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Decoding the Critique Mechanism in Large Reasoning Models

Hoang Phan, Quang H. Nguyen, Hung T. Q. Le, Xiusi Chen, Heng Ji, Khoa D. Doan

arXiv:2603.16331v2cs.LG

TL;DR

The paper asks how LRMs detect and recover from errors when their visible reasoning remains corrupted. It injects arithmetic mistakes, analyzes latent representations, and finds a critique vector whose steering improves error detection and test-time scaling, with stated limitations on transfer and unconditional intervention.

  • Problem

    LRMs’ self-verification is not reliably understood, while long-chain error detection and self-correction remain limited.

  • Method

    The paper injects arithmetic errors into intermediate reasoning, compares thinking and final-answer correctness, and extracts a critique vector from feature-space differences.

  • Results

    55%–78% of R1 GSM8K-Error cases show correct final answers despite intact injected errors, and steering the critique vector improves error detection across models and benchmarks.

  • Takeaways & Limitations

    Hidden critique is a latent mechanism that can be interpreted and steered to control error detection and improve test-time scaling without extra training.

  • Takeaways & Limitations

    GSM8K-derived steering transfers weakly to AIME, while unconditional steering can add little signal or over-revise correct traces.

Abstract

from arXiv · show

Large Reasoning Models (LRMs) exhibit backtracking and self-verification mechanisms that enable them to revise intermediate steps and reach correct solutions, yielding strong performance on complex logical benchmarks. We hypothesize that such behaviors are beneficial only when the model has sufficiently strong ``critique'' ability to detect its own mistakes. This work systematically investigates how current LRMs recover from errors by inserting arithmetic mistakes in their intermediate reasoning steps. Notably, we discover a peculiar yet important phenomenon: despite the error propagating throughout the entire chain-of-thought (CoT) without any verbalized correction, the model still reaches the correct final answer after the thinking process finishes. This recovery implies the existence of an internal mechanism helping the model to detect errors and trigger self-correction, which we refer to as the \textit{hidden critique ability}. Building on feature space analysis, we identify a highly interpretable \textit{critique vector} representing this behavior. Extensive experiments across multiple model scales and families demonstrate that steering latent representations with this vector improves the model's error detection capability and enhances the performance of test-time scaling at no extra training cost. Our findings provide a valuable understanding of LRMs' critique behavior, suggesting a promising direction to control and improve their self-verification mechanism. Our code is available at: https://github.com/mail-research/lrm-critique-vectors.

1 Introduction

The paper argues that LRMs’ critique ability is weak and poorly understood, then reveals hidden self-correction and extracts a critique vector to improve error detection and test-time scaling.

  • Motivation: LRMs use backtracking and self-verification, but redundant reasoning and self-doubt can cause overthinking and degrade performance.The paper defines critique, self-critique, and self-correction as detecting and rectifying errors.
  • Hidden self-correction: Injecting arithmetic errors into intermediate reasoning exposes cases where corrupted reasoning is followed by a correct final answer.The model continues thinking after the injected error, enabling scalable recovery analysis without labeling every reasoning step.
  • Critique vector: Feature-space analysis identifies a critique vector as the activation difference between intervened recovery runs and standard runs.Logit lens analysis is used to validate the vector’s semantic meaning across model families.
  • Steering: Positive steering with the critique vector improves mistake identification, while negative steering worsens it.The vector is also used to control test-time scaling without additional training.

2 Related Work

Prior work studies representation steering, unfaithful reasoning traces, error detection, and test-time scaling, but persistent limits remain in reliable self-verification.

  • Representation Engineering in LLMs: Representation engineering extracts activation vectors to steer LLM behavior without fine-tuning, including applications to reasoning-model control.The cited work covers style, refusal, instruction-following, thinking-budget, and trace-editing control.
  • Faithfulness of Chain-of-Thought Reasoning: Reasoning traces can be unfaithful because models may omit true computations, generate misleading explanations, or produce decorative reasoning.This paper extends that line by locating corrupted-reasoning recovery in latent space and controlling it with a critique vector.
  • Error Detection and Correction: Existing error-detection and self-correction methods improve verification, yet models struggle with long traces and often require external guidance or known error locations.Prior approaches include condition verification, confidence–critique decomposition, and reinforcement learning.
  • Test-Time Scaling: Test-time scaling allocates more inference computation, but its gains depend on self-verification capacity and are not consistent across settings.Prior methods use reasoning-trace fine-tuning, “Wait” tokens, compute-optimal allocation, verification, tools, and reward models.

