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REVIEW 4 major objections 4 minor 1 cited by

NOVER: Incentive Training for Language Models via Verifier-Free Reinforcement Learning

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read NOVER replaces the external verifier in incentive training with a reasoning-perplexity proxy, making RL applicable to any text-to-text task and beating a same-size R1 distillation by 7.7 percent.

desk verdict Genuinely novel verifier-free RL recipe with honest reporting, but the reward proxy's external validity is asserted rather than measured, so the headline gain is conditional. read the letter →

arxiv 2505.16022 v2 pith:B76QZQP7 submitted 2025-05-21 cs.CL cs.AIcs.LG

Wei Liu , Siya Qi , Xinyu Wang , Chen Qian , Yali Du , Yulan He This is my paper · ORCID
classification cs.CLcs.AIcs.LG
keywords verifier-freereinforcementlearningincentivetrainingreasoningperplexityrewardproxyGRPOtext-to-texttaskshackinginverse
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

The paper introduces NOVER (No-Verifier Reinforcement Learning), a method that lets language models be trained with R1-style incentive signals without any external grader. Its idea is to reward reasoning indirectly: instead of checking whether an answer is right, NOVER computes the perplexity of the human-written reference answer given the model's own reasoning tokens, treating a low value as evidence that the reasoning is on the right track. Because this proxy can be computed from any ordinary supervised fine-tuning dataset, the paper argues that incentive training can now be applied to writing, social reasoning, translation, and other open-ended text-to-text tasks where rule-based verifiers do not exist. The headline empirical claim is that Qwen2.5-7B trained with NOVER averages 47.31% accuracy across seven benchmarks, beating R1-Distill-Qwen-7B, a same-size model distilled from a 671B teacher, by 7.69 percentage points.

What carries the argument

The load-bearing object is the reasoning-perplexity proxy $P_r$ (Eq. 8): the teacher-forcing probability of the reference answer conditioned on the model's own reasoning tokens, divided by a log-length normalizer so longer reasoning is not automatically penalized. The stability machinery consists of (i) policy-proxy synchronization $\pi_p \leftarrow \alpha \pi_p + (1-\alpha) \pi_\theta$, (ii) discretizing raw perplexity into rank-based reasoning rewards $R_r$, (iii) an efficiency reward $R_e$ that rewards shorter-and-better reasoning, and (iv) the conditional reward combination $R_{\text{total}} = w_f R_f + \mathbb{I}(R_f=1)(w_r R_r + w_e R_e)$, which zeros all proxy rewards when the tag format fails. These components together are what convert an unverifiable quality signal into a stable GRPO training signal.

What would settle it

One concrete test: sample completions for a fixed prompt and reference, compute each completion's $P_r$, and ask human judges to rank the answers; if the lowest-perplexity completion is not among the best, the proxy is separable from quality. A training-level test: run NOVER past the reported number of steps and watch whether accuracy stagnates or falls while $P_r$ keeps dropping, which would show the model optimizing the proxy rather than the answer.

Watch

Extended reading notes

Core claim

On its own terms, the central discovery is that reasoning perplexity is a usable universal reward for incentive training. Given a prompt $p$, a ground-truth answer $g$, and a completion with reasoning tokens $t$, NOVER defines $P_r$ as the teacher-forcing probability of $g$ under the proxy model $\pi_p$ conditioned on $p$ and $t$, normalized by answer length and a log factor of reasoning length; low $P_r$ means the reasoning has made the correct answer predictable. The paper claims this signal, fed through rank-based rewards and an efficiency bonus in a GRPO loop with periodic policy-proxy synchronization, trains models that outperform base, CoT, and SFT baselines everywhere it is tested, and that the same machinery can be inverted to optimize stories against rubrics instead of reference answers.

Load-bearing premise

The load-bearing premise is that the proxy reward stays aligned with true answer quality: that a completion with lower reasoning perplexity is actually the better completion, across all the open-ended tasks NOVER is used on.

