Roll the dice & look before you leap: Going beyond the creative limits of next-token prediction

Aditi Raghunathan; Charles Ding; Chen Henry Wu; Vaishnavh Nagarajan

REVIEW 3 major objections 4 minor 4 cited by

Roll the dice & look before you leap: Going beyond the creative limits of next-token prediction

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Multi-token training beats next-token prediction on four minimal creativity tasks.

desk verdict Well-run empirical study: multi-token training beats NTP on four synthetic creativity tasks and seed-conditioning is a real surprise, but the paper overreaches by asserting a transfer guarantee its own limitations undercut. read the letter →

arxiv 2504.15266 v4 pith:OBR2JOXC submitted 2025-04-21 cs.LG cs.AIcs.CL

Vaishnavh Nagarajan , Chen Henry Wu , Charles Ding , Aditi Raghunathan This is my paper · ORCID

classification cs.LGcs.AIcs.CL

keywords next-tokenpredictionteacherlesstrainingdiscretediffusionalgorithmiccreativityseed-conditioningopen-endedgenerationcreativeleap-of-thoughtmemorization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Next-token prediction is the standard training objective for language models, but this paper argues it is myopic for open-ended creative generation. On a new suite of four minimal algorithmic tasks, multi-token training objectives consistently beat next-token training at producing outputs that are coherent, unique, and absent from the training set. Two of the tasks, sibling discovery and triangle discovery, require recalling and combining facts stored in a graph within the model's weights; the other two, circle and line construction, require inventing adjacency lists that secretly resolve to a circle or a line. The paper also finds that for Transformers, conditioning on a random meaningless prefix (seed-conditioning) with greedy decoding matches or beats temperature sampling. If these results hold, they give concrete evidence that both the next-token loss and output-level temperature are replaceable design choices for open-ended generation.

What carries the argument

The machinery is a suite of minimal generative tasks in which coherence is a global property of the whole string, paired with a metric called algorithmic creativity that counts the fraction of generated strings that are coherent, unique, and not in the training set. Two combinational tasks store a knowledge graph in the model's weights: sibling discovery asks for a parent node whose two revealed siblings both belong to it, and triangle discovery asks for three nodes whose pairwise edges all exist. Two exploratory tasks ask for an edge list that can be rearranged, under some permutation, into a circle or a line graph. The argument rides on a mechanism the authors call the Clever Hans cheat: a next-token model can predict late tokens from earlier ones without learning the latent plan, and the simplicity bias of gradient training makes that shortcut irresistible, after which gradient starvation removes any push to learn the plan. Teacherless training and diffusion are the two multi-token alternatives used to break that shortcut.

What would settle it

Train a next-token Transformer on the same task families with a token order that reveals the hidden plan early (parent-first for sibling discovery, or an explicit permutation token for circle and line construction) under matched data, compute, and decoding; if algorithmic creativity reaches or exceeds the multi-token models, the gap is an artifact of token ordering rather than next-token learning itself. Alternatively, run the same comparison on real knowledge graphs with semantic nodes: if the multi-token advantage disappears, the transfer premise fails.

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Extended reading notes

Core claim

The paper's central claim is that creative leap-of-thought tasks are misaligned with next-token learning. In each task, the most natural generative rule is to settle a random latent plan first — the hidden parent node, the edges of a triangle, or the resolving permutation of an adjacency list — while the surface token order either reveals that plan last or not at all. A next-token learner can shortcut the plan by predicting late tokens from early ones, a "Clever Hans cheat" that starves the gradient signal for the latent structure and pushes the model toward memorizing its training set. Multi-token objectives, by contrast, force the model to commit to all tokens at once: teacherless training predicts every response token from the prompt alone, and discrete diffusion refines a fully corrupted sequence. The result is the paper's headline finding: in all four tasks, multi-token training attains higher algorithmic creativity than next-token training, and for Transformers, seed-conditioning with greedy decoding is as creative as temperature sampling.

