code generation tasks in function and class level and provide rich text description to prompt the model. By contrast, such descriptive prompt is commonly unavailable in real development and code completion can occur in wider range of situations such as in the middle of a function or a code block. These limitations makes the evaluation poorly align with the practical scenarios of code completion tools. In this paper, we propose RepoMasterEval, a novel benchmark for evaluating code completion models constructed from real-world Python and TypeScript repositories. Each benchmark datum is generated by masking a code snippet (ground truth) from one source code file with existing test suites. To improve test accuracy of model generated code, we employ mutation testing to measure the effectiveness of the test cases and we manually crafted new test cases for those test suites with low mutation score. Our empirical evaluation on 6 state-of-the-art models shows that test argumentation is critical in improving the accuracy of the benchmark and RepoMasterEval is able to report difference in model performance in real-world scenarios. The deployment of RepoMasterEval in a collaborated company for one month also revealed that the benchmark is useful to give accurate feedback during model training and the score is in high correlation with the model's performance in practice. Based on our findings, we call for the software engineering community to build more LLM benchmarks tailored for code generation tools taking the practical and complex development environment into consideration.

The recent development of Large Language Models (LLMs) has been accompanied by an effervescence of novel ideas and methods to better optimize the loss of deep learning models. Claims from those methods are myriad: from faster convergence to removing reliance on certain hyperparameters. However, the diverse experimental protocols used to validate these claims make direct comparisons between methods challenging. This study presents a comprehensive evaluation of recent optimization techniques across standardized LLM pretraining scenarios, systematically varying model size, batch size, and training duration. Through careful tuning of each method, we provide guidance to practitioners on which optimizer is best suited for each scenario. For researchers, our work highlights promising directions for future optimization research. Finally, by releasing our code and making all experiments fully reproducible, we hope our efforts can help the development and rigorous benchmarking of future methods.

Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the Decomposition of thought with code assistance and self-correction for mathematical reasoning, dubbed as DotaMath. DotaMath models tackle complex mathematical tasks by decomposing them into simpler logical subtasks, leveraging code to solve these subtasks, obtaining fine-grained feedback from the code interpreter, and engaging in self-reflection and correction. By annotating diverse interactive tool-use trajectories and employing query evolution on GSM8K and MATH datasets, we generate an instruction fine-tuning dataset called DotaMathQA with 574K query-response pairs. We train a series of base LLMs using imitation learning on DotaMathQA, resulting in DotaMath models that achieve remarkable performance compared to open-source LLMs across various in-domain and out-of-domain benchmarks. Notably, DotaMath-deepseek-7B showcases an outstanding performance of 64.8% on the competitive MATH dataset and 86.7% on GSM8K. Besides, DotaMath-deepseek-7B maintains strong competitiveness on a series of in-domain and out-of-domain benchmarks (Avg. 80.1%). Looking forward, we anticipate that the DotaMath paradigm will open new pathways for addressing intricate mathematical problems. Our code is publicly available at https://github.com/ChengpengLi1003/DotaMath.

Block-based programming languages like Scratch are increasingly popular for programming education and end-user programming. Recent program analyses build on the insight that source code can be modelled using techniques from natural language processing. Many of the regularities of source code that support this approach are due to the syntactic overhead imposed by textual programming languages. This syntactic overhead, however, is precisely what block-based languages remove in order to simplify programming. Consequently, it is unclear how well this modelling approach performs on block-based programming languages. In this paper, we investigate the applicability of language models for the popular block-based programming language Scratch. We model Scratch programs using n-gram models, the most essential type of language model, and transformers, a popular deep learning model. Evaluation on the example tasks of code completion and bug finding confirm that blocks inhibit predictability, but the use of language models is nevertheless feasible. Our findings serve as foundation for improving tooling and analyses for block-based languages.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

Despite widespread adoption, the impact of AI tools on software development in the wild remains understudied. We conduct a randomized controlled trial (RCT) to understand how AI tools at the February-June 2025 frontier affect the productivity of experienced open-source developers. 16 developers with moderate AI experience complete 246 tasks in mature projects on which they have an average of 5 years of prior experience. Each task is randomly assigned to allow or disallow usage of early 2025 AI tools. When AI tools are allowed, developers primarily use Cursor Pro, a popular code editor, and Claude 3.5/3.7 Sonnet. Before starting tasks, developers forecast that allowing AI will reduce completion time by 24%. After completing the study, developers estimate that allowing AI reduced completion time by 20%. Surprisingly, we find that allowing AI actually increases completion time by 19%--AI tooling slowed developers down. This slowdown also contradicts predictions from experts in economics (39% shorter) and ML (38% shorter). To understand this result, we collect and evaluate evidence for 20 properties of our setting that a priori could contribute to the observed slowdown effect--for example, the size and quality standards of projects, or prior developer experience with AI tooling. Although the influence of experimental artifacts cannot be entirely ruled out, the robustness of the slowdown effect across our analyses suggests it is unlikely to primarily be a function of our experimental design.

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

Large language models (LLMs) show strong performance across natural language processing (NLP), mathematical reasoning, and programming, and recent large reasoning models (LRMs) further emphasize explicit reasoning. Yet their computational limits, particularly spatial complexity constrained by finite context windows, remain poorly understood. While recent works often focus on problems within the NP complexity class, we push the boundary by introducing a novel benchmark grounded in two PSPACE-complete regular expression (regex) problems: equivalence decision (RegexEQ) and minimization (RegexMin). PSPACE-complete problems serve as a more rigorous standard for assessing computational capacity, as their solutions require massive search space exploration. We perform a double-exponential space exploration to construct a labeled dataset of over a million regex instances with a sound filtering process to build the benchmark. We conduct extensive evaluations on 6 LLMs and 5 LRMs of varying scales, revealing common failure patterns such as verbosity and repetition. With its well-defined structure and quantitative evaluation metrics, this work presents the first empirical investigation into the spatial computational limitations of LLMs and LRMs, offering a new framework for evaluating their advanced reasoning capabilities. Our code is available at https://github.com/hyundong98/RegexPSPACE .

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

We introduce Syntax-Aware Fill-In-the-Middle (SAFIM), a new benchmark for evaluating Large Language Models (LLMs) on the code Fill-in-the-Middle (FIM) task. This benchmark focuses on syntax-aware completions of program structures such as code blocks and conditional expressions, and includes 17,720 examples from multiple programming languages, sourced from recent code submissions after April 2022 to minimize data contamination. SAFIM provides a robust framework with various prompt designs and novel syntax-aware post-processing techniques, facilitating accurate and fair comparisons across LLMs. Our comprehensive evaluation of 15 LLMs shows that FIM pretraining not only enhances FIM proficiency but also improves Left-to-Right (L2R) inference using LLMs. Our findings challenge conventional beliefs and suggest that pretraining methods and data quality have more impact than model size. SAFIM thus serves as a foundational platform for future research in effective pretraining strategies for code LLMs. The evaluation toolkit and dataset are available at https://github.com/gonglinyuan/safim, and the leaderboard is available at https://safimbenchmark.com.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

We prove that completing an untimed, unbounded track in TrackMania Nations Forever is NP-complete by using a reduction from 3-SAT and showing that a solution can be checked in polynomial time.

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. Afterward, we analyze the variety of self-improvement strategies proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We critically consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox.

Recent development of large language models (LLMs) for code like CodeX and CodeT5+ demonstrates tremendous promise in achieving code intelligence. Their ability of synthesizing code that completes a program for performing a pre-defined task has been intensively tested and verified on benchmark datasets including HumanEval and MBPP. Yet, evaluation of these LLMs from more perspectives (than just program synthesis) is also anticipated, considering their broad scope of applications in software engineering. In this paper, we explore the ability of LLMs for testing programs/code. By performing thorough analyses of recent LLMs for code in program testing, we show a series of intriguing properties of these models and demonstrate how program testing ability of LLMs can be improved. Following recent work which utilizes generated test cases to enhance program synthesis, we further leverage our findings in improving the quality of the synthesized programs and show +11.77% and +4.22% higher code pass rates on HumanEval+ comparing with the GPT-3.5-turbo baseline and the recent state-of-the-art, respectively.

The rapid advancement of large language models (LLMs) has led to the widespread adoption of AI-powered coding assistants integrated into a development environment. On one hand, low-latency code completion offers completion suggestions but is fundamentally constrained to the cursor's current position. On the other hand, chat-based editing can perform complex modifications, yet forces developers to stop their work, describe the intent in natural language, which causes a context-switch away from the code. This creates a suboptimal user experience, as neither paradigm proactively predicts the developer's next edit in a sequence of related edits. To bridge this gap and provide the seamless code edit suggestion, we introduce the task of Next Edit Prediction, a novel task designed to infer developer intent from recent interaction history to predict both the location and content of the subsequent edit. Specifically, we curate a high-quality supervised fine-tuning dataset and an evaluation benchmark for the Next Edit Prediction task. Then, we conduct supervised fine-tuning on a series of models and performed a comprehensive evaluation of both the fine-tuned models and other baseline models, yielding several novel findings. This work lays the foundation for a new interaction paradigm that proactively collaborate with developers by anticipating their following action, rather than merely reacting to explicit instructions.

