# The Aleph Moves Into a Pretrained Trunk: Relays, Registers, and the Two-Regime Dispatch Law **Autoregressive differentiation, part 2.** Sequel to [aleph-autoregressive-differentiation-ft1](https://huggingface.co/blog/AbstractPhil/aleph-autoregressive-differentiation-ft1) and closer of the arc that began with the [aleph-void keystone](https://huggingface.co/blog/AbstractPhil/geometric-vocabulary-patchwork-aleph-void). Code, ledgers, checkpoints, and per-experiment sub-articles: [`AbstractPhil/geolip-aleph-qwen`](https://huggingface.co/AbstractPhil/geolip-aleph-qwen). --- ## TL;DR Ft1 ended inside a bespoke byte-level bed: the aleph address as the sole parameterization of a next-byte distribution, certified structural prior, sign-code parity, the consumption law. This installment asks the question that bed could not: **does any of it survive contact with a real pretrained transformer?** We froze Qwen2.5-0.5B(-Instruct) — every trunk parameter, permanently — and built the whole program as adapters riding it. Nine experiments, six shipped packages in the new repo, two nights on one RTX 4090. Eight results: 1. **The relay retrofit works at 0.5B.** Aleph relay adapters after every frozen block: wikitext ppl 17.798 → 14.09, within 0.16 of a parameter-matched MLP adapter (13.93), at under 1% of trunk parameters, 2 seeds, replication spread <0.02. The ppl *ordering* inverted from the GPT-2 result (substrate-scoped), but the **gate mechanism replicated**: relay gates grow ~1.7× (0.047 → 0.081) while MLP gates shrink, on both substrates. And a stability asymmetry the means don't show: the wide-MLP control diverged to NaN in 1 of 2 seeds; across every relay variant in the campaign, divergences were **zero**. 2. **The certified consumer.** exp002's tournament settled the relay's internal structure: aleph addressing + a constellation *patchwork* consumer (`relay_pw`, ~230k params/block) — the first relay under 14 (13.997 mean, 2 seeds). The consumption law from ft1 held its shape in the new substrate: coverage beats concentration. 3. **Registers differentiate, and it is measurable on the sign-code surface.** Instruct-task training (grounded JSON extraction in three output registers) reduced grounding failures >10× (specialist 0.979/0.958 vs frozen 0.542, 2 seeds) — and exposed **register capture**: a single-register specialist answers *every* register in its own (perfect JSON, 0.0 task-validity elsewhere, both seeds). Multi-task training resolves it (all registers ≥0.875). The register probe — the gauge only the aleph relay has — showed instruct-trained stacks separating the registers ~2× a wikitext-trained stack at depth (inter−intra Hamming 0.22–0.30 vs 0.12–0.15 at L16/L23). 4. **Termination is a property of sample semantics, not adapter capacity.** Trained on packed 1024-token windows, the relay stack learned to write ~3,000-token grounded composite scenes *flawlessly* (0.0 malformed vs frozen 0.833) and never learned to **stop** (truncated 1.000; still 0.938 with the cap lifted to 3000 — true rows average 4,291 tokens, so packed windows almost never contain an ending). Row-aligned samples — each ends with the closing tag — fixed it completely: structural_ok 1.000 / 0.938, truncated 0.0, on 2 seeds. Packed streams train continuation; rows train the artifact. 5. **The two-regime dispatch law.** A dense signed aleph dispatch (no argmax, no top-k, no load-balancing loss — nothing selects) over frozen specialist stacks behaves in two regimes, decided by representational distance. At *register* distance the specialists are **passengers**: a control with random frozen stacks matched the real composite (0.979/0.979/1.0 vs 0.875/1.0/1.0) — the monolith-capacity trainable anchor carries everything. At *domain* distance (stories vs math vs extraction) the specialists are **load-bearing and cleanly decoupled**: story prompts put 0.82 of shadow-winner mass on the story anchor, and disabling it degrades stories while math stays perfect — in both directions. The register probe's separation numbers predict the regime in advance. (Each regime rests on 1 seed — a candidate law pending replication.) 6. **The predictability principle.** The same training recipe taught held-out function evaluation (+25pt on unseen f(x) instances, 0.688 → 0.938) and failed to teach a checkable keyword constraint (0.083, exactly frozen level, despite training on compliant stories). The LM loss teaches exactly what target-token predictability demands: math answers are unpredictable without using the question; story tokens are predictable without reading the instruction. (exp006/exp007, 1 seed each.) 7. **A frozen text trunk can learn discrete image denoising.