Load-bearing premise

The load-bearing premise is that these four minimal tasks faithfully capture the computational core of real creative leaps, so that next-token failure here predicts failure in real open-ended tasks; the paper asserts the one-way transfer without demonstrating it.

Editorial extensions

If this is right

Finetuning a transformer with a multi-token component should raise the diversity and originality of open-ended generations at fixed model size and compute, not just correctness.
Seed-conditioning gives practitioners a cheap diversity knob: train with arbitrary random prefixes, then decode greedily without tuning temperature.
Proposals that try to fix next-token prediction by reordering tokens or predicting infills will not help on the permutation-invariant tasks, since no token order makes the hidden plan local.
Verbatim memorization in open-ended generation is partly a symptom of fitting late tokens via local shortcuts, so multi-token objectives are a direct way to curb memorization.
The positive, if small, diversity gain at fixed ROUGE on XSUM summarization suggests the effect extends beyond toy tasks to realistic generation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The authors' own decomposition suggests seed-conditioning buys diversity while multi-token training buys both diversity and reduced memorization; an obvious extension is to combine them and measure whether the gains add.
If the Clever Hans mechanism is the true cause, then a testable prediction follows: revealing the plan token early, or hiding the sibling evidence, should shrink the next-token versus multi-token gap.
The paper asserts that failure on these minimal tasks guarantees failure on more complex ones, but that transfer claim is not demonstrated; scaling the same tasks to semantically meaningful knowledge graphs would test it directly.
Seed-conditioning helps Transformers but not the diffusion model, so the noise-injection benefit is tied to autoregressive decoding; a diffusion analog would be conditioning on random initial latent states rather than a token prefix.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read it. The empirical core is solid and the seed-conditioning result is genuinely worth knowing. On four synthetic tasks that require global coherence (sibling/triangle discovery, circle/line construction), next-token-trained Gemma 2B is clearly worse at generating coherent, original, diverse strings than teacherless multi-token training, and a small diffusion model beats a comparable GPT-2 on three of the four. The tasks are well-designed, the Eq. 1 metric is transparent, and the paper does the right ablations—LRs picked to favor NTP, a seed-memorization check (Fig 8), a top-K confound for GPT-2, and a decomposition of creativity into diversity vs. memorization.

The surprise is seed-conditioning: a random prefix, paired arbitrarily with each training example, makes a greedy-decoding Transformer produce diverse outputs that match or exceed temperature sampling. That is a real empirical phenomenon, even though it is not explained and does not transfer to diffusion.

The soft spot is not the measurements, it is the scope of the claim. Section 6.1 says failure on minimal tasks 'guarantees failure in more complex tasks,' and the title/abstract push 'the creative limits of next-token prediction' as a general result. That monotonicity is asserted, not shown, and Section 6.2.2—where they concede real creative tasks are out-of-distribution—undercuts it. A complex task can offer different surface statistics, scratchpads, or richer data that sidestep the specific myopia. So the honest reading is: NTP is measurably myopic on these four controlled benchmarks, and that is a useful benchmark result, not a proven general limit.

Minor caveats, all disclosed: teacherless training shows no gain over NTP on the small models, and the seed-conditioning edge over temperature is partly contingent on top-K in some GPT-2 settings.

Who it's for: people working on multi-token objectives, diversity in generation, or best-of-N exploration. I'd bring it to a reading group; I'd cite it. It deserves a serious referee; send it out, but ask the authors to reframe the conclusion as a benchmark and an open phenomenon rather than a limit theorem.

Referee Report

3 major / 4 minor

Summary. The paper introduces four minimal algorithmic tasks (Sibling Discovery, Triangle Discovery, Circle Construction, Line Construction) that are intended as controlled abstractions of open-ended creative tasks, and a quantitative metric called algorithmic creativity (Eq. 1) that rewards coherent, original, and unique generations. Across these tasks, the authors compare standard next-token prediction (NTP) with multi-token objectives: teacherless training on a Gemma 2B model and discrete diffusion (SEDD) on smaller models. They report that multi-token training improves algorithmic creativity on the Gemma 2B model across all four tasks and reduces memorization, while diffusion improves creativity in three of four small-model tasks. They also introduce seed-conditioning, where an arbitrary random prefix is used at training and inference, and report that it induces diversity even under greedy decoding, performing comparably to or better than temperature sampling in several settings. The paper argues that next-token learning is myopic in these tasks and that no token ordering is friendly to NTP in three of the four tasks, extending prior work on the path-star problem.

