{"id":"e92ae5c8-f609-40bf-bfb1-0c1a6ec54d51","arxiv_id":"2509.05602","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"CoPeD trains smaller language models with a correction task for wrong rationales and loss-based sample weighting, improving accuracy and rationale faithfulness on several reasoning benchmarks.","lead":"This paper proposes CoPeD, a training method that improves how small language models learn from large language models' chain-of-thought reasoning. It trains students to answer from correct rationales, correct erroneous ones, and weight examples by how well the rationale supports the answer.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's own Appendix D (Figure 7) shows the student cannot verify rationale correctness, so the claimed correctness-perception mechanism is not operational at inference; reported gains may come from the correction task and reweighting rather than from the claimed spurious-correlation mitigation.","rationale":"The reader's weakest_assumption and my independent reading converge on the same load-bearing concern: the method's central mechanism requires the student to perceive whether its rationale is correct, but Appendix D Figure 7 and the Limitations section explicitly show that the student cannot do this effectively. This directly affects whether the paper's stated contribution—'correctness perception distillation'—is actually realized. The concern is concrete, falsifiable, and supported by the authors' own analysis, which is a strong reason to take it seriously. I also considered the methodological issue that hyperparameters (temperature τ in Table 4 and task-balance α in Table 5) appear to be selected using the reported test sets, which could inflate the headline numbers. That is a real reproducibility problem, but it is secondary: even if the numbers were obtained honestly, the mechanism would still be questionable. The empirical gains might survive the loss of the perception mechanism because the correction task and reweighting could improve performance through other channels, so the right verdict is CONDITIONAL rather than REJECT. The authors should narrow the claim to what is demonstrated, release code and data, report variance, and adopt held-out validation. The concrete oracle-routing test would settle whether the perception mechanism contributes at all. My read does not change the reader's conditional verdict, so I recommend UNCHANGED.","tokens_in":19034,"tokens_out":4020,"duration_ms":37771,"concrete_test":"Run CoPeD-TL on BBH-test in three inference modes: (1) default, where the model generates its own rationale and status; (2) oracle-routed, where GPT-4 (or the teacher) labels each generated rationale as supporting the final answer, and correct rationales are used for answer prediction while erroneous ones are passed through the correction task before re-prediction; and (3) random-status, where the status token is chosen randomly. If oracle-routed accuracy is substantially higher than default, the student's self-verification is the bottleneck and the claimed perception mechanism is not operating. If default matches oracle-routed accuracy, the student has internalized correctness information despite Figure 7, and the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the correctness-aware task setting enables the student to 'predict answers based on correct rationales and revise them when they are incorrect.' For this mechanism to function at inference, the student must be able to determine whether a generated rationale is correct. Appendix D (Figure 7) directly tests this: it compares using the rationale status string as input versus as output and finds 'no significant performance difference between these three settings,' and the Limitations section admits that 'the student model currently struggles to effectively validate whether the rationale derived from its reasoning is indeed correct.' This is not a peripheral caveat; it undercuts the core contribution named in the title and abstract. Without self-verification, the inference-time routing described in Section 2.2 cannot be executed by the student, and the observed gains—on LLaMA2-7B, where the headline 3.0% advantage over CasCoD appears—may be attributable to the auxiliary rationale-correction loss and the correctness-aware sample weighting rather than to the perception-and-routing mechanism. The Mistral-7B results (CoPeD-TL 61.2% vs. CasCoD 61.6%) further weaken the generality of the claim. The method may still be a useful distillation recipe, but the paper's central mechanistic story is unsupported by its own evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes CoPeD, a distillation