** CIFAR-10 as 256 fixed-palette tokens (nothing fitted), uniform-replacement corruption, causal denoising through one relay stack: beats the copy-the-corrupted-token baseline at every noise level (1 seed) — 0.527 vs 0.252 at t=0.75, 0.378 vs 0.002 at pure noise. Two honest halves ride along: greedy iterative decoding mode-collapsed to the all-dark modal image (diversity 0.0 — a decoding property, not a model property; stochastic sampling restored diversity 0.92 and image-like layouts), and class-conditionality is **not demonstrated** (conditional ≈ shuffled histograms). 8. **The family.** Five frozen specialists (three extraction registers, story, math) plus one trainable anchor under **one** dense signed dispatch: **eleven sub-competences at ~specialist level through a single routed model** — including math code-register correctness at 1.0, *above* the specialist's own 0.938, and a 3× lift on the stubborn keyword register. One model that extracts, narrates, and computes, with surgical domain-level decoupling (1 seed; replication is the named next rung). Every number above is asserted from a JSON ledger by a `build_results.py` shipped in its package; every package is standalone-reproducible from inside its folder. --- ## 1. Why leave the bespoke beds The differentiation line (exp011–exp021, now on hold as a finished measurement program) produced laws but no artifact: enrichment lives in the aggregation channel; the address bottleneck is a prior, not a tax; memorization and generalization order inversely; durable memory needs a write-time-frozen key encoder. The honest assessment mid-program was that we were measuring a system we weren't building. The pivot: compose the certified components on a real pretrained substrate and see which laws are substrate properties and which were artifacts of tiny beds. The substrate is deliberately modest — Qwen2.5-0.5B, fp32, one consumer GPU — because the question is architectural, not scale-flexing: *what can a frozen trunk be taught through a geometric adapter surface alone?* ## 2. The bed Every experiment shares one skeleton. The trunk — Qwen2.5-0.5B(-Instruct) ([Qwen Team, 2024](https://arxiv.org/abs/2412.15115)) — loads frozen (`requires_grad=False`, asserted post-run: zero gradient ever reaches it). After every one of the 24 transformer blocks, an adapter reads the block's output and adds a gated residual. The lineage is the adapter/PEFT family ([Houlsby et al., 2019](https://arxiv.org/abs/1902.00751); [Hu et al., 2021](https://arxiv.org/abs/2106.09685)), and the start-silent gating discipline has good company — Flamingo's tanh-gated cross-attention ([Alayrac et al., 2022](https://arxiv.org/abs/2204.14198)), ControlNet's zero convolutions ([Zhang et al., 2023](https://arxiv.org/abs/2302.05543)), LLaMA-Adapter's zero-init attention ([Zhang et al., 2023b](https://arxiv.org/abs/2303.16199)) — but the adapter *body* here is not a bottleneck MLP. The certified adapter is `relay_pw`: a projection into 16 four-dimensional slots, each slot addressed by the aleph closed form ``` M̂ = Σₖ sinh(uₖ)·Aₖ / Σₖ cosh(uₖ), uₖ = cos(x, Aₖ)/τ ``` over 64 oriented half-axes — the addressing object whose code-verified core is the [keystone article](https://huggingface.co/blog/AbstractPhil/geometric-vocabulary-patchwork-aleph-void), inheriting the attractor geometry and binding constant of [structural attractors](https://huggingface.co/blog/AbstractPhil/structural-attractors-in-latent-geometry) — followed by a patchwork consumer (SquaredReLU expansion, LayerNorm, zero-init output; the constellation lineage from [the diffusion-bottleneck article](https://huggingface.co/blog/AbstractPhil/constellation-diffusion-bottleneck)) entering through a gate initialized at −3.0 — adapters start nearly silent and must earn amplitude. ~230k parameters per block, ~5.5M per stack, ~1% of the trunk. Pure Adam, lr 1e-3, weight decay 0 (the optimizer discipline certified in [geometric memory ft3](https://huggingface.co/blog/AbstractPhil/geometric-memory-ft3): weight decay destroys the geometric harmonic — the geometry is the regularization). Perplexity work runs on wikitext-103 ([Merity et al., 2016](https://arxiv.org/abs/1609.07843)). No selector appears anywhere in any forward pass in this program; where multiple anchors must be mixed (exp005/exp009), the mixture is the dense signed dispatch