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arxiv: 2605.19436 · v1 · pith:QZ5WOFU4new · submitted 2026-05-19 · 💻 cs.LG · cs.CL· cs.CV

CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization

Ahmed Heakl , Abdelrahman M. Shaker , Youssef Mohamed , Rania Elbadry , Omar Fetouh , Fahad Shahbaz Khan , Salman Khan This is my paper

Pith reviewed 2026-05-20 07:21 UTC · model grok-4.3

classification 💻 cs.LG cs.CLcs.CV
keywords reinforcement learningpolicy optimizationself-distillationcontrastive learningmultimodal reasoningmathematical reasoningcredit assignmentRLVR
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The pith

CEPO sharpens credit assignment for decisive reasoning tokens in RLVR by using contrastive signals from both correct and wrong answers.

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

The authors introduce Contrastive Evidence Policy Optimization to fix the problem that all tokens receive identical rewards in reinforcement learning with verifiable rewards. CEPO asks whether the correct answer favors a given token while a wrong answer disfavors it, marking only the first as a genuine reasoning step. The wrong answer signal comes from rejected rollouts already available in the training batch. This approach is shown to preserve all safety properties of earlier methods while delivering higher accuracy on multimodal mathematical reasoning tasks at both 2B and 4B model scales.

Core claim

When a model produces a correct solution under RLVR, CEPO constructs a wrong-answer teacher from rejected rollouts in the same batch. At each token it checks if the correct answer favors the token and the wrong answer disfavors it. Tokens meeting both conditions receive sharpened credit; the sharpening vanishes at filler positions. The method inherits the structural safety guarantees of prior state-of-the-art approaches.

What carries the argument

The contrastive evidence query applied at every token, which identifies genuine reasoning steps as those favored by the correct answer and disfavored by the wrong answer constructed from rejected samples.

If this is right

  • CEPO achieves 43.43 percent average accuracy across five multimodal mathematical reasoning benchmarks at 2B scale compared to 41.17 percent for GRPO.
  • CEPO achieves 60.56 percent average accuracy at 4B scale compared to 57.43 percent for GRPO under identical training budgets.
  • The credit improvement is strictly positive at decisive tokens and exactly zero at filler positions.
  • Distribution-matching self-distillation methods fall below the untrained baseline due to predicted information leakage.
  • CEPO inherits all structural safety guarantees from the prior state of the art.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the rejected rollout signal remains unbiased in other domains, CEPO could apply to additional verifiable reward tasks beyond mathematical reasoning.
  • The reuse of batch rejections may lower the computational overhead of contrastive self-distillation in larger training runs.
  • Future work could test whether the token-level sharpening correlates with human judgments of reasoning importance.
  • Applying the same contrastive principle to non-RL settings might improve credit assignment in supervised fine-tuning.

Load-bearing premise

The wrong-answer teacher constructed from rejected rollouts already present in the training batch provides a sufficiently strong and unbiased contrastive signal without introducing leakage or distribution shift.

What would settle it

A run on the same benchmarks where CEPO fails to exceed GRPO accuracy or where the per-token credit sharpening does not disappear at positions identified as fillers would falsify the main claim.

Figures

Figures reproduced from arXiv: 2605.19436 by Abdelrahman M. Shaker, Ahmed Heakl, Fahad Shahbaz Khan, Omar Fetouh, Rania Elbadry, Salman Khan, Youssef Mohamed.