method for small language models that trains the student on two tasks: answer prediction conditioned on a teacher-provided correct rationale, and correction of teacher-provided erroneous rationales. A second component, the Correctness-Aware Weighted Loss, reweights training examples using the student's own rationale and answer losses, with a temperature parameter. Experiments on BBH as the in-distribution set and BB-sub, AGIEval, and ARC as out-of-distribution sets compare CoPeD with several CoT distillation baselines on LLaMA2-7B, Mistral-7B, TinyLLaMA, and LLaMA2-13B. The paper reports that LLaMA2-7B with CoPeD-TL reaches 52.9% average accuracy, outperforming CasCoD by 3.0%, and that CoPeD improves faithfulness and soundness as judged by ChatGPT and GPT-4.","tokens_in":19346,"tokens_out":4410,"duration_ms":42273,"significance":"If the results are reproducible, CoPeD is a useful distillation recipe: the gains on LLaMA2-7B are consistent across IND and most OOD benchmarks, the model-size and data-size ablations are informative, and the use of two LLM evaluators for faithfulness and soundness is a strength. The paper also promises code and data release. At the same time, the paper's central mechanistic claim is not supported by its own evidence: the student model is shown to be almost incapable of verifying rationale correctness, so the claimed inference-time routing between 'answer from correct rationale' and 'revise erroneous rationale' cannot be operational. The practical value therefore rests on the auxiliary correction task and sample reweighting, not on the correctness-perception mechanism advertised in the title and abstract.","major_comments":[{"comment":"The inference-time mechanism that motivates the paper is not operational, as the authors' own analysis shows. Section 2.2 describes routing the student to answer from a correct rationale or to revise an erroneous rationale, but at inference the model is not given a correctness label. Appendix D (Figure 7) reports 'no significant performance difference' between using the rationale status string as input and as output, and the Limitations section states that the student model 'currently struggles to effectively validate whether the rationale derived from its reasoning is indeed correct.' Since the student cannot verify correctness, the claimed 'predict answers based on correct rationales and revise them when they are incorrect' mechanism cannot be executed at inference. The reported gains may come instead from the rationale-correction loss and the sample weighting, not from correctness perception. This is a load-bearing issue for the central claim and requires either an inference-time verification component or a substantial reframing of the contribution.","section":"§2.2, §3.3, Appendix D (Figure 7), Limitations"},{"comment":"The in-distribution result is inflated by hyperparameter selection on the test set. Table 4 in Appendix A tunes the temperature τ on BBH-test, and Table 5 selects α by average performance that includes BBH-test; the same BBH-test is then reported as the IND result in Table 1, including the headline 69.8% versus CasCoD's 60.2%. Because both hyperparameters are chosen to maximize the reported test metric, the IND comparison is not a fair evaluation and the 9.6% IND improvement is not a valid out-of-sample claim. The authors should use a held-out validation split for selection or report the selection procedure and its effect on the comparison.","section":"Appendix A (Tables 4 and 5) and Table 1"},{"comment":"The correctness-aware weighting is self-referential and does not measure rationale-answer alignment. In Eq. (4), the weight w_i is computed from the student's own rationale loss and answer loss, and Algorithm 1 shows that these are cross-entropy losses on the student's generated outputs. A sample with low student loss therefore receives high weight, so the weight represents the student's current ease with the sample, not the degree to which the rationale supports the answer, and it is not an oracle correctness label. The claim that this weighting 'directs the model to focus more on samples where the rationale offers stronger support for the correct answer' is not supported by the definition of w_i. The authors should either provide evidence that low-loss samples correspond to genuinely faithful rationales or reframe the weighting as a self-paced curriculum rather than correctness awareness.","section":"§2.3, Eq. (4), Algorithm 1"},{"comment":"The cross-model generalization claim is weak without variance estimates. For Mistral-7B-v0.2, CoPeD-TL averages 61.2% versus CasCoD's 61.6%, and on ARC-C it is 68.6% versus 75.5%, a 6.9-point