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Expert answers alone teach language models to reason

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2026-08-03 19:55 UTC pith:24DYVYK2

load-bearing objection Worth reading and refereeing, but the 'works without verifiers' claim rests on a poetry benchmark judged only by GPT-5, and the actual algorithm is not covered by the paper's theory. the 4 major comments →

arxiv 2511.21667 v4 pith:24DYVYK2 submitted 2025-11-26 cs.LG cs.AI

Escaping the Verifier: Learning to Reason via Demonstrations

Locke Cai , Max Ryabinin , Ivan Provilkov This is my paper
classification cs.LG cs.AI
keywords inverse reinforcement learningreasoningexpert demonstrationsrelativistic criticadversarial trainingverifier-freechain-of-thoughttest-time scaling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper introduces RARO, a method to train a reasoning language model from expert question–answer demonstrations alone, without task-specific verifiers or human preference labels. It trains a policy and a critic adversarially: the critic compares an expert answer against a policy answer and says which is better or whether they tie, and the policy is rewarded when the critic mistakes its answer for the expert's. The result is that the policy learns to produce expert-like reasoning, reaching 54.4% accuracy on Countdown versus 57.7% for a verifier-based RL oracle. On DeepMath and Poetry Writing, RARO beats every no-verifier baseline while showing the same scaling behavior as verifier RL. This matters because most real tasks—writing, research, finance—lack reliable verifiers despite having abundant expert examples.

Core claim

RARO treats expert demonstrations as the only supervision and frames policy learning as inverse reinforcement learning: a critic that compares expert and policy answers (with a tie option) supplies reward for both sides. The paper claims that this joint adversarial game, stabilized by a replay buffer and shared parameters, makes the policy generate chains of thought that explore, self-correct, and align with task requirements. On the exact-reasoning Countdown task it reaches 54.4% accuracy, close to the 57.7% achieved by verifier-reward RL, and it achieves the best no-verifier results on DeepMath and Poetry Writing across 1.5B, 3B, and 7B models. Removing any of the method's main components—

What carries the argument

The central object is the relativistic critic: a judge that sees a question, an expert answer, and a policy answer, and returns a label of expert, policy, or tie. It is trained by GRPO to identify the expert, while the policy is rewarded for receiving the expert label; a tie yields partial reward to both sides, and a replay buffer of past policy answers keeps the critic from forgetting. This three-way comparison turns the intractable marginal-likelihood objective of chain-of-thought SFT into two tractable RL objectives and provides a natural tournament-based test-time search.

Load-bearing premise

The formal argument assumes the model is already close to the best policy and uses a simpler, separate judge; the real training uses one shared model making three-way comparisons (expert, policy, tie), and no proof covers that setup—only experiments do.

What would settle it

On a fresh random split of Countdown, retrain RARO with the exact supplied hyperparameters and evaluate with the ground-truth arithmetic checker; if accuracy does not replicate roughly 54% (versus 40.7% for SFT), the claim that the adversarial critic provides a verifier-like signal fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Verifier-free reasoning training can nearly match verifier-based RL on exact arithmetic tasks: 54.4% versus 57.7% on Countdown at 1.5B.
  • Improvements grow with model scale on general math: DeepMath accuracy rises from 41.3% at 1.5B to 57.5% at 7B, beating all no-verifier baselines.
  • The learned critic enables test-time scaling: a single-elimination tournament with 16 rollouts pushes 1.5B DeepMath accuracy from 41.3% to 53.6%.
  • Open-ended quality improves: poetry win-rate against expert poems grows from 7.8% at 1.5B to 25.0% at 7B, while SFT peaks near 6%.
  • All core components are necessary: removing the shared critic–policy backbone, tie option, replay buffer, critic reasoning, or relativistic setup each measurably reduces performance.

