{"id":"c27470f2-b003-4caa-b999-4841bc80f223","arxiv_id":"2504.13500","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Training on reasoning traces with tree-search-generated prejudge hints improves accuracy on math and logic benchmarks by roughly 2 to 4 points over CoT and Self-Refine baselines.","lead":"This paper proposes adding 'prejudge' hints, short warnings inserted before a reasoning step that might go wrong, to the training data of language models. The authors report accuracy gains of a few points on competition math and logic benchmarks with 7B and 32B models.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'dead-end' labels that define prejudge nodes are sampled, not proven: a child marked v=0 under the 1024-path/14-step budget may simply be under-searched, so the process-prejudge training data may be built on false premises.","rationale":"The reader and I agree on the weakest spot: the prejudge label is the causal heart of the method, and without reliable dead-end detection the synthesized rationales are not instances of 'process prejudge' as defined in Section 3.1. The budget details (1024 paths, 14 steps) and the use of a 14B generator make the false-negative risk concrete rather than speculative. I also note that the reader's strongest_claim overstates Table 1: PBT#1 loses to Self-Refine#1 on SVAMP for 7B and on GSM8K and GAOKAO for 32B. That is a separate presentation problem, but it does not change the primary concern. Since the reader already conditionalizes on this concern, my verdict is unchanged.","tokens_in":19535,"tokens_out":11741,"duration_ms":101765,"concrete_test":"Sample 200 Phase-1 queries (e.g., 100 from MATH and 100 from AIME/SVAMP) and re-run the Appendix B.1 dynamic tree search with the same 14B generator and 72B judger, but with max step length 30 and max paths 4096 instead of 14 and 1024. For every node labelled v=0 under the original budget, check whether any leaf in the expanded search is judged correct. If more than 5% of v=0 labels flip to v=1, the 'no path' premise behind Eq. 2 is budget-dependent. Complementary check: take the original 14-step leaves that were judged incorrect and continue them for up to 16 more steps with the same model; measure the fraction that reaches a correct final answer.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.1 defines a prejudge node through Eq. 2 using value scores v(zk) from Eq. 1, where a leaf is 1 only if the LLM judger accepts the final answer. A child gets v=0 when no leaf in its sampled subtree is judged correct. The sampling budget is fixed at 1024 total paths (Appendix B.1) and 14 steps (Section 4.1), and the tree is generated by Qwen2.5-14B-Instruct. Thus 'no path toward the correct answer' is operationalized as 'no path found by a 14B model within 14 steps and 1024 paths.' Any correct continuation that is longer than the budget, or that the 14B generator fails to discover, is labelled a dead end. Eq. 2 then marks the parent as a prejudge node, and the critic prompt (Appendix C.3) is asked to produce an error analysis for a path that may simply be incomplete. The Phase-1 rationales are built on these labels and the Phase-2 distillation propagates them at scale. If a material fraction of these v=0 children are merely undersampled, the prejudge training data contains positions that are not true prejudge nodes, and the reported gains may reflect extra verification or length tokens, or the suppression of viable paths, rather than genuine prejudgment. The paper provides no sensitivity analysis showing that labels are stable under larger budgets. Note also that Table 1 does not actually support the text's claim that PBT consistently outperforms Self-Refine on all benchmarks (e.g., 7B SVAMP 90.3 vs 90.7; 32B GSM8K 92.4 vs 92.6 and GAOKAO 78.6 vs 79.4), so the empirical claim is overstated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces 'process prejudge' (PBT), a training-time strategy that conditions LLM reasoning on anticipatory error-avoidance hints. The authors define a prejudge node as a step whose next-step children contain at least one child with no sampled path to a correct answer (Eqs. 1-2). They synthesize rationales containing such prejudge hints via a dynamic tree-search framework in which a single LLM (Qwen2.5-14B-Instruct) generates thoughts, judges answers, critiques incorrect paths, and verifies corrected steps. A two-phase post-training recipe (Phase 1: cold-start SFT on roughly 39k searched rationales from about 21k queries; Phase 2: self-distillation with the cold-start model on roughly 195k rationales, followed by SFT and optionally