Significance. If the results hold, the paper provides a clean, controllable test-bed for studying creative generation and supplies new empirical evidence that multi-token objectives can improve originality and diversity relative to NTP, going beyond the correctness-focused path-star result of Bachmann and Nagarajan. The strengths of the paper include the four well-specified tasks with objective coherence conditions, the seed-memorization control in Fig. 8 that addresses a capacity-control confound, extensive sensitivity analyses across hyperparameters and dataset sizes, and a partly released codebase. The main significance, however, depends on a transfer claim from these minimal tasks to general creative limits of next-token prediction, and that claim is not established by the experiments as presented.

major comments (3)

[Section 6.1, Limitation 1; Section 6.2, Limitation 2; Abstract] The paper's central conclusion about 'the creative limits of next-token prediction' rests on the statement in Section 6.1, Limitation 1, that 'failure here guarantees failure in more complex tasks.' This monotonicity claim is load-bearing but is asserted rather than demonstrated, and the paper's own Section 6.2, Limitation 2, concedes that many real-world creative tasks are 'out-of-distribution' in nature, which the minimal tasks deliberately do not capture. An in-distribution failure on a minimal task does not logically imply failure on an out-of-distribution complex task, because a more complex task can offer additional context, in-context reasoning, or alternative strategies that let an NTP model bypass the specific myopia diagnosed in these four benchmarks. The authors should either provide evidence for the transfer claim, for example by studying a family of tasks of increasing complexity and showing that the NTP-vs-MTP gap persists, or explicitly reframe the contribution as a finding about these minimal algorithmic tasks.
[Section 4, Figs. 3-6] The main quantitative claims, such as the 'nearly a 5x factor' improvement for the discovery datasets and the statement that seed-conditioning 'results in algorithmic creativity comparable to temperature sampling,' are presented without error bars or per-run variability, despite the text stating that results are averaged over 4 runs. This makes it difficult to assess whether the observed differences are stable across seeds or training runs, particularly in the small-model comparisons where teacherless training shows no gain (Fig. 4) and where the seed-conditioning advantage is contingent on top-K sampling in Sibling Discovery and Triangle Discovery (Section 6.1, Limitation 6a). The authors should add error bars, confidence intervals, or per-run values to the main figures, or report statistical tests for the key comparisons.
[Abstract; Section 4.1; Section 6.1, Limitation 6a] The abstract claims that 'multi-token approaches, namely teacherless training and diffusion models, comparatively excel in producing diverse and original output' and that seed-conditioning 'works surprisingly as well as temperature sampling.' These statements are broader than the evidence reported in the paper: teacherless training shows no gains on the smaller GPT-2 model, diffusion is mildly worse than NTP on Sibling Discovery in that setting, and the seed-conditioning advantage does not appear for Sibling Discovery on GPT-2 and is contingent on top-K sampling for Sibling Discovery and Triangle Discovery (Section 6.1, Limitation 6a). The claims should be qualified to the specific model sizes and tasks in which the effect is observed, or the paper should provide a meta-analysis of when the advantage appears and when it does not.

minor comments (4)

[Eq. (1)] The subscript N in the metric \hat{cr}_N(T) is never defined in the main text; please define N or remove the subscript.
[Section 4.1] There is a typo in 'parametersGPT-2 (86M)' which should read 'parameters GPT-2 (86M)'.
[Appendix J] The sentence 'Likewise models like GPT4 and Claude currently underperform...' and the nearby discussion of Walsh et al. lack a full citation marker for the Walsh et al. work; please add the citation.
[Figs. 18-20] The x-axis labels such as 'seed10 greedy' and 'null temp5.0' are long and overlapping; consider rotating the labels, abbreviating the conditions, or using a grouped bar layout to improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the multi-token vs. next-token comparisons are self-contained empirical benchmarks, and the self-citation to B&N'24 is not load-bearing.