deficit. No error bars, multiple seeds, or significance tests are reported for any model. The paper's phrasing that Mistral 'delivers consistently competitive performance' is not enough to support a general claim of effectiveness, and the difference between LLaMA2-7B and Mistral-7B may reflect noise rather than method behavior. The authors should add seeded runs with standard deviations or otherwise establish that the main comparisons are stable.","section":"§3.3, Table 1"}],"minor_comments":[{"comment":"The text says 'we following Dai et al. (2024a) and use its provided prompt templates to guild the teacher'; 'guild' should be 'guide', and the sentence should be rewritten for grammatical correctness.","section":"§2.1"},{"comment":"The method name is written inconsistently as 'CoCPerD' in Figures 3, 6, and 8 and in the Appendix D text, while the rest of the paper uses 'CoPeD'. Please unify the terminology.","section":"Figures 3, 6, 8 and text"},{"comment":"The implementation section says 'We use LLaMA-7B (Touvron et al., 2023) as the base student model', but the tables and the rest of the paper refer to 'LLaMA2-7B'. Also, Table 1 header says 'LLaMA2-7B' while the student row in the table maybe refers to a different version; please confirm the exact model used.","section":"§3.2"},{"comment":"The notation in Eq. (4) is underspecified: the softmax is taken over i, but no domain (batch, dataset) is stated, and the sample-wise losses L_r and L_a are not defined formally as functions of the model outputs and targets. Please clarify.","section":"Eq. (4)"},{"comment":"The table caption contains a footnote marker '♠' and the text says 'the results borrowed from Dai et al. (2024b)', but no '♠' appears in the table body. Please either add the marker to the appropriate rows or remove the footnote.","section":"Table 1"},{"comment":"Some references are incomplete: 'Hu et al.' for LoRA has no year, 'Guo et al.' for BIG-Bench has no full title, and 'Li et al.' for Chain-of-Knowledge has no year. Please provide complete reference entries.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper contains a strong practical distillation recipe, but the central mechanism—correctness perception at inference—is explicitly falsified by the authors' own Appendix D. The editor may want to require the authors to either implement and evaluate an actual inference-time verification step or substantially revise the title, abstract, and framing to describe the contribution as learning from teacher-labeled corrections with self-paced weighting. Without such a change, the paper's main claim is likely to be judged misleading by readers. The hyperparameter tuning on the reported test set is a separate but important integrity issue that should be fixed before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a decent distillation recipe paper whose headline mechanism does not hold up against its own appendix. The LLaMA2-7B gains look real, but the \"correctness perception\" the title sells is not something the student can actually do at inference.\n\nWhat is new: the specific combination of a dual task (answer from correct rationale; revise erroneous rationale) with a loss-based sample weight computed from the student's own rationale and answer losses. Each component exists in prior work, but this integration is new, and the ablations show both pieces contribute. That is a legitimate training recipe.\n\nWhat the paper does well: it reports the negative result that matters. Appendix D, Figure 7 compares using the rationale-status string as input versus output and finds no significant difference; the Limitations section says plainly that the student cannot effectively validate rationale correctness. The paper also shows the correction task helps on its own (Figure 6) and that, under perfect verification, correcting erroneous rationales fixes 15–30% of earlier errors (Figure 8). That kind of honest self-assessment is rare and useful.\n\nSoft spots, in proportion:\n\n1. The claimed mechanism is not operational. The abstract says the model predicts answers based on correct rationales and revises incorrect ones. At inference, it has no way to tell which rationale is correct. So the reported gains on LLaMA2-7B are more plausibly attributable to the auxiliary correction task and the reweighting than to the \"correctness perception and routing\" described in Section 2.2. This is not a minor caveat; it is the title's central claim. The paper should be reframed as a distillation recipe with a correction task and a sample-weighting scheme, not as a mechanism that perceives correctness.