Where Pith is reading between the lines

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

  • Editorial inference: If RARO transfers broadly, any field with large archives of expert answers—legal writing, code review, scientific prose—could get reasoning-focused training without designing a reward, which would substantially lower the barrier to RL post-training.
  • Editorial inference: The critic is a trained comparator, so RARO naturally suggests a cheaper use of test-time search: run the same tournament on an already-trained policy without further fine-tuning.
  • Editorial inference: The poetry evaluation leans on an LLM judge, and the paper itself reports policy–critic oscillations in that domain; human preference ratings on a subset would tell whether the reported win-rates reflect durable poetic quality or judge-specific artifacts.
  • Editorial inference: The replay buffer's central role indicates that catastrophic forgetting—not only reward misspecification—is a main failure mode of adversarial reasoning training, so techniques from continual learning may improve sample efficiency and stability.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes RARO (Relativistic Adversarial Reasoning Optimization), a method for training LLM reasoners from expert demonstrations alone, without task-specific verifiers or preference data. The method alternates between a policy and a relativistic critic that are implemented as a single shared LLM. The policy generates answers and the critic compares policy answers against expert answers, outputting one of two answers or a tie; the policy receives reward when the critic mistakes its answer for the expert's, and the critic receives reward for correct identification, with small tie rewards. The authors frame the approach via inverse reinforcement learning and provide derivations in Appendix A for a simplified binary-critic, separate-parameter version. Experiments cover Countdown (1.5B), DeepMath (1.5B/3B/7B), and a custom Poetry Writing benchmark evaluated by GPT-5. RARO outperforms verifier-free baselines on Countdown (+13.7% over SFT), DeepMath (+8.2% over best baseline at 7B), and Poetry win-rate (+19.1% over SFT at 7B), nearly matching RLVR on Countdown. The paper also reports ablations showing that removing any component degrades performance and documents instabilities in the adversarial training dynamics.

Significance. If the claims hold, RARO would be a significant step toward reasoning training in non-verifiable domains, a currently open problem. The core idea of using expert demonstrations in an adversarial imitation-learning loop is appealing, and the empirical results on verifiable tasks (Countdown, DeepMath) are consistent and reproducible-looking: the method consistently beats strong baselines and scales with model size and token budget. The paper is also transparent in reporting training instabilities, sample-inefficiency relative to RLVR, and failure modes without the replay buffer. However, the paper's central claim is for non-verifiable reasoning, and that evidence currently rests on a single LLM judge with no human validation. Additionally, the theory in Appendix A covers a different algorithm than the one actually run, leaving the principled foundation unverified for RARO as implemented. The verifiable-task results are credible and would alone make a useful empirical contribution; the non-verifiable claim needs substantial strengthening.