full rationale

The paper's central comparisons are not circular: the four tasks (Sibling Discovery, Triangle Discovery, Circle Construction, Line Construction) are fixed, external benchmarks whose coherence conditions are defined independently of any model; the algorithmic creativity metric (Eq. 1) is defined once and applied uniformly to all training objectives; and no constant is fitted from the NTP-versus-MTP gap to produce that gap. The teacherless and diffusion results are measured on unseen test-time samples, with memorized and duplicated generations excluded, and the seed-memorization control in Fig. 8 addresses the capacity-control confound. The only notable self-citation is to Bachmann & Nagarajan (2024) for the 'Clever Hans cheat' concept and the path-star impossibility result, but the present paper's data-inefficiency claim is supported by its own experiments (Figs. 3-4, 12, 22, and the token-reordering study in B.4), so the self-citation is illustrative rather than load-bearing. Section 6.1's assertion that 'failure here guarantees failure in more complex tasks' is an unsupported monotonicity and transfer claim, and Section 6.2.2 concedes that many real-world tasks are 'out-of-distribution' in nature; however, overclaiming scope is a correctness concern, not circularity, because the minimal-task results do not reduce by definition to that guarantee. No equation in the paper defines a predicted quantity in terms of the input that supposedly produces it, so no circular step can be exhibited.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claims rest on the tasks being a valid abstraction of creativity and on the i.i.d. generative setting. The paper provides sensitivity analyses for most experimental hyperparameters, but the transfer assumption from synthetic to real tasks is not validated.

free parameters (3)

Seed length = 10 (default)
Random prefix length used in seed-conditioning. Sensitivity analysis shows longer seeds improve creativity, but the qualitative claim holds across lengths.
Weight on multi-token objective = 0.5 to 0.75
Weight given to the teacherless objective in the hybrid loss. Results are robust across weights according to Figure 13, so the exact value is not load-bearing for the central claim.
Training set size per task = 50k/15k/10k/10k
Sizes used for Sibling, Triangle, Circle, and Line tasks. Sensitivity analysis in Figure 11 shows the gap persists across sizes, so the exact sizes are not fitted to produce the claimed effect.

assumptions (3)

domain assumption Training data are i.i.d. samples from a uniform distribution over coherent strings.
The setup defines D as uniform over the support of the coherence function (Section 2.2), which underpins the algorithmic creativity metric.
ad hoc to paper These four tasks capture the computational core of real creative leaps.
The transferability of the conclusions to real-world tasks rests on this assumption, which the paper acknowledges is a caricature (Section 6.2).
domain assumption Gradient-descent-trained networks exhibit simplicity bias, causing 'Clever Hans' shortcuts.
The explanatory mechanism in Section 2.6 relies on Shah et al. (2020) and Pezeshki et al. (2021); this is a background assumption from the literature, not proven here.

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Pith. "Pith review of Roll the dice & look before you leap: Going beyond the creative limits of next-token prediction." pith.science (2026). https://pith.science/paper/OBR2JOXC

@misc{pith2026250415266,
  author       = {Pith},
  title        = {Pith review of: Roll the dice & look before you leap: Going beyond the creative limits of next-token prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OBR2JOXC}},
  note         = {Machine review of arXiv:2504.15266}
}

read the original abstract

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; multi-token approaches, namely teacherless training and diffusion models, comparatively excel in producing diverse and original output. Secondly, to elicit randomness without hurting coherence, we find that injecting noise at the input layer (dubbed seed-conditioning) works surprisingly as well as (and in some conditions, better than) 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 temperature sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

Figures

Figures reproduced from arXiv: 2504.15266 by the authors.