\n\n2. Mistral-7B results are mixed: CoPeD-TL averages 61.2% versus CasCoD's 61.6%, with a 6.9-point deficit on ARC-C. The headline 3.0-point gain over CasCoD is specific to LLaMA2-7B.\n\n3. No seeds or error bars, and α and τ are tuned on BBH-test, which is then reported as the IND result. That inflates the IND comparison. OOD numbers are less affected, but variance still matters.\n\n4. No code or data released (promised on publication). For a recipe paper, this matters.\n\nNone of these make the paper worthless. The recipe is novel, the ablations are informative, and the negative result on self-verification is actually a useful data point for the distillation community. But the claims need to be narrowed from mechanism to recipe, the artifacts need to be released, and the hyperparameter selection needs a held-out split.\n\nRecommendation: send it to a serious referee as a conditional. The paper deserves engagement, but it should not be accepted with the current framing.","headline":"A useful and honestly reported distillation recipe whose stated correctness-perception mechanism is contradicted by the paper's own Appendix D—worth refereeing as a conditional.","tokens_in":19901,"tokens_out":2938,"would_cite":false,"duration_ms":27039,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A distillation recipe that trains small language models to answer from correct rationales and correct erroneous ones raises average accuracy by 3.0 points over the strongest baseline on reasoning benchmarks.","keywords":["chain-of-thought distillation","knowledge distillation","small language models","spurious correlations","rationale correctness","faithfulness","out-of-distribution generalization","reasoning"],"falsifier":"Permuting the status tokens during training while holding everything else fixed would settle the claim: if accuracy stays near 52.9%, the correctness signal is not what drives the gain. A second comparison that removes the correction task while keeping the weighted loss would show whether the revision objective is the active ingredient.","tokens_in":18824,"feed_emoji":"🧠","tokens_out":7305,"duration_ms":58830,"temperature":0.7,"pith_summary":"Small language models trained on teacher-generated chain-of-thought data can latch onto shortcuts between the question and the final answer, ignoring whether the reasoning actually supports the answer. This paper proposes CoPeD, a distillation recipe that gives the student two tasks: answer from a rationale marked correct, and rewrite a rationale marked wrong. A correctness-aware weighted loss then down-weights training examples whose rationale and answer are poorly aligned. On BIG-Bench Hard and out-of-distribution reasoning sets, the paper reports that a LLaMA2-7B student reaches 52.9% average accuracy, 3.0 points above the strongest baseline, with improved faithfulness and soundness of generated rationales. The practical stakes are that small models could inherit reasoning ability without inheriting the teacher's unreliable rationales.","feed_headline":"Small models gain 3.0 points by trusting only correct rationales","feed_subtitle":"Dual-task distillation lifts LLaMA2-7B to 52.9% average accuracy and raises rationale faithfulness on unseen benchmarks","key_machinery":"The machinery has two coupled parts. The first is a correctness-aware task setting: status strings 'the rationale is right' and 'the rationale is wrong' route the student either to answer prediction conditioned on the rationale or to rationale correction, thereby cutting the direct question–answer shortcut and adding a learn-from-mistakes objective. The second is the Correctness-Aware Weighted loss, whose per-sample confidence weight $w_i = \\operatorname{softmax}_i\\left(-\\frac{L_r^{(i)} + L_a^{(i)} + |L_r^{(i)} - L_a^{(i)}|}{\\tau}\\right)$ is used to up-weight examples where the rationale and answer losses are both low and aligned, and to down-weight noisy or contradictory ones. The status-token gating is the nominal carrier of the spurious-correlation argument; the weighting term is what makes the supervision robust to the heuristic correctness labels.","core_discovery":"The central claim is that reasoning distillation fails when the student learns to predict answers from rationales without checking whether the rationale is right, so CoPeD inserts that check as a training signal. For each question the teacher supplies both a correct and an erroneous rationale, labeled by whether the teacher's predicted answer matches the ground truth. The student is trained, under separate status tokens, either to produce the answer from the correct rationale or to rewrite the erroneous rationale into the correct one. A second component, the Correctness-Aware Weighted