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Reasoning Bias of Next Token Prediction Training

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Next-token prediction beats answer-only training on reasoning tasks because the extra tokens act as a regularizer.

desk verdict Solid empirical comparison of NTP vs CTP on reasoning benchmarks, but the noise-regularization mechanism is not established because the 'noise' tokens are informative reasoning content. read the letter →

arxiv 2502.02007 v2 pith:MJIHFUJ6 submitted 2025-02-04 cs.CL cs.LG

Pengxiao Lin , Zhongwang Zhang , Zhi-Qin John Xu This is my paper · ORCID
classification cs.CLcs.LG
keywords nexttokenpredictioncriticalreasoningbiasimplicitregularizationflatminimageneralizationrobustnessanchorfunction
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 (NTP) trains a model to predict every token in a sequence, while critical token prediction (CTP) trains it only on the answer tokens. This paper aims to show that, contrary to intuition, NTP produces better reasoning ability than CTP when both are trained from scratch on question-answer style reasoning data. The explanation offered is that the non-answer tokens act as noise, and this noise regularizes the training dynamics, steering the model toward flatter loss minima and away from memorizing surface patterns. The paper further claims this makes NTP the better objective for pretraining, while CTP is the better choice for finetuning, where the noise no longer helps. A sympathetic reader would care because the result challenges the idea that focusing a model's loss on the answer is the most direct way to teach reasoning.

What carries the argument

The load-bearing object is the decomposition of the next-token-prediction loss into the critical-token loss plus a residual 'noise loss' on all other positions. With the critical token last, the NTP loss averages a cross-entropy term over every position, while the CTP loss keeps only the final term. The paper argues that the noise loss acts like gradient noise during optimization, creating a two-stage learning process (a 'flattening' stage that learns the sequence distribution, then a 'fitting' stage that focuses on the answer) and steering the model toward flatter minima. The anchor function, a synthetic task with one composite operator hidden from training, serves as the probe that shows NTP prefers the lower-complexity reasoning solution that generalizes, while CTP can settle on a memorized non-reasoning solution.

What would settle it

Train NTP and CTP on a reasoning dataset where the non-answer tokens are replaced by uniform random tokens of the same length and vocabulary, keeping answer positions fixed. If NTP no longer outperforms CTP (or its accuracy drops to CTP's level), the advantage comes from the information content of those tokens, not from noise-induced regularization; if the advantage persists, the noise-regularization mechanism is supported.

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Extended reading notes

Core claim

The paper's central discovery is that training a transformer to predict all tokens in a reasoning sequence—rather than only the answer tokens—imparts a reasoning bias: NTP-trained models generalize to out-of-distribution questions, resist contradictory and poisoned labels, and prefer a compositional 'reasoning' solution over a simpler memorized one on an anchor-function benchmark. The authors attribute this to the non-critical tokens acting as a regularizer that flattens the loss landscape and slows memorization. They find that NTP reaches 100% accuracy on PrOntoQA while CTP plateaus near 80%, that NTP keeps near-perfect accuracy on a reversed and an out-of-vocabulary test set while CTP overfits, and that on the synthetic anchor function NTP shifts the model from the non-reasoning to the reasoning solution. On transfer, NTP-trained models generalize faster during finetuning but also forget the pretrained task more easily. The authors conclude that NTP is instrumental during pretraining and CTP is more effective for finetuning.

Load-bearing premise

The explanation assumes that the non-answer tokens in the training sequences are noise rather than structured information, even though in real reasoning datasets those tokens contain the facts, rules, and questions needed to derive the answer.

Editorial extensions

If this is right

  • Pretraining on question-answer data should keep next-token prediction on all tokens rather than switching to answer-only loss, if reasoning generalization is the goal.
  • For finetuning, answer-only (CTP/SFT) loss is faster and matches or exceeds NTP, so the optimal training recipe switches objectives between phases.
  • NTP-trained models transfer faster to new tasks but forget the old task more readily, so finetuning schedules must budget for catastrophic forgetting.
  • The noise-regularization view predicts that adding noise to a CTP objective (for example, through noisy embeddings) should recover part of NTP's reasoning advantage.
  • Comparisons of training objectives should be evaluated on out-of-distribution and robustness tests, not only on held-out in-distribution accuracy, because that is where the reasoning bias appears.

Reading between the lines

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

  • If the advantage is truly noise-driven, it should scale with the fraction and entropy of non-answer tokens; a quantitative law connecting sequence noise level to reasoning gains could be fitted and tested, which the paper does not provide.
  • The same mechanism may apply to other sequence-prediction settings where the supervisory signal occupies a small part of the output, such as program synthesis and robot-policy learning, making CTP-like objectives there similarly risky.
  • An explicit curriculum that anneals from NTP to CTP loss during pretraining could combine NTP's reasoning generalization with CTP's faster convergence; the paper tests pretraining on noise-only loss followed by CTP, but not a continuous schedule.
  • The catastrophic forgetting asymmetry suggests that NTP-trained models have more malleable representations; this could be an advantage for continual learning if paired with replay, which the paper does not explore.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper compares next-token prediction (NTP) with critical-token prediction (CTP) when training small GPT-2 models from scratch on reasoning datasets. It reports that NTP outperforms CTP in accuracy, out-of-distribution generalization, robustness to embedding and weight perturbations, and resistance to poisoned labels, despite slower early learning. The authors attribute this advantage to a noise-regularization effect of the non-critical tokens and recommend NTP for pretraining and CTP for finetuning. Evidence includes PrOntoQA variants, nine other reasoning and text-classification datasets, an anchor-function synthetic task, finetuning/transfer experiments, and loss-landscape flatness measurements.