We introduce MacroBench, a code-first benchmark that evaluates whether LLMs can synthesize reusable browser-automation programs (macros) from natural-language goals by reading HTML/DOM and emitting Selenium. MacroBench instantiates seven self-hosted sites covering 681 tasks across interaction complexity and targeting difficulty. Our end-to-end protocol validates generated code via static checks, sandboxed execution, and outcome verification (DOM assertions, database snapshots), and includes a safety suite for scraping, spam/abuse, and credential/privacy prompts. Across 2,636 model-task runs, we observe stratified success: GPT-4o-mini (96.8%), GPT-4o (95.3%), Gemini (89.0%), DeepSeek (83.4%). Models handle simple tasks reliably (91.7%) but fail on complex workflows (0.0%), and none meet production-quality coding practices despite functional completion. We release our complete benchmark pipeline, evaluation framework, and experimental results at https://github.com/hyunjun1121/MacroBench to enable reproducible assessment of macro synthesis for web automation.

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PLANSEARCH, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PLANSEARCH generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PLANSEARCH explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PLANSEARCH on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas.

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for large language models (LLMs), even though they have demonstrated promising performance in other reasoning tasks. Within this context, some recent studies use programming languages (e.g., Python) to express the necessary logic for solving a given instance/question (e.g., Program-of-Thought) as inspired by their strict and precise syntaxes. However, it is non-trivial to write an executable code that expresses the correct logic on the fly within a single inference call. Also, the code generated specifically for an instance cannot be reused for others, even if they are from the same task and might require identical logic to solve. This paper presents Think-and-Execute, a novel framework that decomposes the reasoning process of language models into two steps. (1) In Think, we discover a task-level logic that is shared across all instances for solving a given task and then express the logic with pseudocode; (2) In Execute, we further tailor the generated pseudocode to each instance and simulate the execution of the code. With extensive experiments on seven algorithmic reasoning tasks, we demonstrate the effectiveness of Think-and-Execute. Our approach better improves LMs' reasoning compared to several strong baselines performing instance-specific reasoning (e.g., CoT and PoT), suggesting the helpfulness of discovering task-level logic. Also, we show that compared to natural language, pseudocode can better guide the reasoning of LMs, even though they are trained to follow natural language instructions.

The rapid evolution of software libraries presents a significant challenge for code generation models, which must adapt to frequent version updates while maintaining compatibility with previous versions. Existing code completion benchmarks often overlook this dynamic aspect, and the one that does consider it relies on static code prediction tasks without execution-based evaluation, offering a limited perspective on a model's practical usability. To address this gap, we introduce \GitChameleon{}, a novel, manually curated dataset comprising 116 Python code completion problems, each conditioned on specific library versions and accompanied by executable unit tests. is designed to rigorously assess the ability of modern large language models (LLMs) to generate version-specific code that is not only syntactically correct but also functionally accurate upon execution. Our comprehensive evaluations reveal that state-of-the-art LLMs struggle with this task; for instance, GPT-4o achieves a pass@10 of only 39.9\% (43.7\% when provided with error feedback), highlighting the complexity of the problem and the limitations of current models. By providing an execution-based benchmark that emphasizes the dynamic nature of code libraries, serves as a critical tool to advance the development of more adaptable and reliable code generation models. For facilitation for further exploration of version-conditioned code generation, we make our code repository publicly accessible at https://github.com/NizarIslah/GitChameleon.

We consider the task of mapping pseudocode to long programs that are functionally correct. Given test cases as a mechanism to validate programs, we search over the space of possible translations of the pseudocode to find a program that passes the validation. However, without proper credit assignment to localize the sources of program failures, it is difficult to guide search toward more promising programs. We propose to perform credit assignment based on signals from compilation errors, which constitute 88.7% of program failures. Concretely, we treat the translation of each pseudocode line as a discrete portion of the program, and whenever a synthesized program fails to compile, an error localization method tries to identify the portion of the program responsible for the failure. We then focus search over alternative translations of the pseudocode for those portions. For evaluation, we collected the SPoC dataset (Search-based Pseudocode to Code) containing 18,356 programs with human-authored pseudocode and test cases. Under a budget of 100 program compilations, performing search improves the synthesis success rate over using the top-one translation of the pseudocode from 25.6% to 44.7%.

Repository-level code completion aims to generate code for unfinished code snippets within the context of a specified repository. Existing approaches mainly rely on retrieval-augmented generation strategies due to limitations in input sequence length. However, traditional lexical-based retrieval methods like BM25 struggle to capture code semantics, while model-based retrieval methods face challenges due to the lack of labeled data for training. Therefore, we propose RLCoder, a novel reinforcement learning framework, which can enable the retriever to learn to retrieve useful content for code completion without the need for labeled data. Specifically, we iteratively evaluate the usefulness of retrieved content based on the perplexity of the target code when provided with the retrieved content as additional context, and provide feedback to update the retriever parameters. This iterative process enables the retriever to learn from its successes and failures, gradually improving its ability to retrieve relevant and high-quality content. Considering that not all situations require information beyond code files and not all retrieved context is helpful for generation, we also introduce a stop signal mechanism, allowing the retriever to decide when to retrieve and which candidates to retain autonomously. Extensive experimental results demonstrate that RLCoder consistently outperforms state-of-the-art methods on CrossCodeEval and RepoEval, achieving 12.2% EM improvement over previous methods. Moreover, experiments show that our framework can generalize across different programming languages and further improve previous methods like RepoCoder. We provide the code and data at https://github.com/DeepSoftwareAnalytics/RLCoder.

Software engineers mainly write code by editing existing programs. In contrast, large language models (LLMs) autoregressively synthesize programs in a single pass. One explanation for this is the scarcity of open-sourced edit data. While high-quality instruction data for code synthesis is already scarce, high-quality edit data is even scarcer. To fill this gap, we develop a synthetic data generation algorithm called LintSeq. This algorithm refactors existing code into a sequence of code edits by using a linter to procedurally sample across the error-free insertions that can be used to sequentially write programs. It outputs edit sequences as text strings consisting of consecutive program diffs. To test LintSeq, we use it to refactor a dataset of instruction + program pairs into instruction + program-diff-sequence tuples. Then, we instruction finetune a series of smaller LLMs ranging from 2.6B to 14B parameters on both the re-factored and original versions of this dataset, comparing zero-shot performance on code synthesis benchmarks. We show that during repeated sampling, edit sequence finetuned models produce more diverse programs than baselines. This results in better inference-time scaling for benchmark coverage as a function of samples, i.e. the fraction of problems "pass@k" solved by any attempt given "k" tries. For example, on HumanEval pass@50, small LLMs finetuned on synthetic edit sequences are competitive with GPT-4 and outperform models finetuned on the baseline dataset by +20% (+/-3%) in absolute score. Finally, we also pretrain our own tiny LMs for code understanding. We show that finetuning tiny models on synthetic code edits results in state-of-the-art code synthesis for the on-device model class. Our 150M parameter edit sequence LM matches or outperforms code models with twice as many parameters, both with and without repeated sampling, including Codex and AlphaCode.

This paper introduces CodeGemma, a collection of specialized open code models built on top of Gemma, capable of a variety of code and natural language generation tasks. We release three model variants. CodeGemma 7B pretrained (PT) and instruction-tuned (IT) variants have remarkably resilient natural language understanding, excel in mathematical reasoning, and match code capabilities of other open models. CodeGemma 2B is a state-of-the-art code completion model designed for fast code infilling and open-ended generation in latency-sensitive settings.

Machine learning (ML) has been increasingly used in a variety of domains, while solving ML programming tasks poses unique challenges because of the fundamentally different nature and construction from general programming tasks, especially for developers who do not have ML backgrounds. Automatic code generation that produces a code snippet from a natural language description can be a promising technique to accelerate ML programming tasks. In recent years, although many deep learning-based neural code generation models have been proposed with high accuracy, the fact that most of them are mainly evaluated on general programming tasks calls into question their effectiveness and usefulness in ML programming tasks. In this paper, we set out to investigate the effectiveness of existing neural code generation models on ML programming tasks. For our analysis, we select six state-of-the-art neural code generation models, and evaluate their performance on four widely used ML libraries, with newly-created 83K pairs of natural-language described ML programming tasks. Our empirical study reveals some good, bad, and missing aspects of neural code generation models on ML tasks, with a few major ones listed below. (Good) Neural code generation models perform significantly better on ML tasks than on non-ML tasks. (Bad) Most of the generated code is semantically incorrect. (Bad) Code generation models cannot significantly improve developers' completion time. (Good) The generated code can help developers write more correct code by providing developers with clues for using correct APIs. (Missing) The observation from our user study reveals the missing aspects of code generation for ML tasks, e.g., decomposing code generation for divide-and-conquer into two tasks: API sequence identification and API usage generation.

While recent works (e.g. o1, DeepSeek R1) have demonstrated great promise of using long Chain-of-Thought (CoT) to improve reasoning capabilities of language models, scaling it up during test-time is challenging due to inefficient memory usage -- intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We propose PENCIL, which incorporates a reduction mechanism into the autoregressive generation process, allowing the model to recursively clean up intermediate thoughts based on patterns learned from training. With this reduction mechanism, PENCIL significantly reduces the maximal context length required during generation, and thus can generate longer thoughts with limited memory, solving larger-scale problems given more thinking time. For example, we demonstrate PENCIL achieves 97\% accuracy on the challenging Einstein's puzzle -- a task even large models like GPT-4 struggle with -- using only a small 25M-parameter transformer with 2048 context length. Theoretically, we prove PENCIL can perform universal space-efficient computation by simulating Turing machines with optimal time and space complexity, and thus can solve arbitrary computational tasks that would otherwise be intractable given context window constraints.