Editorial extensions

If this is right

  • Qwen2.5-7B trained with NOVER reaches 47.31% average accuracy, outperforming R1-Distill-Qwen-7B's 39.62% by 7.69 percentage points.
  • NOVER beats the base model, CoT prompting, and SFT on all seven task types for both 3B and 7B models.
  • The verifier-free reward costs only about 5% of total training time, so it scales to ordinary SFT datasets without a dedicated verifier pipeline.
  • Inverse incentive training on SS-GEN raises story-generation accuracy from 50.79% to 64.37%, showing the proxy can steer intermediate tokens that are themselves the desired output.
  • Against LLM-as-judge and a trained general verifier on WebInstruct, NOVER trains stably where verifier-based methods suffer reward hacking or training collapse.

Reading between the lines

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

  • A natural extension is to apply NOVER to partially labeled or weakly labeled data, because the proxy only needs a reference answer and the model's own reasoning rather than a verified ground truth.
  • The proxy's teacher-forcing nature will likely reward reasoning that is stylistically fluent and self-consistent with the reference even when the reasoning is not causally correct; measuring that gap against human judgment on hard open-ended tasks would be the decisive stress test.
  • The inverse-training result suggests rubric-based objectives can be optimized without exemplar outputs, which could extend to summarization, dialogue, or instruction-following where rubrics exist but gold texts do not.
  • The FANToM false-premise result implies NOVER inherits the base model's blind spots, so a hybrid SFT-then-NOVER schedule, which the paper itself hints at, is the natural next step for counterintuitive tasks.
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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

4 major / 4 minor

Summary. NOVER proposes a verifier-free reinforcement learning framework for incentive training on arbitrary text-to-text tasks. The core reward is a reasoning perplexity proxy (Eq. 8): the policy model, periodically synchronized with a proxy model (Eq. 10), assigns a teacher-forcing likelihood to the ground-truth answer conditioned on the model's generated reasoning tokens. The reward combines a rank-based reasoning reward (Eq. 11), an efficiency reward (Eq. 12), and a format reward, optimized with GRPO. Experiments cover seven datasets across general reasoning, creative writing, social intelligence, and multilingual translation, with Qwen2.5 3B/7B and additional backends. The paper also reports a FANToM failure, a qualitative 'curse of proxy' analysis, and an inverse incentive training variant for creative writing.

Significance. If the core claim holds, NOVER would meaningfully extend R1-style incentive training beyond domains with rule-based verifiers, and the inverse incentive training idea is a novel and potentially useful way to optimize for rubric-defined outputs without ideal exemplars. The paper has notable strengths: it reports honest failures (Table 3), analyzes training stability and reward hacking (Section 6.3), evaluates across multiple model families, and provides a public demo. The claimed 7.7-point average improvement over R1-Distill-Qwen-7B, however, rests on the validity of reasoning perplexity as a reward proxy, which is currently supported only by one qualitative example and no direct correlation measurement. That gap is load-bearing for the paper's central claim, as are the lack of error bars and the circularity in the rubric-based human evaluation.

major comments (4)
  1. [§4.1–4.2, Eq. (8)–(10), Appendix G] The reward proxy Pr is never validated against an independent measure of answer quality. Because πp is periodically synced to πθ, a low Pr can reflect the policy becoming more self-confident about the ground truth given its own reasoning, rather than the reasoning being objectively better. Appendix G shows only a single qualitative pair; it does not establish a dataset-level correlation. The paper should report, for held-out completions, a correlation (e.g., Spearman or rank correlation) between Pr and an independent quality score (LLM-as-judge or human) before and after training. Without this, the 7.7-point advantage in Table 1 could be attributable to confidence or length changes rather than genuine reasoning quality.
  2. [Table 1, Abstract] The headline 'outperforms ... by 7.7%' is an average across seven datasets, but NOVER-7B loses to R1-Distill-Qwen-7B on Natural Reasoning (38.2 vs 41.0) and WebInstruct (36.6 vs 38.0). There are also no error bars or multiple seeds, so the reader cannot assess whether any of the differences are statistically reliable. The authors should provide confidence intervals or per-dataset significance tests, and the abstract should qualify the aggregate claim with the per-dataset outcome.
  3. [§6.6, Figure 8] The human evaluation of inverse incentive training uses the same rubrics that define the training reward. Since NOVER_RUBRIC explicitly optimizes those rubric dimensions, the human-preference result in Figure 8 is circular evidence for rubric satisfaction and does not demonstrate general creative-writing improvement. The authors should include an evaluation on criteria not used in training (e.g., overall story quality, coherence, or a separate writing benchmark) and report inter-annotator agreement.
  4. [§4.1, Eq. (9); §4.3, Eq. (11)–(13); Table 6] The length normalization N(|t|) and the reward design parameters (k, wr, we, wf, α, Tsync) are fixed choices with no sensitivity analysis or derivation. Since Eq. (8) normalizes perplexity by N(|t|) and Eq. (12) explicitly rewards shorter reasoning, these choices directly shape the learned policy. Without ablations varying N, k, and the reward weights on at least one dataset, it is unclear whether the reported gains are robust to reasonable changes in the reward formulation.
minor comments (4)
  1. [Figure 2] The figure contains garbled, unspaced text (e.g., 'Aphotonasafundamentalparticleisoften…') and the phrase 'familiarizes children with asd' appears to have a typo ('asd' should likely be 'ASD'). The figure is difficult to read and should be cleaned up.
  2. [§2 Related Work] There is a typographical spacing issue: 'V APO' should be 'VAPO' to match the cited work.
  3. [§4.1, Eq. (8)] Equation (8) defines Pr as a function of p, t, and g, but the generated answer tokens a are never used in the reward computation (except through the format reward). This is an unusual design choice worth a brief explanation, since readers may expect the reward to depend on the generated answer content.
  4. [Appendix G] The claim that reasoning perplexity 'discriminates good ones from bad ones' is supported by only two completions with perplexities 1.406 and 1.516. The difference is small and the example is anecdotal; the text should not use this as evidence without the correlation analysis requested above.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: NOVER's reward proxy is explicitly a heuristic, and the headline results rest on held-out evaluation rather than on the proxy itself.