loss, assigns each sample a softmax weight from the combined rationale and answer losses plus their discrepancy, so well-aligned examples dominate training. The paper reports that this dual-task, reweighted recipe outperforms prior distillation baselines on in-domain BBH and on out-of-distribution sets, raises faithfulness and soundness scores, and improves accuracy even at 1.1B scale and with 12.5% of the training data.","pith_inferences":["Because the paper's own Section 6 and Appendix D show that the student cannot reliably verify its rationale, the reported gains are unlikely to come from the claimed answer-from-correct-revise-wrong gating; they more likely come from the correction task and the sample reweighting.","A direct test would permute the status tokens during training: if accuracy holds near 52.9%, then correctness perception is not the active ingredient and CoPeD reduces to weighted multi-task distillation.","The gating mechanism might become operational in a larger student or one paired with an external verifier; the same recipe at 13B or with a verification model could show a larger effect than the 7B experiments do."],"forward_implications":["On LLaMA2-7B, CoPeD-TL averages 52.9% across BBH-test, BB-sub, AGIEval, ARC-E, and ARC-C, beating CasCoD by 3.0 points overall and by 9.6 points on the in-domain BBH-test.","Rationale faithfulness and soundness both improve: GPT-4-averaged faithfulness goes from 77.4% with CasCoD to 81.2%, and soundness from 64.9% to 70.2%.","Using only 12.5% of the BBH-train data, CoPeD-TL beats CasCoD by 16.8% on BBH-test and by 9.4% on BB-sub, indicating strong data efficiency.","At 1.1B scale, the distilled model reaches 113.1% of the teacher's in-domain accuracy, suggesting the recipe is most valuable in low-resource settings."],"supporting_citations":[{"why":"Supplies the prompt templates and dual chain-of-thought extraction used to obtain correct and erroneous rationales from the teacher.","marker":"Dai et al., 2024a"},{"why":"Defines CasCoD, the strongest baseline, and the BBH train/test split and filtered OOD sets used for evaluation.","marker":"Dai et al., 2024b"},{"why":"Motivates the spurious-correlation problem, supplies the faithfulness and soundness evaluation style, and provides the SCOTT baseline.","marker":"Wang et al., 2023a"},{"why":"Defines standard chain-of-thought distillation, the primary baseline the method improves on.","marker":"Magister et al., 2023"},{"why":"Provides the BIG-Bench Hard in-domain benchmark.","marker":"Suzgun et al., 2023"},{"why":"Provides the ARC-Easy and ARC-Challenge out-of-domain evaluation sets.","marker":"Clark et al., 2018"}],"fun_headline_variants":["CoPeD makes small models check rationales before answering","Correctness-aware weighting fixes spurious answer shortcuts","Small models + CoPeD: 3.0 points from rationale self-check","CoPeD lifts OOD reasoning by 3.0 points via rationale filtering","Reweighted CoT distillation lifts small-model accuracy 3 points"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the student can learn to distinguish correct from erroneous rationales and act on that distinction at inference time, but the paper's own Section 6 and Appendix D show that the status string has no significant effect whether used as input or output, so this premise is not met in the reported experiments.","fun_headline_variants_meta":{"raw":{"variants":["CoPeD makes small models check rationales before answering","Correctness-aware weighting fixes spurious answer shortcuts","Small models + CoPeD: 3.0 points from rationale self-check","CoPeD lifts OOD reasoning by 3.0 points via rationale filtering","Reweighted CoT distillation lifts small-model accuracy 3 points"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001154,"raw_usage":{"total_tokens":4802,"prompt_tokens":988,"completion_tokens":3814,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":604,"completion_tokens_details":{"reasoning_tokens":3723}},"tokens_in":604,"tokens_out":3814,"duration_ms":24236,"temperature":1.0,"reasoning_tokens":3723,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:21:47.124937+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Permuting the status tokens during training while holding everything else fixed would settle the claim: if accuracy stays near 52.9%, the correctness signal is not what drives the gain. A second comparison that removes the correction task while keeping the weighted loss would show whether the revision objective is the active ingredient.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines standard chain-of-thought distillation, the primary baseline the method improves on."}],"review_version":2}