3 Uncovering Hidden Self-Correction

The paper injects arithmetic errors into LRM reasoning and compares internal thinking with final answers, revealing frequent hidden recovery across models and benchmarks.

  • 3.1 Error Injection: LRMs generate a reasoning trace between think tokens and then produce a final answer, allowing interventions to be inserted into the reasoning process.Prior prefilling methods represent the intervened continuation as a concatenation of inserted content and generated continuation.
  • 3.1 Error Injection: The study injects an arithmetic error such as 3 + 4 = 6, constructs GSM8K-Error and MATH500-Error, and compares thinking and answers with ground truth.This avoids expensive step-by-step supervision and provides a consistent benchmark across evaluated models.
  • 3.2 Hidden Recovery: The evaluation covers DeepSeek-R1 models at 8B, 14B, and 32B scales plus Qwen3-4B on both error-injected benchmarks.Outcome distributions classify correctness of internal thinking separately from correctness of the final answer.
  • 3.2 Hidden Recovery: A significant fraction of samples retain corrupted visible reasoning while producing correct final answers, a pattern termed hidden self-correction.The analysis focuses on the × Think ✓Answer outcome.
  • 3.2 Hidden Recovery: 55%–78% of R1 GSM8K-Error cases and 41%–59% of MATH500-Error cases show correct answers despite intact injected errors, while explicit corrections remain below 6%.These ranges are reported across R1 model scales.
  • 3.2 Hidden Recovery: Qwen3-4B explicitly backtracks in 42.7% of GSM8K-Error and 81.9% of MATH500-Error cases, while hidden recovery remains at 20.1% and 10.8%.The results support the presence of hidden self-correction across model families.
  • 3.3 Alternative Explanations: Recovery persists on synthetic data and when the question is masked or the answer must reference prior thinking, arguing against memorization or trace-bypassing explanations.The authors conclude that the pattern reflects hidden self-correction.

4 The Geometry of Critique Ability

The paper finds that injected reasoning errors reveal a hidden critique process: despite corrupted intermediate reasoning, models can recover correct final answers, while natural-chain recovery is rare. Feature-space analysis shows this recovery is linearly separable and supports extracting a critique vector whose steering modulates downstream critique behavior.

  • 4 The Geometry of Critique Ability: Injected errors expose hidden recovery: models can produce correct final answers despite incorrect intermediate reasoning, whereas natural-chain recovery is only 1.9% for R1-8B on GSM8K and below 1% elsewhere.The comparison motivates studying intervened runs rather than relying on naturally occurring self-correction.
  • 4 The Geometry of Critique Ability: Paired baseline and intervened runs use identical prompts and both produce correct final answers, while differing in whether intermediate reasoning is correct.The intervened condition combines an injected error with incorrect reasoning and a recovered final answer.
  • 4.2 The Linear Separability of Internal Thoughts: Linear probes achieve near-perfect AUROC across models and datasets, indicating that baseline and intervened activations remain linearly separable despite matching final answers.Table 2 evaluates AUROC and ECE on GSM8K in-distribution and MATH500 out-of-distribution at each model’s best layer.
  • 4.3 Extracting the Critique Vector: The critique vector is extracted as the difference between mean intervened and baseline activations, treating recovered intervened runs as positive examples.The vectors are computed over the training dataset at each layer.
  • 4.4 Steering with the Critique Vector: Steering adds a scaled critique vector to the post-MLP residual stream, with positive α amplifying and negative α suppressing self-critique before later layers generate the continuation.The modified activations propagate through subsequent layers, allowing the steering direction to shape downstream generation.
  • 4.5 Logit Lens Interpretation: Vocabulary projection associates the critique vector with reassessment tokens such as ‘Nope’ and ‘Wait’ and with Chinese adversative markers, suggesting critique behavior across languages.The interpretation uses top-ranked tokens from Qwen3-4B and R1-32B projections.

5 Experiments

Experiments evaluate critique-vector steering across error detection, injected-error recovery, test-time scaling, and standard benchmarks. Positive steering generally improves detection and recovery, while negative steering degrades them, with limited failure modes and scope boundaries.