Figure 1
Figure 1. Figure 1: Accuracy over 50 training steps. CEPO improves faster than GRPO and RLSD, reaching its largest gap around step 40 before partially con￾verging by the final checkpoint. Reinforcement learning with verifiable rewards (RLVR) has become the dominant paradigm for post-training large language models to rea￾son [17, 4, 20]. The core loop is simple: sample rollouts from the current policy, score them against a ver… view at source ↗
Figure 2
Figure 2. Figure 2: CEPO training pipeline and its relationship to GRPO and RLSD. Given a question x, the policy πθ produces G rollouts that are partitioned into correct (G+) and wrong (G−) sets by a verifiable reward. CEPO conditions two frozen teachers on a sampled correct rationale r + ∈ G+ and rejected rationale r − ∈ G−, and defines a per-token contrastive evidence delta ∆CE t that amplifies advantage at decisive tokens … view at source ↗
Figure 3
Figure 3. Figure 3: Hyperparameter sensitivity averaged across 5 reasoning benchmarks). (a) Constant λ schedule: λ = 0.5 peaks at 41.40%, outperforming GRPO (41.17%); sustained high-λ training (λ = 1.0) introduces noise that offsets the credit-assignment benefit. (b) Linear-decay schedule from λ0 = 1.0: a 25-step warmup matches the constant-λ peak (41.25%). (c) Evidence clip bound εw: performance peaks in [0.4, 0.5] at 42.7% … view at source ↗
Figure 4
Figure 4. Figure 4: Contrastive delta fractions during CEPO training. We track the fraction of tokens assigned positive versus negative contrastive evi￾dence. Positive-delta mass increases early, while negative-delta mass decreases. Contrastive delta fractions [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Token-level credit assignment on a parallelogram problem. Green/red/white denote high, low, and neutral token weights. Numbered regions illustrate three claims: ① RLSD over-credits fluent setup prose, while CEPO suppresses it; ② CEPO localizes blame to the misapplied angle-equality inference instead of diffusing penalties; ③ CEPO sharpens credit on the decisive algebraic derivation (x+4 = 3x−6, isolation s… view at source ↗
read the original abstract

When a model produces a correct solution under reinforcement learning with verifiable rewards (RLVR), every token receives the same reward signal regardless of whether it was a decisive reasoning step or a grammatical filler. A natural fix is to condition the model on the correct answer as a teacher, identifying tokens it would have generated differently had it known the answer. Prior work shows this either corrupts training by leaking the answer into the gradient, or produces a weak signal that cannot distinguish decisive steps from filler, since both look equally surprising relative to the model's baseline. We propose Contrastive Evidence Policy Optimization (CEPO), which asks a sharper question at every token: not just "does the correct answer favor this token?" but "does the correct answer favor it while the wrong answer disfavors it?" A token satisfying both is a genuine reasoning step; one satisfying neither is filler. The wrong-answer teacher is constructed from rejected rollouts already in the training batch, incurring no additional sampling cost. We prove CEPO inherits all structural safety guarantees of the prior state of the art while strictly sharpening credit at decisive tokens, with the improvement vanishing exactly at filler positions. Empirically, CEPO achieves 43.43% and 60.56% average accuracy across five multimodal mathematical reasoning benchmarks at 2B and 4B scale, respectively, versus 41.17% and 57.43% for GRPO under identical training budgets. Distribution-matching self-distillation methods (OPSD, SDPO) fall below the untrained baseline, empirically confirming the information leakage our theory predicts. Our code is available at https://github.com/ahmedheakl/CEPO.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Contrastive Evidence Policy Optimization (CEPO) for RLVR self-distillation. It constructs a contrastive signal at each token by checking whether the correct-answer teacher favors the token while a wrong-answer teacher (built from rejected rollouts already present in the current training batch) disfavors it. The authors claim this sharpens credit assignment precisely at decisive reasoning steps while the effect vanishes exactly at filler positions. They prove that CEPO inherits all structural safety guarantees of prior state-of-the-art methods (such as GRPO) and report empirical gains of 43.43% vs 41.17% (2B) and 60.56% vs 57.43% (4B) average accuracy on five multimodal mathematical reasoning benchmarks under identical training budgets. Distribution-matching baselines (OPSD, SDPO) fall below the untrained baseline, which the authors interpret as confirming their leakage theory. Code is released at https://github.com/ahmedheakl/CEPO.

Significance. If the safety-inheritance proof and the exact-vanishing property hold under the stated assumptions, CEPO would offer a low-cost mechanism for improving token-level credit assignment in verifiable-reward RL without additional sampling or leakage. The modest but consistent gains over GRPO on multimodal math benchmarks, together with the negative result for distribution-matching methods, would strengthen the case for contrastive rather than pure matching self-distillation. The public code release is a clear positive for reproducibility.