With generative AI advances, the exciting potential for autonomous agents to manage daily tasks via natural language commands has emerged. However, cur rent agents are primarily created and tested in simplified synthetic environments, substantially limiting real-world scenario representation. In this paper, we build an environment for agent command and control that is highly realistic and reproducible. Specifically, we focus on agents that perform tasks on websites, and we create an environment with fully functional websites from four common domains: e-commerce, social forum discussions, collaborative software development, and content management. Our environment is enriched with tools (e.g., a map) and external knowledge bases (e.g., user manuals) to encourage human-like task-solving. Building upon our environment, we release a set of benchmark tasks focusing on evaluating the functional correctness of task completions. The tasks in our benchmark are diverse, long-horizon, and are designed to emulate tasks that humans routinely perform on the internet. We design and implement several autonomous agents, integrating recent techniques such as reasoning before acting. The results demonstrate that solving complex tasks is challenging: our best GPT-4-based agent only achieves an end-to-end task success rate of 10.59%. These results highlight the need for further development of robust agents, that current state-of-the-art LMs are far from perfect performance in these real-life tasks, and that WebArena can be used to measure such progress. Our code, data, environment reproduction resources, and video demonstrations are publicly available at https://webarena.dev/.

Large Language Models have demonstrated remarkable capabilities in code generation, yet they often struggle with complex programming tasks that require deep algorithmic reasoning. While process supervision through learned reward models shows promise in guiding reasoning steps, it requires expensive training data and suffers from unreliable evaluation. We propose Outcome-Refining Process Supervision, a novel paradigm that treats outcome refinement itself as the process to be supervised. Our framework leverages concrete execution signals to ground the supervision of reasoning steps, while using tree-structured exploration to maintain multiple solution trajectories simultaneously. Experiments demonstrate that our approach enables even smaller models to achieve high success accuracy and performance metrics on competitive programming tasks, creates more reliable verification than traditional reward models without requiring training PRMs. Our approach achieves significant improvements across 5 models and 3 datasets: an average of 26.9% increase in correctness and 42.2% in efficiency. The results suggest that providing structured reasoning space with concrete verification signals is crucial for solving complex programming tasks. We open-source all our code and data at: https://github.com/zhuohaoyu/ORPS

Automatic program repair (APR) is crucial to improve software reliability. Recently, neural machine translation (NMT) techniques have been used to fix software bugs automatically. While promising, these approaches have two major limitations. Their search space often does not contain the correct fix, and their search strategy ignores software knowledge such as strict code syntax. Due to these limitations, existing NMT-based techniques underperform the best template-based approaches. We propose CURE, a new NMT-based APR technique with three major novelties. First, CURE pre-trains a programming language (PL) model on a large software codebase to learn developer-like source code before the APR task. Second, CURE designs a new code-aware search strategy that finds more correct fixes by focusing on compilable patches and patches that are close in length to the buggy code. Finally, CURE uses a subword tokenization technique to generate a smaller search space that contains more correct fixes. Our evaluation on two widely-used benchmarks shows that CURE correctly fixes 57 Defects4J bugs and 26 QuixBugs bugs, outperforming all existing APR techniques on both benchmarks.

Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains underexplored. We identify this challenge as the task of subgoal completion, where an LLM must discharge short but nontrivial proof obligations left unresolved in a human-provided sketch. To study this problem, we introduce FormalML, a Lean 4 benchmark built from foundational theories of machine learning. Using a translation tactic that converts procedural proofs into declarative form, we extract 4937 problems spanning optimization and probability inequalities, with varying levels of difficulty. FormalML is the first subgoal completion benchmark to combine premise retrieval and complex research-level contexts. Evaluation of state-of-the-art provers highlights persistent limitations in accuracy and efficiency, underscoring the need for more capable LLM-based theorem provers for effective subgoal completion,

Much is promised in relation to AI-supported software development. However, there has been limited evaluation effort in the research domain aimed at validating the true utility of such techniques, especially when compared to human coding outputs. We bridge this gap, where a benchmark dataset comprising 72 distinct software engineering tasks is used to compare the effectiveness of large language models (LLMs) and human programmers in producing Python software code. GPT-4 is used as a representative LLM, where for the code generated by humans and this LLM, we evaluate code quality and adherence to Python coding standards, code security and vulnerabilities, code complexity and functional correctness. We use various static analysis benchmarks, including Pylint, Radon, Bandit and test cases. Among the notable outcomes, results show that human-generated code recorded higher ratings for adhering to coding standards than GPT-4. We observe security flaws in code generated by both humans and GPT-4, however, code generated by humans shows a greater variety of problems, but GPT-4 code included more severe outliers. Our results show that although GPT-4 is capable of producing coding solutions, it frequently produces more complex code that may need more reworking to ensure maintainability. On the contrary however, our outcomes show that a higher number of test cases passed for code generated by GPT-4 across a range of tasks than code that was generated by humans. That said, GPT-4 frequently struggles with complex problem-solving that involve in-depth domain knowledge. This study highlights the potential utility of LLMs for supporting software development, however, tasks requiring comprehensive, innovative or unconventional solutions, and careful debugging and error correction seem to be better developed by human programmers. We plot an agenda for the software engineering community.

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches n independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves 82.23% accuracy on the AIME datasets, a 15% improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

Can foundation models be guided to execute tasks involving legal reasoning? We believe that building a benchmark to answer this question will require sustained collaborative efforts between the computer science and legal communities. To that end, this short paper serves three purposes. First, we describe how IRAC-a framework legal scholars use to distinguish different types of legal reasoning-can guide the construction of a Foundation Model oriented benchmark. Second, we present a seed set of 44 tasks built according to this framework. We discuss initial findings, and highlight directions for new tasks. Finally-inspired by the Open Science movement-we make a call for the legal and computer science communities to join our efforts by contributing new tasks. This work is ongoing, and our progress can be tracked here: https://github.com/HazyResearch/legalbench.

Context: Test-driven development (TDD) is a widely employed software development practice that involves developing test cases based on requirements prior to writing the code. Although various methods for automated test case generation have been proposed, they are not specifically tailored for TDD, where requirements instead of code serve as input. Objective: In this paper, we introduce a text-to-testcase generation approach based on a large language model (GPT-3.5) that is fine-tuned on our curated dataset with an effective prompt design. Method: Our approach involves enhancing the capabilities of basic GPT-3.5 for text-to-testcase generation task that is fine-tuned on our curated dataset with an effective prompting design. We evaluated the effectiveness of our approach using a span of five large-scale open-source software projects. Results: Our approach generated 7k test cases for open source projects, achieving 78.5% syntactic correctness, 67.09% requirement alignment, and 61.7% code coverage, which substantially outperforms all other LLMs (basic GPT-3.5, Bloom, and CodeT5). In addition, our ablation study demonstrates the substantial performance improvement of the fine-tuning and prompting components of the GPT-3.5 model. Conclusions: These findings lead us to conclude that fine-tuning and prompting should be considered in the future when building a language model for the text-to-testcase generation task

Machine learning research has advanced in multiple aspects, including model structures and learning methods. The effort to automate such research, known as AutoML, has also made significant progress. However, this progress has largely focused on the architecture of neural networks, where it has relied on sophisticated expert-designed layers as building blocks---or similarly restrictive search spaces. Our goal is to show that AutoML can go further: it is possible today to automatically discover complete machine learning algorithms just using basic mathematical operations as building blocks. We demonstrate this by introducing a novel framework that significantly reduces human bias through a generic search space. Despite the vastness of this space, evolutionary search can still discover two-layer neural networks trained by backpropagation. These simple neural networks can then be surpassed by evolving directly on tasks of interest, e.g. CIFAR-10 variants, where modern techniques emerge in the top algorithms, such as bilinear interactions, normalized gradients, and weight averaging. Moreover, evolution adapts algorithms to different task types: e.g., dropout-like techniques appear when little data is available. We believe these preliminary successes in discovering machine learning algorithms from scratch indicate a promising new direction for the field.

Background: AI-powered code generation, fueled by Large Language Models (LLMs), is revolutionizing software development. Models like OpenAI's Codex and GPT-4, alongside DeepSeek, leverage vast code and natural language datasets. However, ensuring code quality, correctness, and managing complex tasks remains challenging, necessitating thorough evaluation. Methodology: This research compares ChatGPT (version o1) and DeepSeek (version R1) for Python code generation using online judge coding challenges. It evaluates correctness (online judge verdicts, up to three attempts), code quality (Pylint/Flake8), and efficiency (execution time/memory usage). Results: DeepSeek demonstrated higher correctness, particularly on algorithmic tasks, often achieving 'Accepted' on the first attempt. ChatGPT sometimes requires multiple attempts or failures. ChatGPT encountered fewer issues, used comparable or slightly less memory, consumed less execution times and wrote fewer lines of code. Conclusion: DeepSeek exhibited superior correctness in Python code generation, often requiring fewer attempts, suggesting an advantage in algorithmic problem-solving. Both models showed almost similar efficiency in execution time and memory use. Finally, this research provides insights for developers choosing AI coding assistants and informs future AI-driven software development research.