  • Experimental setup: Experiments use Qwen3 and DeepSeek-R1 models across multiple scales, evaluating error detection and recovery on mathematics and logical-reasoning benchmarks.The setup includes ProcessBench, BIG-Bench Mistake, GSM8K-Error, MATH500-Error, and BIG-Bench Mistake.
  • Error detection: Positive steering with α = 1.0 improves ProcessBench error detection accuracy by 5% on all models.On BIG-Bench Mistake, Qwen3-4B rises from 52% to 56%.
  • Caveat: Positive steering can slightly harm correct accuracy in some scenarios, potentially by over-revising already-correct reasoning, but the overall F1 correlation remains positive.The authors describe this drop as insignificant.
  • Injected-error recovery: 77% baseline accuracy on GSM8K-Error rises to nearly 90% with positive steering, while negative steering reduces performance to slightly above 50%.Similar steering trends hold across R1-distilled models and MATH500-Error and BIG-Bench Mistake.
  • Test-time scaling: Appending “Wait” reliably improves injected-error recovery across models and datasets, while positive critique steering further boosts accuracy at every forcing iteration.Negative steering reduces performance, indicating that hidden critique complements rather than is replaced by explicit backtracking.
  • Standard benchmarks: Positive steering consistently improves standard-benchmark performance across all four models, whereas negative steering hurts performance.The same critique direction therefore transfers beyond the injected-error setting.
  • Scope boundary: Modest gains may reflect arithmetic-style derivation data and unconditional steering, which transfer weakly to knowledge-limited tasks and can over-revise saturated traces.The authors leave adaptive steering and broader transfer as future engineering work.

6 Conclusion

The paper identifies hidden critique behavior in LRMs and represents it with a critique vector that controls error detection and recovery. It concludes that this mechanism clarifies how test-time scaling can correct corrupted reasoning, while leaving origins, faithfulness, and broader applications open.

  • Conclusion: The paper identifies LRMs that silently recover from injected CoT mistakes and still produce correct final answers without verbalizing correction.This behavior is termed hidden critique behavior.
  • Conclusion: Feature analysis finds separable activations between intervened recovery runs and standard runs, enabling extraction of a critique vector validated through logit lens analysis.The vector is used to represent the hidden mechanism.
  • Conclusion: Steering the critique vector controls error detection across several benchmarks and models, and combines with test-time scaling to enhance correction performance.The conclusion presents critique ability as central to the observed recovery behavior.
  • Open questions: Future work should examine whether hidden critique emerges from pre-training or post-training and how it affects CoT faithfulness and alignment.The authors also identify verifier-based scaling, self-consistency, and self-correction prompting as open application directions.

B Analysis: Error-Injected Intervention Variants

The analysis tests whether recovery from corrupted CoTs depends on surrounding prompts or merely ignoring the trace. Recovery persists across intervention variants, including settings that force reliance on corrupted reasoning.

  • Intervention variants: Four variants alter context around the same injected error: Wait-once, Misprint, Question-masked, and Answer-prefix.They respectively test explicit backtracking, immediate recovery, reliance on corrupted CoT alone, and prompted trace review.
  • Intervention variants: The variants use R1-32B with the same injected arithmetic mistake, 3 + 4 = 6, after the thinking process begins.The shared question is a GSM8K example with ground truth $18.
  • Quantitative results: Recovery persists in every tested setting, with Misprint achieving the highest recovery rate and larger models retaining the phenomenon under Answer-prefix.Wait-once lowers GSM8K recovery but slightly raises MATH-500 recovery.
  • Ignoring the wrong CoT: Question-masked recovery remains close to baseline even when only the corrupted CoT is available, while Answer-prefix also preserves recovery with a slight decrease.These results test whether the model simply discards the corrupted trace and resolves the problem from scratch.

C Does Memorization Explain the Recovery Phenomenon?

The memorization analysis creates synthetic problems with altered numbers, names, contexts, and answers, then repeats the injected-error recovery protocol. Recovery remains substantial on these unseen examples, arguing against memorization of the original answers as the explanation.

  • Synthetic data construction: Synthetic examples modify numbers, names, and surface context while preserving a logically consistent step-by-step solution and ground-truth answer.Only logically consistent rewrites are retained before applying the corruption protocol.
  • Evaluation: The evaluation applies the intervened-local corruption protocol and measures the same × Think / ✓Final recovery rate on the synthetic dataset.The procedure compares the extracted thinking process and final answer with ground truth.
  • Results: 48.72% recovery for Qwen3-4B and above 68% for all three R1 variants remain on synthetic GSM8K examples.Rates stay close to original GSM8K results for the larger R1 models.
  • Interpretation: Because the synthetic questions, contexts, and final answers were altered and absent from training or distillation data, the results rule out memorization of the original answer as the explanation.The conclusion is specifically about memorization of the original answers.