major comments (2)
  1. [§4] §4 (Proof of safety inheritance and vanishing property): The derivation that the contrastive advantage is exactly zero on filler tokens and that all prior safety guarantees are inherited assumes the wrong-answer policy constructed from rejected rollouts in the current batch remains distributionally close to the baseline policy without introducing batch-induced correlations. No explicit bound or sensitivity analysis is provided for the case where rejection sampling correlates with particular reasoning paths; this assumption is load-bearing for both the vanishing claim and the safety inheritance.
  2. [§5.2] §5.2 (Empirical results): The reported accuracy improvements (2.26 pp at 2B, 3.13 pp at 4B) are presented as averages across five benchmarks, but no per-benchmark breakdowns, standard deviations, or statistical significance tests are shown. Without these, it is difficult to determine whether the gains are robust or driven by a subset of tasks, which directly affects the strength of the claim that CEPO “strictly sharpens credit at decisive tokens.”
minor comments (2)
  1. [Abstract, §3] Abstract and §3: The notation for the correct-teacher and wrong-teacher policies is introduced without an explicit equation reference in the main text; adding a single displayed equation for the contrastive advantage term would improve readability.
  2. [§5.1] §5.1: The statement that distribution-matching methods “fall below the untrained baseline” would benefit from a short table row or footnote giving the exact baseline numbers for OPSD and SDPO.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments on our manuscript. We address each major comment below, indicating the revisions we will incorporate to strengthen the paper.

read point-by-point responses

  1. Referee: [§4] §4 (Proof of safety inheritance and vanishing property): The derivation that the contrastive advantage is exactly zero on filler tokens and that all prior safety guarantees are inherited assumes the wrong-answer policy constructed from rejected rollouts in the current batch remains distributionally close to the baseline policy without introducing batch-induced correlations. No explicit bound or sensitivity analysis is provided for the case where rejection sampling correlates with particular reasoning paths; this assumption is load-bearing for both the vanishing claim and the safety inheritance.

    Authors: We appreciate the referee pointing out this key assumption underlying the proof. The wrong-answer teacher is constructed exclusively from rejected rollouts already present in the current training batch, which are sampled from the policy being optimized and filtered solely by the verifiable reward on the final answer. Because policy updates occur gradually via PPO-style clipping and the rejection criterion depends only on answer correctness rather than intermediate reasoning paths, batch-induced correlations remain limited in practice. Nevertheless, we acknowledge that an explicit sensitivity analysis would make the argument more robust. In the revised manuscript we will add an appendix section with both a brief discussion of the assumption and an empirical sensitivity study across batch sizes and rejection rates, verifying that the vanishing property and inherited safety guarantees hold under moderate distributional shifts. revision: partial

  2. Referee: [§5.2] §5.2 (Empirical results): The reported accuracy improvements (2.26 pp at 2B, 3.13 pp at 4B) are presented as averages across five benchmarks, but no per-benchmark breakdowns, standard deviations, or statistical significance tests are shown. Without these, it is difficult to determine whether the gains are robust or driven by a subset of tasks, which directly affects the strength of the claim that CEPO “strictly sharpens credit at decisive tokens.”

    Authors: We agree that additional statistical detail is necessary to substantiate the robustness of the reported gains. In the revised version we will expand §5.2 (and the corresponding tables) to include per-benchmark accuracy scores for both the 2B and 4B models, standard deviations computed over multiple random seeds, and paired statistical significance tests (e.g., t-tests) against the GRPO baseline. These additions will allow readers to evaluate whether improvements are consistent across tasks or concentrated in particular benchmarks. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external baselines and stated assumptions rather than self-referential reduction.

full rationale

The paper's central claims rest on a mathematical proof of safety inheritance and exact vanishing of the contrastive delta at filler tokens, plus empirical comparisons against GRPO, OPSD, and SDPO. These are presented as independent of the fitted values in the current batch; the wrong-answer teacher is constructed from already-sampled rejected rollouts without additional parameters being tuned to the target metric. No equation is shown to reduce to a prior fit by construction, no uniqueness theorem is imported solely via self-citation, and the leakage theory is tested by reporting that distribution-matching baselines fall below the untrained model. The derivation chain therefore remains self-contained against the external benchmarks and the explicit assumption that batch rejections do not induce new distributional shift at filler positions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard RL assumptions plus the new contrastive construction; no explicit free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption RLVR produces correct final answers that can be used as conditioning signals without corrupting gradients when properly contrasted.
    Invoked when constructing the correct-answer teacher and claiming no leakage.

pith-pipeline@v0.9.0 · 5865 in / 1292 out tokens · 40527 ms · 2026-05-20T07:21:48.865853+00:00 · methodology

discussion (0)

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