described in §6, and the per-token winner is logged **read-only**. The discrete surface comes free: each slot's winner half-axis and orientation is a sign code, cacheable per token per layer. The register probe (§4) and the two-regime prediction (§6) both read this surface; a parameter-matched MLP adapter has nothing comparable — which is the practical argument for the aleph design beyond raw ppl. ## 3. Retrofit and refinement (exp001, exp002) exp001 asked the bare question: do relays retrofit? Five runs, two seeds: frozen 17.798 → relay 14.09; the parameter-matched MLP control 13.93. The GPT-2 ordering (relays beat MLPs) inverted here — worth stating plainly: **which adapter wins on ppl is substrate-scoped.** What replicated across substrates is the mechanism: relay gates grow ~1.7× while MLP gates shrink, and relay training never diverged where the wide MLP control lost 1 of 2 seeds to NaN. exp002 ran the architecture tournament (12 runs): multi-tau strobing, depth, width, ordering, consumers. Verdicts: `relay_pw` certified at 13.997 (first sub-14 relay, 2 seeds); width and strobe saturated; **coverage beats concentration** (spreading the budget across all 24 blocks beat concentrating it on the deepest 12, −0.48 ppl) — the consumption law's signature, surviving translation from bespoke byte-beds to a pretrained trunk; ordering budget-stable at 6k steps. ## 4. Registers and the discrete gauge (exp003) The instrument: 22k COCO captions ([Lin et al., 2014](https://arxiv.org/abs/1405.0312)) rendered through three structurally distinct output registers (grounded literal extraction / bracketed generics / positional placeholders) in native messages+tools format, caption-hash holdout, validators re-implemented from the dataset's own rules ([json-coco-format](https://huggingface.co/datasets/AbstractPhil/json-coco-format)). Hallucination — ungrounded content in generation, the standing failure mode surveyed in [Ji et al., 2023](https://arxiv.org/abs/2202.03629) — is measured here as a per-leaf grounding rate, and the reduction is quantified: the task_1 specialist grounds 0.979/0.958 of held-out extractions vs frozen 0.542 — grounding failures cut from 46% to 2–4%. Register capture, discovered: that same specialist answers *every* register in its own — perfect JSON shape, 0.0 task-validity — both seeds, with cross-register ppl damage. Multi-task training resolves capture (all registers ≥0.875). The probe is the part that only exists because the adapter is an aleph: sign-codes collected at four depths for the same captions under four registers; separation = inter-register minus intra-register Hamming. Instruct-trained stacks: 0.22–0.30 at L16/L23. Wikitext-trained stack, same architecture: 0.12–0.15. Instruct training *reorganizes* the discrete surface into differentiated registers — and this gauge is what later predicts dispatch behavior (§6). Instrument honesty, ledgered: the first validity pass used a non-greedy regex that truncated nested tool-call JSON — a *perfect* generation scored 0. Caught via a ppl-1.05-but-validity-0 contradiction; v2 validators re-judged every checkpoint post-hoc; both generations of rows ship in the ledger. ## 5. Termination is sample semantics (exp004) Scaling the register from ~200-token outputs to multi-kilotoken composite scenes produced the cleanest process finding of the program. The targets are fused multi-entity JSON from a deterministic-first vision pipeline — Grounding DINO ([Liu et al., 2023](https://arxiv.org/abs/2303.05499)), SAM ([Kirillov et al., 2023](https://arxiv.org/abs/2304.02643)), Depth Anything V2 ([Yang et al., 2024](https://arxiv.org/abs/2406.09414)), SigLIP ([Zhai et al., 2023](https://arxiv.org/abs/2303.15343)) fused into one grounded scene per image ([qwen-deepfashion-fused](https://huggingface.co/datasets/AbstractPhil/qwen-deepfashion-fused), [qwen-synth-characters-fused](https://huggingface.co/datasets/AbstractPhil/qwen-synth-characters-fused)); polygons excluded. Act 1 (packed 1024-token windows): the relay learned the composite register flawlessly — json_error 0.0 vs frozen 0.833, held-out ppl 4.063 → 1.427 — and truncated **every single generation** at the 1400 cap. Lifting the cap to 3000 recovered almost nothing (0.938 still unclosed), and the one scene that closed was structurally near-perfect. The v2 cache then measured what the v1 estimate had missed: true rendered rows average **4,291 tokens** (max 9,032). A packed 1024 window almost never contains an ending; stopping was never in the gradient. (Sequence