D Additional Results of Logit Lens Interpretation

Logit Lens reveals model-specific token trajectories associated with self-critique, while layer-wise steering shows the strongest positive–negative separation in middle layers.

  • Layer-wise Steering: The positive–negative steering gap is most noticeable in middle layers, exceeding 38% at Layer 21 of Qwen3-4B.Early and late layers show minimal separation between positive and negative steering.

F Additional Results of Linear Separability of Internal Thoughts

Linear probes distinguish recovered from standard reasoning states across layers, with near-perfect separability but dataset-dependent calibration and a test of whether corruption style explains the signal.

  • Layer-wise Results: AUROC saturates near 1.0 across most network depth, while calibration improves from lower to middle layers.GSM8K is more stable and better calibrated than MATH500, whose ECE has higher variance and erratic spikes.
  • Layer-wise Results: Near-perfect AUROC and low ECE are achieved at several layers for GSM8K and MATH500.Figure 11 reports AUROC and ECE for GSM8K in-distribution and MATH500 out-of-distribution settings.
  • Separability Interpretation: The analysis asks whether probe separability reflects corrupted reasoning style rather than hidden critique behavior.The concern arises because baseline and intervened-and-recovered activations are highly separable despite both producing correct final answers.
  • Separability Interpretation: Two analyses test this concern by projecting unrecovered samples onto the pretrained probe and training a new probe on equally corrupted trajectories.Both analyses are designed to separate corruption-style effects from recovery-related differences.

G.1 Project intervened-and-unrecovered samples onto the pretrained probe

The pretrained probe responds strongly to successful recovery but not to unrecovered corrupted trajectories, supporting a recovery-specific hidden critique signal rather than generic CoT corruption detection.

  • Projection onto the Pretrained Probe: 98.6% or more of recovered trajectories are classified as recovered across models and unseen corruption variants.Unrecovered samples score 33.71%–69.96%, near the 50% binary baseline, despite sharing the same corrupted CoT style.
  • Fresh Probe on Equally Corrupted Trajectories: The fresh recovered-versus-unrecovered probe achieves AUROC above 0.88 on GSM8K-test and above 0.85 on MATH500-test.GSM8K-test ECE is below 0.08 for all models, while MATH500-test calibration is higher for R1-14B and R1-32B.
  • Fresh Probe on Equally Corrupted Trajectories: Recovered and unrecovered trajectories remain separable when both contain the same injected-error style.This rules out explaining the separability solely through corrupted reasoning style within the reported analysis.
  • Steering Validation: The critic vector outperforms a simple “wrong” token embedding as a steering direction across ProcessBench and BIG-Bench Mistake.Critic-vector steering improves both metrics at positive scale and degrades both at negative scale on every model, whereas the token baseline is inconsistent.
  • Cross-source Generalization: MATH-500-sourced vectors generalize to distinct ProcessBench problem sources, with positive steering improving and negative steering degrading error-detection metrics.Reported larger-model deltas include −16.15 Accuracy / −21.75 F1 for R1-14B and −20.15 Accuracy / −26.85 F1 for R1-32B at α=−1.0.

J.2.1 Error Detection

Qualitative cases show positive steering improves detection and recovery from subtle arithmetic or logical errors, while negative steering suppresses verification and reinforces erroneous premises.

  • Error Detection: Positive steering enhances subtle-error detection while avoiding false positives, whereas negative steering causes acceptance of erroneous premises without scrutiny.Figures 13–15 illustrate these opposing effects on ProcessBench and GSM8K examples.
  • Semantic Error Detection: Positive steering helps identify that “entire week” conflicts with assuming a five-day workweek.The steered model analyzes the specific wording rather than accepting the assumption as standard.
  • False-Positive Avoidance: Positive steering verifies that the unpurchased headphone set frees $44, while negative reasoning incorrectly treats the full $48 as available.The example concerns the counterfactual amount available for additional CDs.
  • Logical Error Detection: The baseline correctly revises the hotdog total from 36 to 54 after recognizing that the other half of the guests receives one hotdog each.The example identifies the proposed solution’s omission of those single hotdogs.
  • Arithmetic Error Recovery: In the allowance example, the baseline confirms the erroneous multiplication 5 × 8 = 30 instead of detecting it.The example shows self-verification reinforcing, rather than correcting, the arithmetic error.
  • Arithmetic Error Recovery: During the “Wait” phase, the model corrects $3+$2 from $6 to $5 and changes the lemon-cost answer from $18.75 to $15.Negative steering instead rationalizes and reinforces injected errors rather than correcting them.
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