We present and test the largest benchmark for vericoding, LLM-generation of formally verified code from formal specifications - in contrast to vibe coding, which generates potentially buggy code from a natural language description. Our benchmark contains 12,504 formal specifications, with 3,029 in Dafny, 2,334 in Verus/Rust and 7,141 in Lean. Of these, 6,174 are new unseen problems. We find vericoding success rates of 27% in Lean, 44% in Verus/Rust and 82% in Dafny using off-the-shelf LLMs. Adding natural-language descriptions does not significantly improve performance. We also find that LLM progress has improved progress on pure Dafny verification from 68% to 96% over the past year. The benchmark and vericoding results are shared at https://github.com/Beneficial-AI-Foundation/vericoding-benchmark

The advancements of language language models (LLMs) have piqued growing interest in developing LLM-based language agents to automate scientific discovery end-to-end, which has sparked both excitement and skepticism about the true capabilities of such agents. In this work, we argue that for an agent to fully automate scientific discovery, it must be able to complete all essential tasks in the workflow. Thus, we call for rigorous assessment of agents on individual tasks in a scientific workflow before making bold claims on end-to-end automation. To this end, we present ScienceAgentBench, a new benchmark for evaluating language agents for data-driven scientific discovery. To ensure the scientific authenticity and real-world relevance of our benchmark, we extract 102 tasks from 44 peer-reviewed publications in four disciplines and engage nine subject matter experts to validate them. We unify the target output for every task to a self-contained Python program file and employ an array of evaluation metrics to examine the generated programs, execution results, and costs. Each task goes through multiple rounds of manual validation by annotators and subject matter experts to ensure its annotation quality and scientific plausibility. We also propose two effective strategies to mitigate data contamination concerns. Using our benchmark, we evaluate five open-weight and proprietary LLMs, each with three frameworks: direct prompting, OpenHands, and self-debug. Given three attempts for each task, the best-performing agent can only solve 32.4% of the tasks independently and 34.3% with expert-provided knowledge. These results underscore the limited capacities of current language agents in generating code for data-driven discovery, let alone end-to-end automation for scientific research.

Large language models (LLMs) are a new and powerful tool for a wide span of applications involving natural language and demonstrate impressive code generation abilities. In this paper, we explore the capabilitity of state-of-the-art LLMs, including closed-source options like OpenAI GPT-4 and open-source alternatives like Meta AI Codellama, to automatically generate tests and use these tests to validate and verify compiler implementations of a directive-based programming paradigm, OpenACC. Our approach entails exploring various prompt engineering techniques including a code template, retrieval-augmented generation (RAG) with code template, expressive prompt using RAG with code template, one-shot example, and RAG with one-shot example. This paper focusses on (a) exploring the capabilities of the latest LLMs for code generation, (b) investigating prompt and fine tuning methods, and (c) analyzing the outcome of LLMs generated tests

Large Language Models (LLMs) are increasingly relied upon for solving complex reasoning tasks in domains such as mathematics, logic, and multi-step question answering. A growing line of work seeks to improve reasoning quality by scaling inference time compute particularly through Process Reward Models (PRMs), used to reward the reasoning at intermediate steps. While effective, these methods introduce substantial computational overhead, especially when generating large numbers of solutions in parallel. In this paper, we investigate whether PRMs can be used mid-generation to provide early signals that enable the rejection of suboptimal candidates before full generation of step is complete. We introduce the hypothesis that PRMs are also Partial Reward Models, meaning that the scores they assign to partially completed reasoning step are predictive of final output quality. This allows for principled early rejection based on intermediate token-level signals. We support this hypothesis both theoretically, by proving that the risk of discarding optimal beams decreases exponentially with generation length and empirically, by demonstrating a strong correlation between partial and final rewards across multiple reward models. On math reasoning benchmarks, our method achieves up to 1.4times-9times reduction in inference FLOPs without degrading final performance. These results suggest that early rejection is a powerful mechanism for improving the compute-efficiency of reasoning in LLMs.

Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of general reliability, and business logic blindness. In this work, we propose a novel framework that leverages functional programming and type systems to translate Scala backend code into formal Lean representations. Our pipeline automatically generates theorems that specify the intended behavior of APIs and database operations, and uses LLM-based provers to verify them. When a theorem is proved, the corresponding logic is guaranteed to be correct and no further testing is needed. If the negation of a theorem is proved instead, it confirms a bug. In cases where neither can be proved, human intervention is required. We evaluate our method on realistic backend systems and find that it can formally verify over 50% of the test requirements, which suggests that half of a testing engineer's workload can be automated. Additionally, with an average cost of only $2.19 per API, LLM-based verification is significantly more cost-effective than manual testing and can be scaled easily through parallel execution. Our results indicate a promising direction for scalable, AI-powered software testing, with the potential to greatly improve engineering productivity as models continue to advance.

Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the proofs in formal language can be challenging for humans and machines. The miniF2F benchmark has 20 IMO problems in its test set, yet formal proofs are available only for 6 of these problems (3 of which are only written by mathematicians). The model with best accuracy can only prove 2 of these 20 IMO problems, from 1950s and 60s, while its training set is a secret. In this work, we write complete, original formal proofs for the remaining IMO problems in Lean along with 3 extra problems from IMO 2022 and 2023. This effort expands the availability of proof currently in the public domain by creating 5,880 lines of Lean proof. The goal of the paper is to pave the way for developing AI models that can automatically write the formal proofs for all the IMO problems in miniF2F and beyond by providing an evaluation benchmark. In this pursuit, we devise a method to decompose the proofs of these problems into their building blocks, constructing a dataset of 1,329 lemmas with more than 40k lines of Lean code. These lemmas are not trivial, yet they are approachable, providing the opportunity to evaluate and diagnose the failures and successes of AI models. We evaluate the ability of the SOTA LLMs on our dataset and analyze their success and failure modes from different perspectives. Our dataset and code is available at: https://github.com/roozbeh-yz/IMO-Steps.

In this paper, we study the problem of planning in Minecraft, a popular, democratized yet challenging open-ended environment for developing multi-task embodied agents. We've found two primary challenges of empowering such agents with planning: 1) planning in an open-ended world like Minecraft requires precise and multi-step reasoning due to the long-term nature of the tasks, and 2) as vanilla planners do not consider the proximity to the current agent when ordering parallel sub-goals within a complicated plan, the resulting plan could be inefficient. To this end, we propose "Describe, Explain, Plan and Select" (DEPS), an interactive planning approach based on Large Language Models (LLMs). Our approach helps with better error correction from the feedback during the long-haul planning, while also bringing the sense of proximity via goal Selector, a learnable module that ranks parallel sub-goals based on the estimated steps of completion and improves the original plan accordingly. Our experiments mark the milestone of the first multi-task agent that can robustly accomplish 70+ Minecraft tasks and nearly doubles the overall performances. Finally, the ablation and exploratory studies detail how our design beats the counterparts and provide a promising update on the ObtainDiamond grand challenge with our approach. The code is released at https://github.com/CraftJarvis/MC-Planner.

The task of repository-level code completion is to continue writing the unfinished code based on a broader context of the repository. While for automated code completion tools, it is difficult to utilize the useful information scattered in different files. We propose RepoCoder, a simple, generic, and effective framework to address the challenge. It streamlines the repository-level code completion process by incorporating a similarity-based retriever and a pre-trained code language model in an iterative retrieval-generation pipeline. RepoCoder makes effective utilization of repository-level information for code completion and has the ability to generate code at various levels of granularity. Moreover, we propose a new benchmark RepoEval, which consists of the latest and high-quality real-world repositories covering line, API invocation, and function body completion scenarios. Experimental results indicate that RepoCoder significantly improves the In-File completion baseline by over 10% in all settings and consistently outperforms the vanilla retrieval-augmented code completion approach. Furthermore, we validate the effectiveness of RepoCoder through comprehensive analysis, providing valuable insights for future research. Our source code and benchmark are publicly available: https://github.com/microsoft/CodeT/tree/main/RepoCoder

Background. Due to the widespread adoption of Artificial Intelligence (AI) and Machine Learning (ML) for building software applications, companies are struggling to recruit employees with a deep understanding of such technologies. In this scenario, AutoML is soaring as a promising solution to fill the AI/ML skills gap since it promises to automate the building of end-to-end AI/ML pipelines that would normally be engineered by specialized team members. Aims. Despite the growing interest and high expectations, there is a dearth of information about the extent to which AutoML is currently adopted by teams developing AI/ML-enabled systems and how it is perceived by practitioners and researchers. Method. To fill these gaps, in this paper, we present a mixed-method study comprising a benchmark of 12 end-to-end AutoML tools on two SE datasets and a user survey with follow-up interviews to further our understanding of AutoML adoption and perception. Results. We found that AutoML solutions can generate models that outperform those trained and optimized by researchers to perform classification tasks in the SE domain. Also, our findings show that the currently available AutoML solutions do not live up to their names as they do not equally support automation across the stages of the ML development workflow and for all the team members. Conclusions. We derive insights to inform the SE research community on how AutoML can facilitate their activities and tool builders on how to design the next generation of AutoML technologies.