Significance. If the empirical ranking is reproducible, the paper offers a useful counterpoint to token-selection methods such as RHO-1 and suggests a concrete role for full-sequence prediction in reasoning tasks. The anchor-function experiments provide a clean synthetic demonstration that full-sequence training can shift a model from a non-reasoning to a reasoning solution, and the poisoned-label experiments are a valuable robustness probe. However, the central explanatory claim—that the advantage is caused by 'noise' regularization—is not yet established for natural-language reasoning data, because the extra tokens in those datasets are informative rather than random. The paper would be considerably strengthened by ablations that separate informative-token prediction from random-noise regularization, and by quantitative reproducibility information for the main comparisons.

major comments (3)
  1. [§3.2, §7.1, Eqs. (3)-(4), Fig. 10(b)] The proposed mechanism identifies the non-critical terms in Eq. (3) with 'noise,' and Section 7.1 calls the residual beyond the CTP term the 'noise loss.' However, in PrOntoQA and the other natural-language reasoning benchmarks, these positions contain the facts, rules, and question that determine the answer (see the underlined inference chain in Appendix 7.3). Predicting those tokens is structured supervision, not random perturbation. The observed NTP advantage could therefore come from access to a richer learning signal rather than from noise-induced regularization. The anchor-function experiments in Section 4.3 use genuinely random padding and support the noise-regularization mechanism in that synthetic setting, but Fig. 10(b) only shows that gradient norms on non-critical positions decrease late in training; it does not establish that their role during optimization was regularization. To sustain the mechanism claim, the authors should isolate the property of the extra tokens, for example by comparing CTP trained with additional loss on the informative chain tokens against CTP trained with added random tokens, and report whether only the former reproduces the NTP advantage.
  2. [§6.3, Fig. 9] The abstract and Section 6 claim that NTP reaches flatter minima, but the text of Section 6.3 states that 'the flatness disparity between the two training approaches becomes considerably more nuanced' and that 'the flatness analysis under this specific scenario favors CTP' on PrOntoQA reverse and PARARULE plus, with a post-hoc explanation in terms of search-space size. Because flatness is the main mechanistic evidence offered for the generalization claim, this admission directly weakens the central explanation. Please report the flatness comparison quantitatively for all tasks, specify the range of perturbation strengths used in Eq. (6), and either reconcile the contradictory results with the noise-regularization account or remove flatness from the load-bearing evidence.
  3. [Figs. 2, 4, 6, 7, 8] Most accuracy and robustness comparisons are shown for a single training run without error bars or seed information; only Fig. 5 reports standard deviations over three runs. Since several reported gaps (for example, the text-classification results in Fig. 4 and the finetuning curves in Fig. 6) are small or variable, single-run curves are insufficient to support the claim that NTP 'consistently outperforms' CTP. Please report means and variances over at least three seeds for the main comparisons, or clearly mark which differences are reproducible.
minor comments (4)
  1. [§7.4.1, §7.4.2, §7.3] There are several typos: 'vallina' should be 'vanilla' in Sections 7.4.1 and 7.4.2, 'THe' should be 'The' in the ReCOGS description, and 'LTP' should be 'CTP' in the RobustLR paragraph.
  2. [§3.2, Eq. (4) vs. §7.4.2] Equation (4) defines CTP as the loss on a single final token x_T, but Appendix 7.4.2 says the CTP loss is calculated on all tokens between the [SEP] symbols, which for multi-token answers includes more than one token; please reconcile the formal definition with the experimental implementation.
  3. [§7.3, SimpleLogic] The text says 'we introduce 192,000 training dataset and 1,0000 testing dataset'; the '1,0000' appears to be a typo for '10,000'.
  4. [Figure 2 and §4.1] The figure caption for panel (c) says '1-hop specific PrOntoQA on OOV data,' while the main text explains that the authors downgraded from 2-hop to 1-hop because both methods struggled on 2-hop OOV; please state this limitation directly in the caption and clarify the scope of the OOV claim.

Circularity Check

1 steps flagged · score 2.0 of 10

Empirical NTP-vs-CTP comparison is self-contained; the mechanism label is definitional but not load-bearing.

  1. self definitional [Sec. 7.1, with Eq. (3) and Eq. (4) in Sec. 3.2]
    "To our knowledge, the NTP loss function incorporates a component from CTP. We can isolate the CTP portion within the NTP loss and refer to the remaining part as the "noise loss"."