packing is standard practice for throughput — [Krell et al., 2021](https://arxiv.org/abs/2107.02027) — but its *semantics* for what a small adapter can learn about document boundaries is exactly what this gate measured.) Act 2 (row-aligned SFT: every sample is one complete conversation ending with the closing tag, ≤4096 tokens, over-cap rows skipped and counted): structural_ok **1.000** (16/16) on seed 0, 0.938 on seed 1 (one malformed JSON; truncation 0.0 on both). The identical architecture that scored truncated 1.000 under packed windows scores ok 1.000 under rows. For long structured emission through frozen-trunk adapters, **window semantics are part of the task definition.** The caveats ship asserted: entity over-emission (1.667/1.311× the reference — the model invents plausible extras) and weak caption-grounding. Construction is solved; *faithfulness* is the next line. An ops law fell out too, the expensive way: at 4096-token rows with an adapter after every block, fp32 activations plus the seq×vocab logits exceed 24GB — and the Windows driver's sysmem-fallback **silently** spills to shared memory instead of OOMing (42.8GB observed; steps at PCIe speed; the tell is ~100W draw at "100% util"). Gradient checkpointing + chunked cross-entropy + a hard memory-fraction cap: 66GB spill → 8.8GB peak at 1.03s/step. The shipped beds print peak memory at step 50. ## 6. The dispatch, its confound, and the two-regime law (exp005, exp009) Mixture-of-experts, in its standard form, is a *selector*: a gate picks top-k experts and a load-balancing loss fights the collapse that selection invites ([Shazeer et al., 2017](https://arxiv.org/abs/1701.06538); [Fedus et al., 2021](https://arxiv.org/abs/2101.03961)). This program's standing failure class forbids exactly that — comparative selectors near the aleph collapse its paths — so the question is asked doctrine-legally, closest in spirit to fully dense soft mixtures ([Puigcerver et al., 2023](https://arxiv.org/abs/2308.00951)) but with signed weights and a geometric key: anchors are whole frozen relay stacks; per block, mixing weights are `wₖ = sinh(uₖ)/Σⱼcosh(uⱼ)` with `u = cos(Px, C)/τ`, key projection **frozen at init** (the write-time-frozen key law from the [predecessor line's exp021](https://huggingface.co/AbstractPhil/geolip-aleph-differentiation), satisfied by construction), codebook trainable, weights dense and signed. No selection event exists, and no load-balancing loss — nothing pushes usage toward uniformity except the task mixture itself; the argmax|u| "shadow winner" is logged read-only. exp005 (three frozen register specialists + one trainable anchor, 1 seed): the routed composite serves all registers (0.875/1.0/1.0), usage stays dense (perplexity 3.74–3.91 of 4, all paths alive — no collapse), the shadow winner leans to the domain anchor. The headline died in review before it shipped: the trainable anchor is itself monolith-capacity (5,524,008 params ≈ the multi-task stack's 5,517,864) trained on all registers interleaved — the exact recipe that already resolved capture — and the composite's numbers equal that monolith's seed-0 numbers exactly. So the package shipped with its own control: specialists replaced by **random** frozen stacks. The control *matched* (0.979/0.979/1.0). At register distance, the specialists were passengers; removal of one even ticked its neighbors up. exp009 (1 seed) re-ran the architecture where the anchors are far apart: three extraction registers + a story anchor (four request registers) + a math anchor (four ask-registers), five frozen stacks + one trainable, one dispatch. Eleven sub-competences through one model: extraction 0.854/1.0/1.0; stories 1.0 on continuation/instruct/JSON; math perfect on all four registers including code at 1.0 — above its own specialist. Usage concentrated *without a selector*: story prompts 0.820 on the story anchor, math 0.508 on math, extraction registers blended. And the decouple tests are surgical in both directions: story anchor off → stories fall (instruct 1.0 → 0.667) while math stays perfect everywhere; math anchor off → math degrades (code 1.0 → 0.75) while stories hold untouched. Together: **whether a frozen anchor carries load or rides along is a function of representational separation — and the sign-code register probe measures that separation before you ever build the dispatch.