The field of machine learning has achieved striking progress in recent years, witnessing breakthrough results on language modelling, protein folding and nitpickingly fine-grained dog breed classification. Some even succeeded at playing computer games and board games, a feat both of engineering and of setting their employers' expectations. The central contribution of this work is to carefully examine whether this progress, and technology more broadly, can be expected to continue indefinitely. Through a rigorous application of statistical theory and failure to extrapolate beyond the training data, we answer firmly in the negative and provide details: technology will peak at 3:07 am (BST) on 20th July, 2032. We then explore the implications of this finding, discovering that individuals awake at this ungodly hour with access to a sufficiently powerful computer possess an opportunity for myriad forms of long-term linguistic 'lock in'. All we need is a large (>> 1W) data centre to seize this pivotal moment. By setting our analogue alarm clocks, we propose a tractable algorithm to ensure that, for the future of humanity, the British spelling of colour becomes the default spelling across more than 80% of the global word processing software market.

Our everyday lives now heavily rely on artificial intelligence (AI) powered large language models (LLMs). Like regular users, programmers are also benefiting from the newest large language models. In response to the critical role that AI models play in modern software development, this study presents a thorough evaluation of leading programming assistants, including ChatGPT, Gemini(Bard AI), AlphaCode, and GitHub Copilot. The evaluation is based on tasks like natural language processing and code generation accuracy in different programming languages like Java, Python and C++. Based on the results, it has emphasized their strengths and weaknesses and the importance of further modifications to increase the reliability and accuracy of the latest popular models. Although these AI assistants illustrate a high level of progress in language understanding and code generation, along with ethical considerations and responsible usage, they provoke a necessity for discussion. With time, developing more refined AI technology is essential for achieving advanced solutions in various fields, especially with the knowledge of the feature intricacies of these models and their implications. This study offers a comparison of different LLMs and provides essential feedback on the rapidly changing area of AI models. It also emphasizes the need for ethical developmental practices to actualize AI models' full potential.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Recent progress in autonomous code generation has fueled excitement around AI agents capable of accelerating scientific discovery by running experiments. However, there is currently no benchmark that evaluates whether such agents can implement scientific ideas when given varied amounts of code as a starting point, interpolating between reproduction (running code) and from-scratch replication (fully re-implementing and running code). We introduce AutoExperiment, a benchmark that evaluates AI agents' ability to implement and run machine learning experiments based on natural language descriptions in research papers. In each task, agents are given a research paper, a codebase with key functions masked out, and a command to run the experiment. The goal is to generate the missing code, execute the experiment in a sandboxed environment, and reproduce the results. AutoExperiment scales in difficulty by varying the number of missing functions n, ranging from partial reproduction to full replication. We evaluate state-of-the-art agents and find that performance degrades rapidly as n increases. Agents that can dynamically interact with the environment (e.g. to debug their code) can outperform agents in fixed "agentless" harnesses, and there exists a significant gap between single-shot and multi-trial success rates (Pass@1 vs. Pass@5), motivating verifier approaches to our benchmark. Our findings highlight critical challenges in long-horizon code generation, context retrieval, and autonomous experiment execution, establishing AutoExperiment as a new benchmark for evaluating progress in AI-driven scientific experimentation. Our data and code are open-sourced at https://github.com/j1mk1m/AutoExperiment .

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis, and artificial intelligence. While the long-term goal of autoformalization seemed elusive for a long time, we show large language models provide new prospects towards this goal. We make the surprising observation that LLMs can correctly translate a significant portion (25.3%) of mathematical competition problems perfectly to formal specifications in Isabelle/HOL. We demonstrate the usefulness of this process by improving a previously introduced neural theorem prover via training on these autoformalized theorems. Our methodology results in a new state-of-the-art result on the MiniF2F theorem proving benchmark, improving the proof rate from 29.6% to 35.2%.

Recent studies operationalize self-improvement through coding agents that edit their own codebases. They grow a tree of self-modifications through expansion strategies that favor higher software engineering benchmark performance, assuming that this implies more promising subsequent self-modifications. However, we identify a mismatch between the agent's self-improvement potential (metaproductivity) and its coding benchmark performance, namely the Metaproductivity-Performance Mismatch. Inspired by Huxley's concept of clade, we propose a metric (CMP) that aggregates the benchmark performances of the descendants of an agent as an indicator of its potential for self-improvement. We show that, in our self-improving coding agent development setting, access to the true CMP is sufficient to simulate how the G\"odel Machine would behave under certain assumptions. We introduce the Huxley-G\"odel Machine (HGM), which, by estimating CMP and using it as guidance, searches the tree of self-modifications. On SWE-bench Verified and Polyglot, HGM outperforms prior self-improving coding agent development methods while using less wall-clock time. Last but not least, HGM demonstrates strong transfer to other coding datasets and large language models. The agent optimized by HGM on SWE-bench Verified with GPT-5-mini and evaluated on SWE-bench Lite with GPT-5 achieves human-level performance, matching the best officially checked results of human-engineered coding agents. Our code is available at https://github.com/metauto-ai/HGM.

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

As we consider entrusting Large Language Models (LLMs) with key societal and decision-making roles, measuring their alignment with human cognition becomes critical. This requires methods that can assess how these systems represent information and facilitate comparisons to human understanding across diverse tasks. To meet this need, we developed Turing Representational Similarity Analysis (RSA), a method that uses pairwise similarity ratings to quantify alignment between AIs and humans. We tested this approach on semantic alignment across text and image modalities, measuring how different Large Language and Vision Language Model (LLM and VLM) similarity judgments aligned with human responses at both group and individual levels. GPT-4o showed the strongest alignment with human performance among the models we tested, particularly when leveraging its text processing capabilities rather than image processing, regardless of the input modality. However, no model we studied adequately captured the inter-individual variability observed among human participants. This method helped uncover certain hyperparameters and prompts that could steer model behavior to have more or less human-like qualities at an inter-individual or group level. Turing RSA enables the efficient and flexible quantification of human-AI alignment and complements existing accuracy-based benchmark tasks. We demonstrate its utility across multiple modalities (words, sentences, images) for understanding how LLMs encode knowledge and for examining representational alignment with human cognition.

Code completion aims to enhance programming productivity by predicting potential code based on the current programming context. Recently, pretrained language models (LMs) have become prominent in this field. Various approaches have been proposed to fine-tune LMs using supervised fine-tuning (SFT) techniques for code completion. However, the inherent exposure bias of these models can cause errors to accumulate early in the sequence completion, leading to even more errors in subsequent completions. To address this problem, deep reinforcement learning (DRL) is an alternative technique for fine-tuning LMs for code completion, which can improve the generalization capabilities and overall performance. Nevertheless, integrating DRL-based strategies into code completion faces two major challenges: 1) The dynamic nature of the code context requires the completion model to quickly adapt to changes, which poses difficulties for conventional DRL strategies that focus on delayed rewarding of the final code state. 2) It is difficult to evaluate the correctness of partial code, thus the reward redistribution-based strategies cannot be adapted to code completion. To tackle these challenges, we propose IRCoCo, a code completion-specific DRL-based fine-tuning framework. This framework is designed to provide immediate rewards as feedback for detecting dynamic context changes arising from continuous edits during code completion. With the aid of immediate feedback, the fine-tuned LM can gain a more precise understanding of the current context, thereby enabling effective adjustment of the LM and optimizing code completion in a more refined manner. Experimental results demonstrate that fine-tuning pretrained LMs with IRCoCo leads to significant improvements in the code completion task, outperforming both SFT-based and other DRL-based baselines.

This paper explores the limits of the current generation of large language models for program synthesis in general purpose programming languages. We evaluate a collection of such models (with between 244M and 137B parameters) on two new benchmarks, MBPP and MathQA-Python, in both the few-shot and fine-tuning regimes. Our benchmarks are designed to measure the ability of these models to synthesize short Python programs from natural language descriptions. The Mostly Basic Programming Problems (MBPP) dataset contains 974 programming tasks, designed to be solvable by entry-level programmers. The MathQA-Python dataset, a Python version of the MathQA benchmark, contains 23914 problems that evaluate the ability of the models to synthesize code from more complex text. On both datasets, we find that synthesis performance scales log-linearly with model size. Our largest models, even without finetuning on a code dataset, can synthesize solutions to 59.6 percent of the problems from MBPP using few-shot learning with a well-designed prompt. Fine-tuning on a held-out portion of the dataset improves performance by about 10 percentage points across most model sizes. On the MathQA-Python dataset, the largest fine-tuned model achieves 83.8 percent accuracy. Going further, we study the model's ability to engage in dialog about code, incorporating human feedback to improve its solutions. We find that natural language feedback from a human halves the error rate compared to the model's initial prediction. Additionally, we conduct an error analysis to shed light on where these models fall short and what types of programs are most difficult to generate. Finally, we explore the semantic grounding of these models by fine-tuning them to predict the results of program execution. We find that even our best models are generally unable to predict the output of a program given a specific input.

Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI O1/O3 and Deepseek R1. In this work, we investigate the entire posttraining of ATP, aiming to align it with breakthroughs in reasoning models in natural languages.To begin, we continual train current ATP models with a hybrid dataset, which consists of numerous statement-proof pairs, and additional data aimed at incorporating cognitive behaviors that emulate human reasoning and hypothesis refinement. Next, we explore reinforcement learning with the use of outcome reward returned by Lean 4 compiler. Through our designed continual training and reinforcement learning processes, we have successfully improved existing formal provers, including both DeepSeek-Prover-v1.5 and Goedel-Prover, achieving state-of-the-art performance in the field of whole-proof generation. For example, we achieve a 59.8% pass rate (pass@32) on MiniF2F. This is an on-going project and we will progressively update our findings, release our data and training details.