    Eq. (4) defines CTP loss and Eq. (3) defines NTP loss, so the residual the paper calls 'noise loss' is, by construction, exactly the sum over non-critical tokens that separates NTP from CTP. Attributing NTP's advantage to 'the regularizing influence of noise' (Abstract) then reduces to saying that this residual term matters, which is an arithmetic identity of the comparison rather than an independently established mechanism. In PrOntoQA and similar reasoning datasets, the residual contains the facts, rules, and question needed for the answer, so treating it as random noise is an assumption; the anchor-function experiments with genuine noise provide only partial, synthetic support.

full rationale

The central empirical claim, that NTP outperforms CTP on reasoning benchmarks, is obtained by training from scratch on external datasets such as PrOntoQA, LogicInference, RobustLR, and PARARULE Plus, so it is not derived from a fitted parameter and is not circular. The paper contains no fitted input passed off as a prediction. The main circularity-adjacent move is terminological: Section 7.1 defines the residual NTP loss as 'noise loss,' and the Abstract explains NTP's advantage as 'the regularizing influence of noise.' Because that residual is exactly what distinguishes NTP from CTP, the explanatory label is definitional; whether the residual acts as noise regularization in natural-language reasoning is not established by the equations. The use of the authors' prior anchor-function work (Zhang et al. 2024a,b) is a self-citation, but it supports a supporting synthetic experiment rather than the main benchmark ranking, so it is not load-bearing. These issues lower confidence in the proposed mechanism but do not make the empirical result circular; hence a low score of 2.

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

The central mechanistic claim rests on an empirically unverified classification of informative tokens as noise, and on a large extrapolation from tiny synthetic models to LLM pretraining. No new physical entities are introduced.

assumptions (3)
  • ad hoc to paper Non-answer tokens in question-answer sequences are noise that carries no task-relevant signal.
    The regularization explanation (Sections 4.3, 7.2) depends on treating intermediate tokens as noise, yet these tokens contain the facts and question used to derive the answer.
  • domain assumption Findings from GPT-2 125M trained from scratch on synthetic reasoning datasets transfer to LLM pretraining practice.
    The abstract and Section 7 generalize from small models on synthetic benchmarks to optimal pretraining/finetuning strategy for LLMs.
  • domain assumption Classification accuracy on the chosen synthetic benchmarks is a valid measure of reasoning ability.
    The paper equates benchmark accuracy, e.g., PrOntoQA, with 'reasoning ability' throughout Section 4.

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Cite this review

Pith. "Pith review of Reasoning Bias of Next Token Prediction Training." pith.science (2026). https://pith.science/paper/MJIHFUJ6

@misc{pith2026250202007,
  author       = {Pith},
  title        = {Pith review of: Reasoning Bias of Next Token Prediction Training},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MJIHFUJ6}},
  note         = {Machine review of arXiv:2502.02007}
}
read the original abstract

Since the inception of Large Language Models (LLMs), the quest to efficiently train them for superior reasoning capabilities has been a pivotal challenge. The dominant training paradigm for LLMs is based on next token prediction (NTP). Alternative methodologies, called Critical Token Prediction (CTP), focused exclusively on specific critical tokens (such as the answer in Q\&A dataset), aiming to reduce the overfitting of extraneous information and noise. Contrary to initial assumptions, our research reveals that despite NTP's exposure to noise during training, it surpasses CTP in reasoning ability. We attribute this counterintuitive outcome to the regularizing influence of noise on the training dynamics. Our empirical analysis shows that NTP-trained models exhibit enhanced generalization and robustness across various benchmark reasoning datasets, demonstrating greater resilience to perturbations and achieving flatter loss minima. These findings illuminate that NTP is instrumental in fostering reasoning abilities during pretraining, whereas CTP is more effective for finetuning, thereby enriching our comprehension of optimal training strategies in LLM development.

Figures

Figures reproduced from arXiv: 2502.02007 by the authors.

Figure 1
Figure 1. The schematic illustration comparing NTP and CTP. In the context of arithmetic addition tasks, CTP’s [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (a) Accuracy of NTP and CTP on the original/cloze PrOntoQA task over training epochs. In the original [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The description of different PrOntoQA tasks: Original, cloze, reverse, OOV test and its variation ProsQA [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Performance comparison of NTP and CTP across various reasoning tasks. NTP consistently outperforms [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Accuracy on non-reasoning and reasoning solution of anchor function with different layers. The NTP could [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Finetuning results with multiple tasks. NTP+CTP means the model is NTP-trained on previous task and CTP-finetuned on post task; CTP+CTP means the model is CTP-trained on previous task and CTP-finetuned on post task. train from scratch means the model is trained from sc…
Figure 7
Figure 7. Figure 7: Effect of embedding noise on model performance in different reasoning tasks. The x-axis represents the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Comparison of NTP and CTP on the addition task with varying poisoned samples. The [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: The flatness for task anchor function, PrOntoQA reverse, and PARARULE plus tasks. To alleviate the [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: (a) The original 2-hop PrOntoQA task trained on the pretrained models. The legend entry [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: The NTP and CTP training process of reasoning tasks and text classification tasks. CTP outperforms NTP [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: The illustration of anchor function data generation. Anchor function is a simple linear mapping but we add [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.