**Figure 1.** Minimal tasks inspired by combinational creativity: Skills like research, humor and analogies often require identifying novel multi-hop connections from known pair-wise relationships in a knowledge graph. For instance, creating the wordplay “What kind of shoes do spies wear? Sneakers.” requires searching over a semantic graph, and carefully planning a pair of words (shoes, spies) that lead to a mutual neighbor (s… view at source ↗

**Figure 2.** Minimal tasks inspired by exploratory creativity: Skills like designing problem sets, novel proteins and plots require devising patterns that can be resolved in novel ways through some general rules. Inspired by this, we design a task where during training, we expose the model to “adjacency lists” that implicitly resolve into a specific structure (a circle or a line graph) under some permutation. The model must inf… view at source ↗

**Figure 3.** Multi-token teacherless finetuning improves algorithmic creativity (top; Eq 1) and reduces memorization (bottom; fraction of generations seen during training) on our four openended algorithmic tasks for a Gemma v1 (2B) model. at the output — temperature sampling — we contrast this with injecting randomness into the model. Concretely, we study seed-conditioning, where we train and test with a random prefix string … view at source ↗

Figures from the paper (32 more)

**Figure 4.** Figure 4: Multi-token diffusion training improves algorithmic creativity (top; Eq 1) on three of our four open-ended tasks on GPT-2 (86M) and similarly-sized diffusion model, SEDD (90M). We report the best performance after tuning the sampling hyperparameters – temperature from …

**Figure 5.** Figure 5: Seed-conditioning significantly improves algorithmic creativity of both next- and multi-token prediction on Gemma v1 (2B) model. The X-axis labels denote the prefix (at training and inference) and the temperature (at inference). experiments on token-reordering and expe…

**Figure 7.** Figure 7: Multi-token training improves diversity scores for XSUM summarization for large GPT-2 models: We observe gaps in diversity for a fixed quality over the course of finetuning. 5. Discussion 5.1. Intuition for seed-conditioning Seed-conditioning produces non-trivial algor…

**Figure 8.** Figure 8: Even if multi-token prediction reduces memorization (on unseen seeds), it has enough capacity to memorize training data on the seen seeds (denoted by seed-memorization). Note that the best algorithmic creativity for NTP and MTP are achieved at step 10k and 40k, respect…

**Figure 9.** Figure 9: Minimal tasks inspired by combinational creativity: The in-weights graph represents the underlying knowledge graph used to generate the training data (not provided in-context). Based on our definition of algorithmic creativity in Eq. (1), generated samples that are inc…

**Figure 10.** Figure 10: Tasks inspired by exploratory creativity: The constructed graph visualizes the graph induced by the training or generated sample. Edge indices represent the order of edge appearing in the string. Based on our definition of algorithmic creativity in Eq. (1), generated …

**Figure 11.** Figure 11: for train set size, [PITH_FULL_IMAGE:figures/full_fig_p026_11.png]

**Figure 12.** Figure 12: Task complexity and algorithmic creativity for Gemma v1 (2B): Algorithmic creativity increases under multi-token prediction across (reasonable) variations in the dataset parameters (as described in §C). E.1. Varying sampling methods [PITH_FULL_IMAGE:figures/full_fig_…

**Figure 13.** Figure 13: Weight given to multi-token objective and algorithmic creativity for Gemma v1 (2B): Algorithmic creativity increases under multi-token prediction across various weights given to the multi-token component of the objective, barring some deviations for Line Construction.…

**Figure 14.** Figure 14: Weight given to multi-token objective and memorization score for Gemma v1 (2B): Memorization reduces under multitoken prediction across various weights given to the multi-token component of the objective. 5e-3 1e-3 5e-4 1e-4 5e-5 1e-5 Learning Rate 0.0 0.2 0.4 0.6 Cr…

**Figure 15.** Figure 15: Learning rate and algorithmic creativity for Gemma v1 (2B): Algorithmic creativity increases under multi-token prediction across various learning rates. 7500 25000 Num Train Steps 0.0 0.2 0.4 0.6 Creativity SiblingDiscovery 10000 30000 Num Train Steps 0.00 0.25 0.50 0…