The cycle of scientific discovery is frequently bottlenecked by the slow, manual creation of software to support computational experiments. To address this, we present an AI system that creates expert-level scientific software whose goal is to maximize a quality metric. The system uses a Large Language Model (LLM) and Tree Search (TS) to systematically improve the quality metric and intelligently navigate the large space of possible solutions. The system achieves expert-level results when it explores and integrates complex research ideas from external sources. The effectiveness of tree search is demonstrated across a wide range of benchmarks. In bioinformatics, it discovered 40 novel methods for single-cell data analysis that outperformed the top human-developed methods on a public leaderboard. In epidemiology, it generated 14 models that outperformed the CDC ensemble and all other individual models for forecasting COVID-19 hospitalizations. Our method also produced state-of-the-art software for geospatial analysis, neural activity prediction in zebrafish, time series forecasting and numerical solution of integrals. By devising and implementing novel solutions to diverse tasks, the system represents a significant step towards accelerating scientific progress.

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem proving is hindered by a lack of training data. To address this issue, we introduce an approach to generate extensive Lean 4 proof data derived from high-school and undergraduate-level mathematical competition problems. This approach involves translating natural language problems into formal statements, filtering out low-quality statements, and generating proofs to create synthetic data. After fine-tuning the DeepSeekMath 7B model on this synthetic dataset, which comprises 8 million formal statements with proofs, our model achieved whole-proof generation accuracies of 46.3% with 64 samples and 52% cumulatively on the Lean 4 miniF2F test, surpassing the baseline GPT-4 at 23.0% with 64 samples and a tree search reinforcement learning method at 41.0%. Additionally, our model successfully proved 5 out of 148 problems in the Lean 4 Formalized International Mathematical Olympiad (FIMO) benchmark, while GPT-4 failed to prove any. These results demonstrate the potential of leveraging large-scale synthetic data to enhance theorem-proving capabilities in LLMs. Both the synthetic dataset and the model will be made available to facilitate further research in this promising field.

We investigate the mathematical capabilities of ChatGPT by testing it on publicly available datasets, as well as hand-crafted ones, and measuring its performance against other models trained on a mathematical corpus, such as Minerva. We also test whether ChatGPT can be a useful assistant to professional mathematicians by emulating various use cases that come up in the daily professional activities of mathematicians (question answering, theorem searching). In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, only cover elementary mathematics. We address this issue by introducing a new dataset: GHOSTS. It is the first natural-language dataset made and curated by working researchers in mathematics that (1) aims to cover graduate-level mathematics and (2) provides a holistic overview of the mathematical capabilities of language models. We benchmark ChatGPT on GHOSTS and evaluate performance against fine-grained criteria. We make this new dataset publicly available to assist a community-driven comparison of ChatGPT with (future) large language models in terms of advanced mathematical comprehension. We conclude that contrary to many positive reports in the media (a potential case of selection bias), ChatGPT's mathematical abilities are significantly below those of an average mathematics graduate student. Our results show that ChatGPT often understands the question but fails to provide correct solutions. Hence, if your goal is to use it to pass a university exam, you would be better off copying from your average peer!

Large Language Models are becoming an increasingly popular tool for software development. Their ability to model and generate source code has been demonstrated in a variety of contexts, including code completion, summarization, translation, and lookup. However, they often struggle to generate code for more complex tasks. In this paper, we explore the ability of state-of-the-art language models to generate parallel code. We propose a benchmark, PCGBench, consisting of a set of 420 tasks for evaluating the ability of language models to generate parallel code, and we evaluate the performance of several state-of-the-art open- and closed-source language models on these tasks. We introduce novel metrics for comparing parallel code generation performance and use them to explore how well each LLM performs on various parallel programming models and computational problem types.

Scientific discovery is a complex cognitive process that has driven human knowledge and technological progress for centuries. While artificial intelligence (AI) has made significant advances in automating aspects of scientific reasoning, simulation, and experimentation, we still lack integrated AI systems capable of performing autonomous long-term scientific research and discovery. This paper examines the current state of AI for scientific discovery, highlighting recent progress in large language models and other AI techniques applied to scientific tasks. We then outline key challenges and promising research directions toward developing more comprehensive AI systems for scientific discovery, including the need for science-focused AI agents, improved benchmarks and evaluation metrics, multimodal scientific representations, and unified frameworks combining reasoning, theorem proving, and data-driven modeling. Addressing these challenges could lead to transformative AI tools to accelerate progress across disciplines towards scientific discovery.

With easier access to powerful compute resources, there is a growing trend in the field of AI for software development to develop larger and larger language models (LLMs) to address a variety of programming tasks. Even LLMs applied to tasks from the high-performance computing (HPC) domain are huge in size (e.g., billions of parameters) and demand expensive compute resources for training. We found this design choice confusing - why do we need large LLMs trained on natural languages and programming languages unrelated to HPC for HPC-specific tasks? In this line of work, we aim to question design choices made by existing LLMs by developing smaller LLMs for specific domains - we call them domain-specific LLMs. Specifically, we start off with HPC as a domain and propose a novel tokenizer named Tokompiler, designed specifically for preprocessing code in HPC and compilation-centric tasks. Tokompiler leverages knowledge of language primitives to generate language-oriented tokens, providing a context-aware understanding of code structure while avoiding human semantics attributed to code structures completely. We applied Tokompiler to pre-train two state-of-the-art models, SPT-Code and Polycoder, for a Fortran code corpus mined from GitHub. We evaluate the performance of these models against the conventional LLMs. Results demonstrate that Tokompiler significantly enhances code completion accuracy and semantic understanding compared to traditional tokenizers in normalized-perplexity tests, down to ~1 perplexity score. This research opens avenues for further advancements in domain-specific LLMs, catering to the unique demands of HPC and compilation tasks.

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.

We design a suite of minimal algorithmic tasks that are a loose abstraction of open-ended real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model. Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended stochastic planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; comparatively, multi-token approaches, namely teacherless training and diffusion models, excel in producing diverse and original output. Secondly, in our tasks, we find that to elicit randomness from the Transformer without hurting coherence, it is better to inject noise right at the input layer (via a method we dub hash-conditioning) rather than defer to temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and softmax-based sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

With the rise of prolific ChatGPT, the risk and consequences of AI-generated text has increased alarmingly. To address the inevitable question of ownership attribution for AI-generated artifacts, the US Copyright Office released a statement stating that 'If a work's traditional elements of authorship were produced by a machine, the work lacks human authorship and the Office will not register it'. Furthermore, both the US and the EU governments have recently drafted their initial proposals regarding the regulatory framework for AI. Given this cynosural spotlight on generative AI, AI-generated text detection (AGTD) has emerged as a topic that has already received immediate attention in research, with some initial methods having been proposed, soon followed by emergence of techniques to bypass detection. This paper introduces the Counter Turing Test (CT^2), a benchmark consisting of techniques aiming to offer a comprehensive evaluation of the robustness of existing AGTD techniques. Our empirical findings unequivocally highlight the fragility of the proposed AGTD methods under scrutiny. Amidst the extensive deliberations on policy-making for regulating AI development, it is of utmost importance to assess the detectability of content generated by LLMs. Thus, to establish a quantifiable spectrum facilitating the evaluation and ranking of LLMs according to their detectability levels, we propose the AI Detectability Index (ADI). We conduct a thorough examination of 15 contemporary LLMs, empirically demonstrating that larger LLMs tend to have a higher ADI, indicating they are less detectable compared to smaller LLMs. We firmly believe that ADI holds significant value as a tool for the wider NLP community, with the potential to serve as a rubric in AI-related policy-making.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

Turing machine and decision tree have developed independently for a long time. With the recent development of differentiable models, there is an intersection between them. Neural turing machine(NTM) opens door for the memory network. It use differentiable attention mechanism to read/write external memory bank. Differentiable forest brings differentiable properties to classical decision tree. In this short note, we show the deep connection between these two models. That is: differentiable forest is a special case of NTM. Differentiable forest is actually decision tree based neural turing machine. Based on this deep connection, we propose a response augmented differential forest (RaDF). The controller of RaDF is differentiable forest, the external memory of RaDF are response vectors which would be read/write by leaf nodes.

Research on Machine Translation (MT) has achieved important breakthroughs in several areas. While there is much more to be done in order to build on this success, we believe that the language industry needs better ways to take full advantage of current achievements. Due to a combination of factors, including time, resources, and skills, businesses tend to apply pragmatism into their AI workflows. Hence, they concentrate more on outcomes, e.g. delivery, shipping, releases, and features, and adopt high-level working production solutions, where possible. Among the features thought to be helpful for translators are sentence-level and word-level translation auto-suggestion and auto-completion. Suggesting alternatives can inspire translators and limit their need to refer to external resources, which hopefully boosts their productivity. This work describes our submissions to WMT's shared task on word-level auto-completion, for the Chinese-to-English, English-to-Chinese, German-to-English, and English-to-German language directions. We investigate the possibility of using pre-trained models and out-of-the-box features from available libraries. We employ random sampling to generate diverse alternatives, which reveals good results. Furthermore, we introduce our open-source API, based on CTranslate2, to serve translations, auto-suggestions, and auto-completions.