** Registers (sep 0.2–0.3) blend; domains (sep 0.35–0.5) specialize. The MoE design variable is not the gate; it is the distance between what the anchors know. Both regimes stand on 1 seed each — a candidate law, not yet replicated. ## 7. The predictability principle (exp006, exp007) Two anchors (1 seed each) trained by the identical recipe, judged by checkable constraints: - **Story anchor** (TinyStories, [Eldan & Li, 2023](https://arxiv.org/abs/2305.07759); four request methods): continuation, instruct, and JSON registers all reach 1.0 validity (frozen: 0.667/0.833/0.833). The keyword register — "write a story using these three words," fully checkable — stays at **0.083, exactly frozen level**, despite every training story containing its keywords. - **Math anchor** (synthetic, four ask-methods, ground truth computable): format locks to 1.0 everywhere (frozen NL format: 0.312), correctness never degrades, and held-out f(x) evaluation improves 0.688 → 0.938 (audited: 5 of 16 judged code problems have zero recall channel — unseen coefficient combinations). Same trunk, same adapter, same optimizer, same steps. The difference is in the targets: an arithmetic answer is unpredictable without using the question, so the loss routes computation through the adapter; a story's tokens are predictable without reading the instruction, so the constraint is ignorable and stays unlearned. **Teacher forcing teaches what target-token predictability demands — nothing more.** This is teacher forcing's known blind spot ([Williams & Zipser, 1989](https://doi.org/10.1162/neco.1989.1.2.270); the train/inference mismatch that motivated scheduled sampling, [Bengio et al., 2015](https://arxiv.org/abs/1506.03099)) meeting shortcut learning ([Geirhos et al., 2020](https://arxiv.org/abs/2004.07780)) in its cleanest form: the shortcut is *ignoring the instruction entirely*, and a matched-everything pair of tasks makes it measurable. (The family's mixture pressure later tripled keyword compliance to 0.25 — real but far from solved; a keyword-first target format is the recorded follow-on.) ## 8. Images as tokens through a text trunk (exp008) The most speculative directive — *a CIFAR-10 diffusion model in tokens through the gated adapter, if possible* — gets a split verdict (1 seed), all halves ledgered. The reference points: images as autoregressive token streams is iGPT ([Chen et al., 2020](https://proceedings.mlr.press/v119/chen20s.html)); discrete diffusion over token corruption is D3PM ([Austin et al., 2021](https://arxiv.org/abs/2107.03006)) and its masked-parallel cousin MaskGIT ([Chang et al., 2022](https://arxiv.org/abs/2202.04200)); and frozen language models acquiring non-text competence through small trainable surfaces is the Frozen/universal-computation line ([Tsimpoukelli et al., 2021](https://arxiv.org/abs/2106.13884); [Lu et al., 2021](https://arxiv.org/abs/2103.05247)). This bed sits at their intersection with one deliberate deviation: **no fitted tokenizer** — where iGPT used k-means color clusters and the VQ family learns its codebook ([van den Oord et al., 2017](https://arxiv.org/abs/1711.00937)), this program's failure class forbids fitted quantizers near the aleph, so the palette is fixed arithmetic: CIFAR-10 ([Krizhevsky, 2009](https://www.cs.toronto.edu/~kriz/learning-features-2009-TR.pdf)) at 16×16, 8 uniform levels per channel, palette id = 512 fixed vocabulary slots. Corruption replaces tokens uniformly at rate t; the training sample is `[class, level, corrupted×256, SEP, clean×256]` with loss on the clean half; inference walks the noise schedule down. The denoiser is real: teacher-forced reconstruction beats the identity baseline (copy the corrupted token: (1−t)+t/512) at every level — 0.840 vs 0.751 (t=0.25), 0.689 vs 0.501, 0.527 vs 0.252, and 0.378 vs 0.002 at t=1.0, where the corrupted view carries nothing and reconstruction comes entirely from learned position/smoothness/class priors. The frozen trunk's own zero-shot 0.259 at t=1.0 is a finding in itself — an emergent copy-local-context strategy. The two honest halves: greedy argmax in the iterative refinement loop mode-collapsed to a single all-dark image (diversity 0.0; conditional == shuffled to four decimals) — deterministic decoding in an iterative denoiser collapses to the global mode, the visual sibling of greedy text degeneration ([Holtzman et al., 2019](https://arxiv.org/abs/1904.09751)), and a *decoding* property: multinomial sampling from the same checkpoint restores diversity 0.92 — horizon lines, sky/ground splits, coherent palettes in the shipped grids. And class-conditionality is **not demonstrated**: conditional histogram distance ≈ shuffled. A frozen text trunk + 5.5M adapter learned image *statistics*, not yet image *classes*. ## 9. What ships, what's next Six packages (`exp004_composite` through `exp009_family`), each with scrubbed standalone code, a self-asserting results builder run green before upload, the full JSON ledger including every failed act and instrument bug, checkpoints, and a sub-article. Two nights, one 4090, ~60 logged GPU runs. The recorded next rungs: the family with the image-token anchor joined; sub-capacity trainable anchors (make specialists load-bearing at register distance); keyword-first targets for constraint binding; faithfulness training against entity over-emission; and the geofractal tower port — the family's anchors are homogeneous relay stacks, which is exactly what the tower machinery wants. The aleph started this arc as a codebook differentiation device in toy reconstruction beds. It ends this installment as the addressing surface of a composable adapter family on a frozen pretrained transformer — with its discrete sign-code gauge doing real predictive work that a parameter-matched MLP cannot offer: telling you, before you build the mixture, whether your experts will carry or coast. --- ## This program's corpus The aleph line is self-published and cumulative; the installments this article stands on directly: - [aleph-autoregressive-differentiation-ft1](https://huggingface.co/blog/AbstractPhil/aleph-autoregressive-differentiation-ft1) — the predecessor: bottleneck prior (7/7), the consumption law and the comparative-selector pathology this program's dispatch design obeys, sign-code parity, shell transit, projective objective-independence. - [geometric-vocabulary-patchwork-aleph-void](https://huggingface.co/blog/AbstractPhil/geometric-vocabulary-patchwork-aleph-void) — the keystone: the aleph closed form, code-verified. - [structural-attractors-in-latent-geometry](https://huggingface.co/blog/AbstractPhil/structural-attractors-in-latent-geometry) — the binding constant and the attractor geometry the addressing objects inherit. - [constellation-diffusion-bottleneck](https://huggingface.co/blog/AbstractPhil/constellation-diffusion-bottleneck) — the 16s constellation system the patchwork consumer descends from. - [geometric-tri-band-ft2](https://huggingface.co/blog/AbstractPhil/geometric-tri-band-ft2) — the projective codebook law, carried here unchanged. - [geometric-memory-ft3](https://huggingface.co/blog/AbstractPhil/geometric-memory-ft3) — the optimizer discipline (pure Adam, wd 0): weight decay destroys the geometric harmonic; the geometry is the regularization. - [geolip-svae-transformer-ft1](https://huggingface.co/blog/AbstractPhil/geolip-svae-transformer-ft1) — the two-year differentiation survivor: reconstruction-cultivated sign codes, the origin of "read the signs, not the probabilities." Repositories: [geolip-aleph-qwen](https://huggingface.co/AbstractPhil/geolip-aleph-qwen) (this line: code, ledgers, checkpoints, per-experiment sub-articles) and [geolip-aleph-differentiation](https://huggingface.co/AbstractPhil/geolip-aleph-differentiation) (the measurement program, exp011–exp021). Datasets: [json-coco-format](https://huggingface.co/datasets/AbstractPhil/json-coco-format), [qwen-deepfashion-fused](https://huggingface.co/datasets/AbstractPhil/qwen-deepfashion-fused), [qwen-synth-characters-fused](https://huggingface.co/datasets/AbstractPhil/qwen-synth-characters-fused). ## References - Alayrac, J.-B., et al. (2022). *Flamingo: a Visual Language Model for Few-Shot Learning.* [arXiv:2204.14198](https://arxiv.org/abs/2204.14198) - Austin, J., Johnson, D. D., Ho, J., Tarlow, D., & van den Berg, R. (2021). *Structured Denoising Diffusion Models in Discrete State-Spaces.* [arXiv:2107.03006](https://arxiv.org/abs/2107.03006) - Bengio, S., Vinyals, O., Jaitly, N., & Shazeer, N. (2015). *Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks.* [arXiv:1506.03099](https://arxiv.org/abs/1506.03099) - Chang, H., Zhang, H., Jiang, L., Liu, C., & Freeman, W. T. (2022). *MaskGIT: Masked Generative Image Transformer.* [arXiv:2202.04200](https://arxiv.org/abs/2202.04200) - Chen, M., et al. (2020). *Generative Pretraining from Pixels.* ICML 2020. [PMLR 119](https://proceedings.mlr.press/v119/chen20s.html) - Eldan, R., & Li, Y. (2023). *TinyStories: How Small Can Language Models Be and Still Speak Coherent English?* [arXiv:2305.07759](https://arxiv.org/abs/2305.07759) - Fedus, W., Zoph, B., & Shazeer, N. 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