major comments (4)
  1. [§3.1, Appendix A.3, Algorithm 2] The theoretical derivation in Appendix A is for a binary critic c_ϕ(ℓ|a,q) with separate parameters and the approximation π_{θ⋆(ϕ)} ≈ π_θ. The actual RARO algorithm (Algorithm 2) uses a shared-parameter relativistic critic with three labels (1,2,tie) and a tie reward. The gradient for the relativistic objective is never derived, and it is unclear how the closed-form optimal policy or the IRL gradient applies to a critic that compares two answers and outputs a tie. If RARO is intended as a practical heuristic, the paper should say so and justify the deviations empirically; as written, the 'principled IRL' framing overstates the theoretical support for the actual algorithm.
  2. [§3.3, §3.4, Table 5, Figure 12] The tie reward τ_pol=0.6, together with the observation in Figure 12 that the critic outputs 'tie' for ~70% of pairs at steady state, creates a potential degeneracy: the policy can earn substantial reward by producing outputs that reliably elicit ties rather than by matching expert quality. This concern is reinforced by the final Poetry win-rate of only 25% against expert poems at 7B (Table 3). The paper should analyze the resulting game's equilibria or, at minimum, provide evidence that the policy's reward is not dominated by tie exploitation (e.g., by reporting reward decomposition, or by showing the policy's outputs are judged as expert-like by an independent evaluator).
  3. [§5.3, Table 3, Appendix C.2] The Poetry Writing results — the only evidence for the non-verifiable setting — are evaluated solely by GPT-5 as judge, with no human baseline. LLM judges are known to have biases and can be gamed by style or length, and the paper does not report inter-judge agreement or human validation of the judge's preferences. Since the central claim of the paper is that RARO enables reasoning learning when verifiers are unavailable, the absence of any human evaluation is a load-bearing gap. At minimum, a small human study with several independent judges should be included, along with calibration of GPT-5 against human judgments.
  4. [Appendix D.2, Figure 14, Appendix B] The paper itself documents that without the replay buffer the policy 'cycles through a fixed set of strategies to hack the critic reward' and eventually collapses to tie outputs. This demonstrates that the learned critic is not a reliable quality signal under adversarial pressure. While the replay buffer stabilizes training in the reported runs, the paper does not address whether the same exploit could occur at test time or with the shared critic under distribution shift. The oscillations on Poetry (Appendix B, Figure 6) further show that the method has not fully converged in the non-verifiable setting. The paper should provide a more thorough analysis of the critic's reliability, e.g., by reporting accuracy of the critic against ground-truth labels on a held-out set (for verifiable tasks) and by comparing final policy outputs against expert quality with human judges.
minor comments (5)
  1. [Notation] The use of θ for both the policy in Algorithm 1 and the shared policy/critic in Algorithm 2 is confusing. Introduce distinct symbols for shared and separate parameters, or explicitly state the overloading.
  2. [Appendix C.4, Table 5] The tie rewards τ_pol and τ_crit and the loss weights λ_pol/λ_crit are introduced without any sensitivity analysis. Since the tie rewards directly affect the reward balance, a small grid or ablation over these values would help establish robustness.
  3. [Appendix C.3] The RL-Logit reward variants are described with vaguely motivated formulas (e.g., 'max(0.1*logπ_θ, -1.0)'). It would help to provide the exact reward definition used in the best-performing variant and to explain the choice of clipping.
  4. [Figure 8] The sample-efficiency figure lacks axis labels in the text description; please add explicit x- and y-axis labels and a legend.
  5. [References] The reference to GPT-5 (OpenAI, 2025) is given as an unreleased technical report; please include a version/date or, if not public, explain how the model was accessed. Also, the reference to 'Poetry Foundation' is incomplete.

Circularity Check

0 steps flagged

No constructed circularity: RARO's verifier-checked results and its KL-regularized IRL derivation are self-contained; noted weaknesses are robustness/external-validity concerns, not circular reductions.

full rationale

The paper's derivation chain is not circular by construction. Appendix A.1 starts from a standard KL-regularized reward-maximization objective and derives the closed-form optimal policy; Appendix A.2 differentiates the resulting log-likelihood; Appendix A.3 uses the log-derivative trick to express the reward gradient as a critic policy-gradient objective. None of these steps equates the claimed result to an input assumption. The later algorithm differs from the derived binary-critic setup: Section 3.4 shares parameters between policy and critic and Section 3.3 adds a tie option, and the paper does not derive a gradient for that relativistic objective. That is a theory-practice gap and an omitted-support issue, not a circularity. The central measured claims on Countdown and DeepMath are validated by exact ground-truth verifiers, so the main 'strong reasoning from demonstrations' result is externally checkable. The Poetry results rely on GPT-5 as judge without a human baseline, and Appendix D.2 documents a reward-hacking/cycling failure mode when the replay buffer is removed; these are robustness and evaluation-validity weaknesses, not reductions of the output to the input by construction. There are no load-bearing self-citations or imported uniqueness theorems. Therefore no significant circularity is present.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central algorithm depends on task-specific tie rewards and loss weights, plus several unproven approximations: the policy-gradient-to-optimal-policy approximation, the shared-parameter design, and the relativistic critic as a valid reward. No new physical or symbolic entities are introduced; the 'relativistic critic' is a model architecture choice.