Generative AI and large language models hold great promise in enhancing computing education by powering next-generation educational technologies for introductory programming. Recent works have studied these models for different scenarios relevant to programming education; however, these works are limited for several reasons, as they typically consider already outdated models or only specific scenario(s). Consequently, there is a lack of a systematic study that benchmarks state-of-the-art models for a comprehensive set of programming education scenarios. In our work, we systematically evaluate two models, ChatGPT (based on GPT-3.5) and GPT-4, and compare their performance with human tutors for a variety of scenarios. We evaluate using five introductory Python programming problems and real-world buggy programs from an online platform, and assess performance using expert-based annotations. Our results show that GPT-4 drastically outperforms ChatGPT (based on GPT-3.5) and comes close to human tutors' performance for several scenarios. These results also highlight settings where GPT-4 still struggles, providing exciting future directions on developing techniques to improve the performance of these models.

Modern code completion engines, powered by large language models (LLMs), assist millions of developers with their strong capabilities to generate functionally correct code. Due to this popularity, it is crucial to investigate the security implications of relying on LLM-based code completion. In this work, we demonstrate that state-of-the-art black-box LLM-based code completion engines can be stealthily biased by adversaries to significantly increase their rate of insecure code generation. We present the first attack, named INSEC, that achieves this goal. INSEC works by injecting an attack string as a short comment in the completion input. The attack string is crafted through a query-based optimization procedure starting from a set of carefully designed initialization schemes. We demonstrate INSEC's broad applicability and effectiveness by evaluating it on various state-of-the-art open-source models and black-box commercial services (e.g., OpenAI API and GitHub Copilot). On a diverse set of security-critical test cases, covering 16 CWEs across 5 programming languages, INSEC increases the rate of generated insecure code by more than 50%, while maintaining the functional correctness of generated code. We consider INSEC practical -- it requires low resources and costs less than 10 US dollars to develop on commodity hardware. Moreover, we showcase the attack's real-world deployability, by developing an IDE plug-in that stealthily injects INSEC into the GitHub Copilot extension.

Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to construct high-quality math QA data for training. However, these efforts primarily focus on generating correct reasoning paths and answers, while largely overlooking the validity of the questions themselves. In this work, we propose Math Question Verification (MathQ-Verify), a novel five-stage pipeline designed to rigorously filter ill-posed or under-specified math problems. MathQ-Verify first performs format-level validation to remove redundant instructions and ensure that each question is syntactically well-formed. It then formalizes each question, decomposes it into atomic conditions, and verifies them against mathematical definitions. Next, it detects logical contradictions among these conditions, followed by a goal-oriented completeness check to ensure the question provides sufficient information for solving. To evaluate this task, we use existing benchmarks along with an additional dataset we construct, containing 2,147 math questions with diverse error types, each manually double-validated. Experiments show that MathQ-Verify achieves state-of-the-art performance across multiple benchmarks, improving the F1 score by up to 25 percentage points over the direct verification baseline. It further attains approximately 90% precision and 63% recall through a lightweight model voting scheme. MathQ-Verify offers a scalable and accurate solution for curating reliable mathematical datasets, reducing label noise and avoiding unnecessary computation on invalid questions. Our code and data are available at https://github.com/scuuy/MathQ-Verify.

Recent advancements in large language models (LLMs) have significantly advanced the automation of software development tasks, including code synthesis, program repair, and test generation. More recently, researchers and industry practitioners have developed various autonomous LLM agents to perform end-to-end software development tasks. These agents are equipped with the ability to use tools, run commands, observe feedback from the environment, and plan for future actions. However, the complexity of these agent-based approaches, together with the limited abilities of current LLMs, raises the following question: Do we really have to employ complex autonomous software agents? To attempt to answer this question, we build Agentless -- an agentless approach to automatically solve software development problems. Compared to the verbose and complex setup of agent-based approaches, Agentless employs a simplistic two-phase process of localization followed by repair, without letting the LLM decide future actions or operate with complex tools. Our results on the popular SWE-bench Lite benchmark show that surprisingly the simplistic Agentless is able to achieve both the highest performance (27.33%) and lowest cost (\$0.34) compared with all existing open-source software agents! Furthermore, we manually classified the problems in SWE-bench Lite and found problems with exact ground truth patch or insufficient/misleading issue descriptions. As such, we construct SWE-bench Lite-S by excluding such problematic issues to perform more rigorous evaluation and comparison. Our work highlights the current overlooked potential of a simple, interpretable technique in autonomous software development. We hope Agentless will help reset the baseline, starting point, and horizon for autonomous software agents, and inspire future work along this crucial direction.

Dense process rewards have proven a more effective alternative to the sparse outcome-level rewards in the inference-time scaling of large language models (LLMs), particularly in tasks requiring complex multi-step reasoning. While dense rewards also offer an appealing choice for the reinforcement learning (RL) of LLMs since their fine-grained rewards have the potential to address some inherent issues of outcome rewards, such as training efficiency and credit assignment, this potential remains largely unrealized. This can be primarily attributed to the challenges of training process reward models (PRMs) online, where collecting high-quality process labels is prohibitively expensive, making them particularly vulnerable to reward hacking. To address these challenges, we propose PRIME (Process Reinforcement through IMplicit rEwards), which enables online PRM updates using only policy rollouts and outcome labels through implict process rewards. PRIME combines well with various advantage functions and forgoes the dedicated reward model training phrase that existing approaches require, substantially reducing the development overhead. We demonstrate PRIME's effectiveness on competitional math and coding. Starting from Qwen2.5-Math-7B-Base, PRIME achieves a 15.1% average improvement across several key reasoning benchmarks over the SFT model. Notably, our resulting model, Eurus-2-7B-PRIME, surpasses Qwen2.5-Math-7B-Instruct on seven reasoning benchmarks with 10% of its training data.

The role-play ability of Large Language Models (LLMs) has emerged as a popular research direction. However, existing studies focus on imitating well-known public figures or fictional characters, overlooking the potential for simulating ordinary individuals. Such an oversight limits the potential for advancements in digital human clones and non-player characters in video games. To bridge this gap, we introduce ECHO, an evaluative framework inspired by the Turing test. This framework engages the acquaintances of the target individuals to distinguish between human and machine-generated responses. Notably, our framework focuses on emulating average individuals rather than historical or fictional figures, presenting a unique advantage to apply the Turing Test. We evaluated three role-playing LLMs using ECHO, with GPT-3.5 and GPT-4 serving as foundational models, alongside the online application GPTs from OpenAI. Our results demonstrate that GPT-4 more effectively deceives human evaluators, and GPTs achieves a leading success rate of 48.3%. Furthermore, we investigated whether LLMs could discern between human-generated and machine-generated texts. While GPT-4 can identify differences, it could not determine which texts were human-produced. Our code and results of reproducing the role-playing LLMs are made publicly available via https://github.com/CUHK-ARISE/ECHO.

Large Language Models (LLMs) have demonstrated strong capabilities across various domains, with recent advancements in challenging reasoning tasks such as mathematics and programming. However, solving reasoning tasks often requires long decoding chains (of thoughts), which incur O(N) time and memory consumption, where N is the chain length. To mitigate O(N) time and memory consumption, existing sparsity-based algorithms propose retaining only the most critical token's intermediate data (i.e., key-value cache) and discarding the rest. However, these existing algorithms struggle with the ``impossible trinity'' of accuracy, time, and memory. For example, the state-of-the-art algorithm, Quest, achieves high accuracy with O(L) time but O(N) memory (L is the cache budget, L ll N). To address this issue, in this paper, we identify a new attention pattern during the decode stage of reasoning tasks, where milestone tokens (analogous to lemmas in mathematical proofs) emerge, are utilized, and then become unimportant afterward. Based on this pattern, we propose a new algorithm named RaaS that identifies and retains milestone tokens only until they are no longer needed, achieving high accuracy with O(L) time and O(L) memory complexity.

Large language models (LLMs) have reshaped the landscape of program synthesis. However, contemporary LLM-based code completion systems often hallucinate broken code because they lack appropriate context, particularly when working with definitions not in the training data nor near the cursor. This paper demonstrates that tight integration with the type and binding structure of a language, as exposed by its language server, can address this contextualization problem in a token-efficient manner. In short, we contend that AIs need IDEs, too! In particular, we integrate LLM code generation into the Hazel live program sketching environment. The Hazel Language Server identifies the type and typing context of the hole being filled, even in the presence of errors, ensuring that a meaningful program sketch is always available. This allows prompting with codebase-wide contextual information not lexically local to the cursor, nor necessarily in the same file, but that is likely to be semantically local to the developer's goal. Completions synthesized by the LLM are then iteratively refined via further dialog with the language server. To evaluate these techniques, we introduce MVUBench, a dataset of model-view-update (MVU) web applications. These applications serve as challenge problems due to their reliance on application-specific data structures. We find that contextualization with type definitions is particularly impactful. After introducing our ideas in the context of Hazel we duplicate our techniques and port MVUBench to TypeScript in order to validate the applicability of these methods to higher-resource languages. Finally, we outline ChatLSP, a conservative extension to the Language Server Protocol (LSP) that language servers can implement to expose capabilities that AI code completion systems of various designs can use to incorporate static context when generating prompts for an LLM.