full rationale

The paper does not present reasoning perplexity as a derived theorem; Eq. 8 defines a training reward proxy, and the sentence 'A lower reasoning perplexity Pr indicates a higher probability of generating the correct answer' is a restatement of the definition rather than a prediction derived from it. The central empirical claims (Table 1) are measured with held-out accuracy or LLM-as-a-judge evaluation, which are external to the reward signal. Although Eq. 10 synchronizes the proxy model to the policy, making Pr a self-consistency score of the policy's own likelihood of the ground truth, this is a known limitation of the proxy design and not a circularity in the derivation of the reported results, because the reported gains are not computed from Pr. The inverse incentive training experiment uses human rubric evaluation that shares the rubric definitions with the training target, but human judgment is an independent measurement rather than a mathematical consequence of the reward. Self-citations (e.g., Liu et al. 2024, Qi et al. 2024, Yan et al. 2024) appear only in related work or auxiliary analysis and are not load-bearing for the main claim. The absence of a dataset-level correlation between Pr and answer quality is a genuine correctness risk, but it is not circularity under the standards requiring a specific reduction of a prediction to its inputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The reward is defined through the policy's own conditional likelihood of ground truth answers, which is a heuristic proxy not derived from first principles. The method relies on several hand-set hyperparameters (k, weights, sync rate, length normalization) that shape the reward, and on the validity of LLM-as-judge for evaluation. No new physical or architectural entities are introduced.

free parameters (4)
  • Rank cutoff k = 1 or nvalid (per task type)
    Controls whether only the best completion receives reward or all ranked completions do; chosen by task objectivity (Section 4.3, Eq. 11).
  • Reward weights wf, wr, we = 1.0, 1.0, 1.0
    Relative weights of format, reasoning, and efficiency rewards; set to 1 in Table 6 without reported tuning.
  • Length normalization N(|t|) = max(1, 1+log(|t|))
    Heuristic to remove reasoning-length bias from perplexity; no derivation or ablation is provided (Eq. 9).
  • Sync coefficient alpha and interval Tsync = alpha=0.9, Tsync=100
    Exponential smoothing for policy-proxy synchronization; chosen by hand and reported in Table 6.
assumptions (4)
  • domain assumption Teacher-forcing perplexity of the ground truth conditioned on the model's reasoning tokens is a valid proxy for answer quality.
    Invoked in Section 4.1, Eq. 8; supported only by a qualitative example in Appendix G, not by a derivation or controlled study.
  • domain assumption The policy model itself can serve as a stable proxy when synchronized with exponential smoothing.
    Introduced in Section 4.2, Eq. 10; the curse-of-proxy analysis in Section 6.3 acknowledges this assumption can fail without careful conditioning.
  • domain assumption GRPO group normalization adequately calibrates the perplexity reward across samples.
    Section 4.3 states relative perplexity gain is unnecessary because GRPO normalizes advantages; no experiment directly validates this substitution.
  • domain assumption LLM-as-a-judge (Gemini-2.0-flash) provides accurate accuracy labels for open-ended answers.
    Used for evaluation in Section 5 and Appendix E; no inter-annotator agreement, judge accuracy, or bias checks are reported.