free parameters (4)
  • τ_pol (policy tie reward) = 0.6 (Countdown, DeepMath, Poetry)
    Hyperparameter controlling reward when critic declares a tie for the policy; chosen per task (Table 5) to stabilize the adversarial game.
  • τ_crit (critic tie reward) = 0.55 (Countdown, DeepMath), 0.5 (Poetry)
    Hyperparameter controlling critic reward on ties; tuned per task.
  • λ_pol (policy loss weight) = 1/2 (Countdown), 1/9 (DeepMath), 1/3 (Poetry)
    Weight balancing policy vs critic objectives in the shared-parameter update; task-specific.
  • λ_crit (critic loss weight) = 1/2 (Countdown), 8/9 (DeepMath), 2/3 (Poetry)
    Weight balancing critic objective; task-specific, complements λ_pol.
axioms (5)
  • domain assumption The expert demonstrations are near-optimal under some underlying reward, so inverse RL is applicable (Section 3.1).
    All imitation-from-demonstrations methods assume expert data is informative; for Poetry, the original poems are treated as expert output without proving this.
  • ad hoc to paper The current policy π_θ is a sufficient approximation of the optimal KL-regularized policy π_θ⋆(ϕ) for the gradient update (Section 3.1, Algorithm 1).
    The theoretical gradient in Appendix A.2 uses the optimal policy, but the algorithm uses one GRPO step with the current policy; the approximation error is not analyzed.
  • ad hoc to paper A shared-parameter model can simultaneously serve as policy and critic and yield a meaningful adversarial game (Section 3.4).
    This design is justified only empirically by ablations; it is not derived from the IRL objective and introduces a self-referential loop.
  • ad hoc to paper The relativistic critic's pairwise judgment with a tie option provides a valid reward signal for the policy (Section 3.3).
    The tie rewards are new hyperparameters, and the gradient for the relativistic critic is not derived in the appendices.
  • domain assumption GPT-5's poetry evaluations reflect expert-level human quality (Section 4.1, 5.3).
    No human baseline is provided; the 'win-rate against expert poems' is measured by an LLM judge.

pith-pipeline@v1.3.0-alltime-deepseek · 26918 in / 10661 out tokens · 97954 ms · 2026-08-03T19:55:46.183672+00:00 · methodology

0 comments
read the original abstract

Training Large Language Models (LLMs) to reason often relies on Reinforcement Learning (RL) with task-specific verifiers. However, many real-world reasoning-intensive tasks lack verifiers, despite offering abundant expert demonstrations that remain under-utilized for reasoning-focused training. We introduce RARO (Relativistic Adversarial Reasoning Optimization), which learns strong reasoning capabilities from expert demonstrations alone via Inverse Reinforcement Learning. RARO sets up an adversarial game between a policy and a relativistic critic: the policy learns to mimic expert answers, while the critic aims to identify the experts among expert-policy answer pairs. Both the policy and the critic are trained jointly and continuously via RL, and we identify the key stabilization techniques required for robust learning. Empirically, RARO significantly outperforms strong verifier-free baselines across all evaluation tasks: +13.7% accuracy on Countdown (1.5B), +8.2% accuracy on DeepMath (7B), and +19.1% win-rate on Poetry Writing (7B) against expert poems. RARO also exhibits similar robust scaling trends as RL with verifiers. These results demonstrate that RARO effectively elicits strong reasoning performance from expert demonstrations alone, enabling robust reasoning learning even when task-specific verifiers are unavailable.

Figures

Figures reproduced from arXiv: 2511.21667 by Ivan Provilkov, Locke Cai, Max Ryabinin.