Large Language Models (LLMs) have shown impressive performance across a wide array of tasks involving both structured and unstructured textual data. Recent results on various benchmarks for code generation, repair, or completion suggest that certain models have programming abilities comparable to or even surpass humans. In this work, we demonstrate that high performance on such benchmarks does not correlate to humans' innate ability to understand structural control flow in code. To this end, we extract solutions from the HumanEval benchmark, which the relevant models perform strongly on, and trace their execution path using function calls sampled from the respective test set. Using this dataset, we investigate the ability of seven state-of-the-art LLMs to match the execution trace and find that, despite their ability to generate semantically identical code, they possess limited ability to trace execution paths, especially for longer traces and specific control structures. We find that even the top-performing model, Gemini, can fully and correctly generate only 47% of HumanEval task traces. Additionally, we introduce a subset for three key structures not contained in HumanEval: Recursion, Parallel Processing, and Object-Oriented Programming, including concepts like Inheritance and Polymorphism. Besides OOP, we show that none of the investigated models achieve an accuracy over 5% on the relevant traces. Aggregating these specialized parts with HumanEval tasks, we present Benchmark CoCoNUT: Code Control Flow for Navigation Understanding and Testing, which measures a model's ability to trace execution of code upon relevant calls, including advanced structural components. We conclude that current LLMs need significant improvement to enhance code reasoning abilities. We hope our dataset helps researchers bridge this gap.

Language models typically need to be trained or finetuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this work, we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate kNN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. On benchmarks including code and mathematics, we find that the model is capable of making use of newly defined functions and theorems during test time.

Large language models of code (Code-LLMs) have recently brought tremendous advances to code completion, a fundamental feature of programming assistance and code intelligence. However, most existing works ignore the possible presence of bugs in the code context for generation, which are inevitable in software development. Therefore, we introduce and study the buggy-code completion problem, inspired by the realistic scenario of real-time code suggestion where the code context contains potential bugs -- anti-patterns that can become bugs in the completed program. To systematically study the task, we introduce two datasets: one with synthetic bugs derived from semantics-altering operator changes (buggy-HumanEval) and one with realistic bugs derived from user submissions to coding problems (buggy-FixEval). We find that the presence of potential bugs significantly degrades the generation performance of the high-performing Code-LLMs. For instance, the passing rates of CodeGen-2B-mono on test cases of buggy-HumanEval drop more than 50% given a single potential bug in the context. Finally, we investigate several post-hoc methods for mitigating the adverse effect of potential bugs and find that there remains a large gap in post-mitigation performance.

The foundation of reproducible science lies in protocols that are precise, logically ordered, and executable. The autonomous generation of these protocols through natural language queries could greatly improve the efficiency of the reproduction process. However, current leading large language models (LLMs) often generate incomplete or inconsistent protocols, limiting their utility. To address this limitation, we first introduce SciRecipe, a large-scale dataset of over 12K structured protocols spanning 27 biological subfields and encompassing both comprehension and problem-solving tasks. To further improve protocol generation, we propose the "Sketch-and-Fill" paradigm, which separates analysis, structuring, and expression to ensure each step is explicit and verifiable. Complementing this, the structured component-based reward mechanism evaluates step granularity, action order, and semantic fidelity, aligning model optimization with experimental reliability. Building on these components, we develop Thoth, trained through a staged Knowledge-to-Action process that progresses from knowledge acquisition to operational reasoning and ultimately to robust, executable protocol generation. Across multiple benchmarks, Thoth consistently surpasses both proprietary and open-source LLMs, achieving significant improvements in step alignment, logical sequencing, and semantic accuracy. Our approach paves the way for reliable scientific assistants that bridge knowledge with experimental execution. All data, code, and models will be released publicly.

The emergence of large language models (LLMs) has significantly pushed the frontiers of program synthesis. Advancement of LLM-based program synthesis calls for a thorough evaluation of LLM-generated code. Most evaluation frameworks focus on the (functional) correctness of generated code; efficiency, as an important measure of code quality, has been overlooked in existing evaluations. In this work, we develop ENAMEL (EfficeNcy AutoMatic EvaLuator), a rigorous and high-standard benchmark for evaluating the capability of LLMs in generating efficient code. Firstly, we propose a new efficiency metric called eff@k, which generalizes the pass@k metric from correctness to efficiency and appropriately handles right-censored execution time. Furthermore, we derive an unbiased and variance-reduced estimator of eff@k via Rao--Blackwellization; we also provide a numerically stable implementation for the new estimator. Secondly, to set a high-standard for efficiency evaluation, we employ a human expert to design best algorithms and implementations as our reference solutions of efficiency, many of which are much more efficient than existing canonical solutions in HumanEval and HumanEval+. Moreover, to ensure a rigorous evaluation, we employ a human expert to curate strong test case generators to filter out wrong code and differentiate suboptimal algorithms. An extensive study across 30 popular LLMs using our benchmark ENAMEL shows that LLMs still fall short of generating expert-level efficient code. Using two subsets of our problem set, we demonstrate that such deficiency is because current LLMs struggle in designing advanced algorithms and are barely aware of implementation optimization. Our benchmark is publicly available at https://github.com/q-rz/enamel .

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

A key challenge on the path to developing agents that learn complex human-like behavior is the need to quickly and accurately quantify human-likeness. While human assessments of such behavior can be highly accurate, speed and scalability are limited. We address these limitations through a novel automated Navigation Turing Test (ANTT) that learns to predict human judgments of human-likeness. We demonstrate the effectiveness of our automated NTT on a navigation task in a complex 3D environment. We investigate six classification models to shed light on the types of architectures best suited to this task, and validate them against data collected through a human NTT. Our best models achieve high accuracy when distinguishing true human and agent behavior. At the same time, we show that predicting finer-grained human assessment of agents' progress towards human-like behavior remains unsolved. Our work takes an important step towards agents that more effectively learn complex human-like behavior.

The imperative need to scale computation across numerous nodes highlights the significance of efficient parallel computing, particularly in the realm of Message Passing Interface (MPI) integration. The challenging parallel programming task of generating MPI-based parallel programs has remained unexplored. This study first investigates the performance of state-of-the-art language models in generating MPI-based parallel programs. Findings reveal that widely used models such as GPT-3.5 and PolyCoder (specialized multi-lingual code models) exhibit notable performance degradation, when generating MPI-based programs compared to general-purpose programs. In contrast, domain-specific models such as MonoCoder, which are pretrained on MPI-related programming languages of C and C++, outperform larger models. Subsequently, we introduce a dedicated downstream task of MPI-based program generation by fine-tuning MonoCoder on HPCorpusMPI. We call the resulting model as MPIrigen. We propose an innovative preprocessing for completion only after observing the whole code, thus enabling better completion with a wider context. Comparative analysis against GPT-3.5 zero-shot performance, using a novel HPC-oriented evaluation method, demonstrates that MPIrigen excels in generating accurate MPI functions up to 0.8 accuracy in location and function predictions, and with more than 0.9 accuracy for argument predictions. The success of this tailored solution underscores the importance of domain-specific fine-tuning in optimizing language models for parallel computing code generation, paving the way for a new generation of automatic parallelization tools. The sources of this work are available at our GitHub MPIrigen repository: https://github.com/Scientific-Computing-Lab-NRCN/MPI-rigen

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Code completion models have made significant progress in recent years, yet current popular evaluation datasets, such as HumanEval and MBPP, predominantly focus on code completion tasks within a single file. This over-simplified setting falls short of representing the real-world software development scenario where repositories span multiple files with numerous cross-file dependencies, and accessing and understanding cross-file context is often required to complete the code correctly. To fill in this gap, we propose CrossCodeEval, a diverse and multilingual code completion benchmark that necessitates an in-depth cross-file contextual understanding to complete the code accurately. CrossCodeEval is built on a diverse set of real-world, open-sourced, permissively-licensed repositories in four popular programming languages: Python, Java, TypeScript, and C#. To create examples that strictly require cross-file context for accurate completion, we propose a straightforward yet efficient static-analysis-based approach to pinpoint the use of cross-file context within the current file. Extensive experiments on state-of-the-art code language models like CodeGen and StarCoder demonstrate that CrossCodeEval is extremely challenging when the relevant cross-file context is absent, and we see clear improvements when adding these context into the prompt. However, despite such improvements, the pinnacle of performance remains notably unattained even with the highest-performing model, indicating that CrossCodeEval is also capable of assessing model's capability in leveraging extensive context to make better code completion. Finally, we benchmarked various methods in retrieving cross-file context, and show that CrossCodeEval can also be used to measure the capability of code retrievers.

As the capabilities of code large language models (LLMs) continue to expand, their applications across diverse code intelligence domains are rapidly increasing. However, most existing datasets only evaluate limited application domains. To address this gap, we have developed a comprehensive code evaluation dataset FullStack Bench focusing on full-stack programming, which encompasses a wide range of application domains (e.g., basic programming, data analysis, software engineering, mathematics, and machine learning). Besides, to assess multilingual programming capabilities, in FullStack Bench, we design real-world instructions and corresponding unit test cases from 16 widely-used programming languages to reflect real-world usage scenarios rather than simple translations. Moreover, we also release an effective code sandbox execution tool (i.e., SandboxFusion) supporting various programming languages and packages to evaluate the performance of our FullStack Bench efficiently. Comprehensive experimental results on our FullStack Bench demonstrate the necessity and effectiveness of our FullStack Bench and SandboxFusion.