**Figure 16.** Figure 16: Training steps and algorithmic creativity for Gemma v1 (2B): Algorithmic creativity under multi-token prediction across lengths of training. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_16.png]

**Figure 17.** Figure 17: Batch size and algorithmic creativity for Gemma v1 (2B): Algorithmic creativity increases under multi-token prediction across various batch sizes. Note that here batch size is effectively proportional to the model sequence length, since we pack multiple finetuning exa…

**Figure 18.** Figure 18: Algorithmic creativity under various sampling conditions for Gemma v1 (2B): Across all conditions, and in almost all datasets (with a few exceptions in Line Construction), multi-token prediction improves creativity. Furthermore, seed-conditioning achieves best algorit…

**Figure 19.** Figure 19: Memorization under various sampling conditions for Gemma v1 (2B): Barring a few conditions, the most prominent trend is that memorization reduces under multi-token prediction for various sampling conditions. Observe that the null and pause-conditioned models do produc…

**Figure 20.** Figure 20: Coherence under various sampling conditions for Gemma v1 (2B): Surprisingly, coherence of all models is high or at least noticeable, across various sampling conditions. This suggests that the low algorithmic creativity of the null-conditioned models in the previous pl…

**Figure 21.** Figure 21: Learning rates and algorithmic creativity for the SEDD (90M)model vs. GPT-2 (86M): MTP achieves higher algorithmic creativity than NTP when both are trained at their optimal learning rates. We use greedy decoding in this plot. F.2. Effect of seed length We provide an …

**Figure 22.** Figure 22: Task complexity and algorithmic creativity of SEDD (90M) model vs. GPT-2 (86M): MTP consistently outperforms NTP under varying task configurations, with some exceptions in the Line Constructionand Circle Constructiondatasets. We use greedy decoding in this plot. F.3. …

**Figure 23.** Figure 23: GPT-2 (86M) Transformer achieves higher algorithmic creativity with longer seeds (top): We report algorithmic creativity with seeds of length 4 and 10, with both NTP and teacherless MTP (with greedy decoding). We do not see gains of seed-conditioning when it comes to …

**Figure 24.** Figure 24: reports the algorithmic creativity scores of NTP vs teacherless MTP training with seed-conditioning and top-K sampling where K=50. NTP w/ top-k w/ seed Teacherless w/ top-k w/ seed 0.0 0.2 0.4 0.6 0.8 Creativity Sibling Discovery Temperature greedy temp0.5 temp1.0 tem…

**Figure 25.** Figure 25: Memorization scores for NTP vs teacherless MTP training with seed-conditioning + top-K sampling where K = 50. Training Objective Standard (Next-Token) Teacherless (Multi-Token) Diffusion-Absorb (Multi-Token) Diffusion-Uniform (Multi-Token) Edge rep 999 Edge rep 500 No…

**Figure 26.** Figure 26: Sensitivity to formatting of the sequence in Triangle Discovery: We find that all our small models perform equally poorly with a node-wise representation of the input sequence, whereas there was a stark difference in performance with the edge-wise representation. We u…

**Figure 27.** Figure 27: Seed conditioning improves creativity. “Best with seed” and “best without seed” stand for the best creativity score in each setting after we tune the sampling temperature from {0, 0.5, 1, 2}. decomposition using the Sibling Discovery task. Formally, we define the dive…

**Figure 28.** Figure 28: Ablations on GPT-2 (86M) for (1) NTP vs teacherless MTP training, (2) effect of seed conditioning, (3) effect of top-K, and (4) effect of temperature sampling of best algorithmic creativity. We see that seed-conditioning contributes to higher diversity but does little…

**Figure 29.** Figure 29: On a medium-sized (∼400M) model, multi-token diffusion training improves algorithmic creativity from Eq 1 (top) on our four open-ended algorithmic tasks. We use greedy decoding in this plot. 0 10k 20k 30k 40k Num Train Step 0.0 0.5 1.0 Creativity Diversity 0.04 0.02 0…