Figure 1
Figure 1. Figure 1: Overview of RARO. The method creates an adversarial game between a policy and a rel￾ativistic critic that share the same weights. The critic is rewarded for identifying the experts among (expert, policy) answer pairs, while the policy is rewarded for deceiving the critic. Additionally, the critic can declare tie, yielding stable rewards when the it is unsure. Both the policy and the critic are trained join… view at source ↗
Figure 2
Figure 2. Figure 2: Performance scaling. RARO con￾sistently improves with model size (1.5B to 7B) across both DeepMath and Poetry Writing [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Test-time Scaling (TTS) on Deep￾Math. Performance improves as the number of rollouts (N) increases for all model sizes. See Ta￾ble 9 in Appendix E for detailed data. Effective Test-Time Scaling. Another key advantage of RARO is that our learned critic enables natural Test-Time Scaling (TTS) to fur￾ther improve the policy’s performance. Specifi￾cally, our critic’s pairwise comparison setup al￾lows for a sin… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative examples for Countdown (1.5B), DeepMath (7B), and Poetry Writing (7B). For each task, we show the input (top) and the truncated reasoning and answer sampled from policies trained with RARO (bottom). See Appendix E for full examples as well as example critic inputs and outputs. plans. Specifically, in Poetry Writing, it decomposes the prompt into key themes (e.g., “sensory details”, “fragmented … view at source ↗
Figure 6
Figure 6. Figure 6: Poetry Writing (7B) Training Dynamics. During training, the policy and critic rewards oscillate on the Poetry Writing task (left). The validation reward similarly oscillates despite an overall upward trend (right) [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Countdown and DeepMath (1.5B) Training Dynamics. Stable policy and critic rewards during training for Countdown and DeepMath [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Sample Efficiency Comparison. Un￾der the same hyperparameters, our method is less sample-efficient than RLVR on Countdown. Sample Efficiency. While RARO achieves strong final performance, it can be less sample￾efficient than RLVR when applied to verifiable tasks. As shown in [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: RARO similarly degrades from 1.5B to 3B. D.2 ABLATION STUDIES Method DeepMath 1.5B accuracy (%) ↑ w/o critic reasoning 35.9 ± 1.9 w/o relativistic critic 36.9 ± 1.9 w/o tie option 38.6 ± 1.9 w/o replay buffer 35.4 ± 1.8 w/o shared LLM 39.4 ± 1.9 RARO 41.3 ± 1.9 [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: No Critic Reasoning. Without critic reasoning, the critic always outputs tie, pre￾venting the policy from learning [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: No Replay Buffer. Without a replay buffer, the training suffers from severe oscilla￾tions and eventual collapse. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Full qualitative example for the RARO policy for Countdown at 1.5B. [PITH_FULL_IMAGE:figures/full_fig_p029_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Full qualitative example for the RARO policy for DeepMath at 7B. [PITH_FULL_IMAGE:figures/full_fig_p031_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Full qualitative example for the RARO policy for Poetry Writing at 7B. [PITH_FULL_IMAGE:figures/full_fig_p032_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Qualitative example of the RARO critic for Countdown at 1.5B. [PITH_FULL_IMAGE:figures/full_fig_p033_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Qualitative example of the RARO critic for DeepMath at 7B. [PITH_FULL_IMAGE:figures/full_fig_p034_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Qualitative example of the RARO critic for Poetry Writing at 7B. [PITH_FULL_IMAGE:figures/full_fig_p035_20.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Learning to Reason by Analogy via Retrieval-Augmented Reinforcement Fine-Tuning

    cs.CL 2026-06 unverdicted novelty 6.0

    RA-RFT trains a retriever to rank contexts by expected reasoning benefit and uses the retrieved analogies inside reinforcement fine-tuning, yielding 7.1 and 2.8 point gains on AIME 2025 over GRPO for two Qwen3 models.