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Cite this review

Pith. "Pith review of NOVER: Incentive Training for Language Models via Verifier-Free Reinforcement Learning." pith.science (2026). https://pith.science/paper/B76QZQP7

@misc{pith2026250516022,
  author       = {Pith},
  title        = {Pith review of: NOVER: Incentive Training for Language Models via Verifier-Free Reinforcement Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B76QZQP7}},
  note         = {Machine review of arXiv:2505.16022}
}
read the original abstract

Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the generation of intermediate reasoning steps. However, these methods fundamentally rely on external verifiers, which limits their applicability to domains like mathematics and coding where such verifiers are readily available. Although reward models can serve as verifiers, they require high-quality annotated data and are costly to train. In this work, we propose NOVER, NO-VERifier Reinforcement Learning, a general reinforcement learning framework that requires only standard supervised fine-tuning data with no need for an external verifier. NOVER enables incentive training across a wide range of text-to-text tasks and outperforms the model of the same size distilled from large reasoning models such as DeepSeek R1 671B by 7.7 percent. Moreover, the flexibility of NOVER enables new possibilities for optimizing large language models, such as inverse incentive training.

Figures

Figures reproduced from arXiv: 2505.16022 by the authors.

Figure 1
Figure 1. Comparison of NOVER with other post￾training paradigms. Learning with Verifiable Reward (RLVR). It has been demonstrated that such incentivized reasoning ability can generalize to areas like multi-modality (Shen et al., 2025; Zhang et al., 2025; Yang et al., 2025; Feng et al., 2025b) or language agent (Xia and Luo, 2025; Jin et al., 2025; Song et al., 2025; Wang et al., 2025; Feng et al., 2025a). However, the succes… view at source ↗
Figure 2
Figure 2. Examples of Qwen2.5-7B-NOVER on a range of text-to-text tasks, demonstrating its ability to handle [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. The overall process of NOVER. It can be seen in Equation 1 that the incentive training described above requires a verifier to com￾pute Rrule. NOVER eliminates the need for a veri￾fier by introducing reasoning perplexity as a reward proxy, which can be calculated on any SFT data. 4.1 Reasoning Perplexity as Proxy The core idea of NOVER is that the perplexity of the ground truth answer, conditioned on the model’s reas… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Accuracy of NOVER on three general reasoning tasks by the distribution of different aspects. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: The curse of proxy: inaccurate proxy reward [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Change of reasoning patterns over steps. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Comparison between standard NOVER train [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Human judgment on different rubrics for SS [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Profiling of the training time in NOVER. [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 11
Figure 11. Figure 11: System prompt for choice-format tasks. System Prompt for Translation Translate the following text from {source_lang_name} to {target_lang_name}: {source_text} Answer the question and return in the following for￾mat: <think> ... </think> <answer> ... </answer> [PITH_F…
Figure 12
Figure 12. Figure 12: System prompt for translation tasks. Judge Prompt Please determine if the following Model answer matches the Ground truth. Only consider if the response matches the reference, regardless of how detailed or comprehensive it is. Ground truth: {reference} Model answer: {…
Figure 10
Figure 10. Figure 10: System prompt for most general reasoning [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 14
Figure 14. Figure 14: Judge prompt (the lenient version) used in [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: Judge prompt from the official code of gen [PITH_FULL_IMAGE:figures/full_fig_p016_15.png]
Figure 16
Figure 16. Figure 16: A case in the OPUS translation dataset, where the base model generates hallucinated CoT that leads to [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]
Figure 17
Figure 17. Figure 17: We show two completions from NOVER on the Natural Reasoning dataset, showing how reasoning [PITH_FULL_IMAGE:figures/full_fig_p018_17.png]
Figure 18
Figure 18. Figure 18: A false premise example in FANToM (Kim et al., 2023) dataset, where the question cannot be an￾swered [PITH_FULL_IMAGE:figures/full_fig_p019_18.png]

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    2024 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.