**Figure 30.** Figure 30: Algorithmic creativity and diversity are not necessarily correlated, exhibiting distinct dynamics: We find that NTP has a high diversity score through training, even higher than MTP. However, its algorithmic creativity reaches only a mediocre peak before descending, w…

**Figure 31.** Figure 31: Decomposition of algorithmic creativity for GPT-2 (86M) in Sibling Discovery: We report algorithmic creativity, diversity and memorization at the checkpoint of best algorithmic creativity. We see that seed-conditioning contributes to higher diversity but does not help…

**Figure 32.** Figure 32: Data scaling curve for algorithmic creativity and diversity: As we increase the training data (for a fixed underlying graph), the theoretically expected maximum algorithmic creativity decreases as expected, while the theoretically expected maximum diversity stays the …

**Figure 33.** Figure 33: Multi-Token Objective has no effect on diversity for smaller GPT models on XSUM. Training Objective: Standard (Next-Token) Teacherless (Multi-Token) 0.140 0.142 0.144 0.146 0.148 0.150 Quality (ROUGE) 0.940 0.942 0.944 0.946 0.948 0.950 0.952 0.954 Diversity (1 - Self…

**Figure 34.** Figure 34: Multi-Token Objective increases diversity for GPT-L and GPT-M but not for GPT-XL or GPT-S on CNN/DailyMail 39 [PITH_FULL_IMAGE:figures/full_fig_p039_34.png]

**Figure 35.** Figure 35: Seed-conditioning has no effect on diversity for GPT models on XSUM summarization with next-token prediction. Training Objective: Null (Multi-Token) Seed (Multi-Token) 0.14250.14500.14750.15000.15250.15500.15750.1600 ROUGE 0.930 0.935 0.940 0.945 0.950 0.955 0.960 Div…

**Figure 36.** Figure 36: Seed-conditioning has no effect on diversity for GPT models on XSUM summarization with multi-token prediction. J. More related works Empirical studies of creativity in LLMs. There is a long line of recent works that measure novelty and creativity of LLMs and LLM-assis…

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Word games: Some word games require identifying a set of words that simultaneously have pairwise relationships with each other. (a) For example, standard crosswords would require identifying sets of 4 or more words that have various simultaneous pairwise intersections in the letters used. (b) Devising “& Lit.” clues in cryptic crosswords are an altogether...

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and learnability (Malach, 2023; Wies et al., 2023) of autoregressive Transformers as long as there is a sufficiently long chain of thought. Multi-token training. While multi-token methods employ diverse strategies, a common feature is their reliance on objec- tives that capture dependencies across entire sequences. Representative examples include teacherl...

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

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This may require identifying two or more facts that together result in an implication that contradicts another fact

Discovering contradictions: Consider identifying non-trivial contradictions within (a large body) of knowledge (like a legal system, or a proof based on many lemmas, or the literature spanning many papers in a certain field). This may require identifying two or more facts that together result in an implication that contradicts another fact

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Discovering feedback loops: Fields like biology, ecology, climate science and economics may involve discovering non-trivial feedback loops. Unlike feedback loops where two events encourage each other, a non-trivial loop would be one where anEvent A encouragesEvent B, that in turn encouragesEvent C that in turn encouragesEvent A

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work page 2024

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Some assassin in Japan

Word games: Some word games require identifying a set of words that simultaneously have pairwise relationships with each other. (a) For example, standard crosswords would require identifying sets of 4 or more words that have various simultaneous pairwise intersections in the letters used. (b) Devising “& Lit.” clues in cryptic crosswords are an altogether...

work page arXiv 2018

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remarks on generalization

and learnability (Malach, 2023; Wies et al., 2023) of autoregressive Transformers as long as there is a sufficiently long chain of thought. Multi-token training. While multi-token methods employ diverse strategies, a common feature is their reliance on objec- tives that capture dependencies across entire sequences. Representative examples include teacherl...

work page 2024