Reference graph

Works this paper leans on

34 extracted references · 3 linked inside Pith · cited by 1 Pith paper

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    (48 - 11) * (19 - 6) = 37 * 13 = 481 (too high)

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    Xueguang Ma, Qian Liu, Dongfu Jiang, Ge Zhang, Zejun Ma, and Wenhu Chen

    Notion Blog. Xueguang Ma, Qian Liu, Dongfu Jiang, Ge Zhang, Zejun Ma, and Wenhu Chen. General-reasoner: Advancing llm reasoning across all domains, 2025. URLhttps://arxiv.org/abs/2505. 14652. Andrew Y . Ng and Stuart J. Russell. Algorithms for inverse reinforcement learning. InProceedings of the Seventeenth International Conference on Machine Learning, IC...

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    (48 * 11) / (19 - 6) = 528 / 13 = 40.615 (too high)

  4. [4]

    48 / (19 - 11) + 6 = 48 / 8 + 6 = 6 + 6 = 12 (too low)

  5. [5]

    (48 - 11) * (19 / 6) = 37 * 3.167 = 115.167 (too high)

  6. [6]

    (48 - 19) * (11 - 6) = 29 * 5 = 145 (too high)

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    48 / (19 - 6) + 11 = 48 / 13 + 11 = 3.769 + 11 = 14.769 (too low)

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    11 * (48 / (19 - 6)) = 11 * (48 / 13) = 11 * 3.769 = 41.459 (too low)

  9. [10]

    (48 / (19 - 11)) * 6 = (48 / 8) * 6 = 6 * 6 = 36 (too low)

  10. [11]

    19 - (48 / (11 - 6)) = 19 - (48 / 5) = 19 - 9.6 = 9.4 (too low)

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    (48 - 11) + (19 - 6) = 37 + 13 = 50 (too low)

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    (19 - 11) * (48 / 6) = 8 * 8 = 64 (too high)

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    (19 + 11) - (48 / 6) = 30 - 8 = 22 (too low)

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    48 / (11 - (19 - 6)) = 48 / (11 - 13) = 48 / -2 = -24 (too low)

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    19 - (48 / (11 + 6)) = 19 - (48 / 17) = 19 - 2.764 = 16.236 (too low)

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    (48 / (19 - 6)) + 11 = (48 / 13) + 11 = 3.769 + 11 = 14.769 (too low)

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    29 DeepMath Find the equation of the normal line to the curve(x 2 +y 2)3/2 = 2xyat the point 1√ 2 , 1√ 2

    48 / (19 - (11 + 6)) = 48 / (19 - 17) = 48 / 2 = 24 (correct) The final answer is:\boxed{48 / (19 - (11 + 6))} </think> 48/(19−(11 + 6)) Figure 15: Full qualitative example for the RARO policy for Countdown at 1.5B. 29 DeepMath Find the equation of the normal line to the curve(x 2 +y 2)3/2 = 2xyat the point 1√ 2 , 1√ 2 . RARO Policy <think> To find the eq...

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    (48 / 6) + (19 - 11) = 8 + 8 = 16 (too low)

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    Differentiate the curve implicitly to find the slope of the tangent line at the given point

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    Write the equation of the normal line using the point-slope form. Let’s start with implicit differentiation. Given the equation: (x2 +y 2)3/2 = 2xy Differentiate both sides with respect tox: d dx (x2 +y 2)3/2 = d dx (2xy) Using the chain rule on the left side: 3 2 (x2 +y 2)1/2 · d dx (x2 +y 2) = 2y+ 2xdy dx Now, differentiatex 2 +y 2 with respect tox: 3 2...

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    Subtract 23:110−23 = 87 Answer 2 is incorrect. </think> Answer 1 Figure 18: Qualitative example of the RARO critic for Countdown at 1.5B. 33 DeepMath You are an expert mathematics critic whose goal is to compare two answers to a math problem and determine which one is correct. . . . Question: <question> Evaluate the double integral R R R x2 +y 2 dx dywher...

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