GRPO/DPO RL) is evaluated on eight reasoning benchmarks with Qwen2.5-7B and 32B backbones. Table 1 reports PBT#1 outperforming CoT on all sixteen benchmark/backbone pairs and improved averages over Self-Refine, with Phase-2 and RL variants adding further gains; ablations (w/o Verify, w. CoT, number of prejudge hints, pass@N with/without hints) are used to attribute the gains.","tokens_in":19973,"tokens_out":20970,"duration_ms":171627,"significance":"If the reported gains hold, PBT is a useful contribution to the growing self-training and self-correction literature: it proposes a concrete, automated way to inject anticipatory error-avoidance into rationales, it is backbone-agnostic, and the two-phase recipe produces meaningful average gains on small open models (e.g., +3.5 and +2.4 points over CoT for the 7B and 32B backbones). The paper's strengths include released code and data, broad benchmark coverage, internal ablations (w/o Verify, w. CoT, hint-count, RL), and a separate analysis showing that the synthesized prejudge hints improve pass@N when given at test time. The significance is moderated, however, by the fact that several per-benchmark deltas are within a few questions of one another, by the unsupported claim of universal superiority over Self-Refine, and by the reliance on budget-relative 'dead-end' labels without sensitivity analysis. The conceptual distinction between prejudging and reactive correction is interesting and worth validating with the strengthened evidence requested below.","major_comments":[{"comment":"The definition of a prejudge node ('no paths toward the correct answer') is operationalized only within the sampled subtree built by Qwen2.5-14B-Instruct under a 14-step horizon and a 1,024-path budget. A child marked v=0 in Eq. (1) means 'no correct leaf was found within budget,' not 'no correct continuation exists,' so Eq. (2) can mark as prejudge nodes positions whose children are merely undersampled or beyond the horizon, and the error analysis and hints of Section 3.2 are then built on those possibly false premises. The paper provides no sensitivity analysis showing label stability under larger budgets or a longer horizon. I ask for (i) an explicit restatement that all 'no path' claims are budget-relative; (ii) a label-stability study (e.g., the fraction of v=0 children that become v=1 as the path budget is doubled or the horizon is extended); and, if labels flip materially, a re-synthesis or restriction to stable prejudge positions. Since the generator (14B) is weaker than the trained 32B model, a correct branch that the 14B fails to discover will also be mislabeled as a dead end.","section":"§3.1, Eqs. (1)-(2); §4.1; Appendix B.1"},{"comment":"SVAMP is listed as a Phase-1 training source (700 queries sampled, 700 trained) and also appears as one of the eight evaluation benchmarks in Table 1, with no statement that the 700 training queries were excluded from the SVAMP evaluation set. Under the standard usage of SVAMP as a 1,000-question test set, up to 70% of the evaluation set could have been seen during SFT, which would make the SVAMP rows in Table 1 (and the all-eight-benchmarks claim) uninterpretable. Please clarify the exact split used, remove the 700 training queries from the evaluation set (or re-evaluate on a disjoint subset), and report the resulting SVAMP numbers for all methods.","section":"Table 4 and Table 1 (SVAMP)"},{"comment":"The sentence 'PBT consistently outperforms CoT training and Self-Refine across all benchmarks using both 7B and 32B backbones' is contradicted by Table 1 itself: Self-Refine#1 is higher than PBT#1 on 7B SVAMP (90.7 vs 90.3), 32B GSM8K (92.6 vs 92.4), and 32B GAOKAO (79.4 vs 78.6). The claim should be weakened to PBT being better on average and better than CoT on all sixteen benchmark/backbone pairs; the three exceptions should be acknowledged, and the Abstract's 'significantly enhance' should be made consistent with the per-benchmark results.","section":"§4.4"},{"comment":"No error bars, significance tests, or random-seed information are reported, and several headline deltas are at the resolution of the benchmark. For example, AIME-2024 contains 30 problems, so 13.3% vs 6.7% is 4 vs 2 correct answers; TheoremQA and GAOKAO deltas of roughly 1-2 points correspond to a handful of questions. The average gains of 3.5 and 2.4 points aggregate these small per-benchmark differences. Please report variance over at least three seeds (or bootstrap confidence intervals over sampled responses) and indicate which per-benchmark differences exceed chance; the consistent sign of the PBT-vs-CoT differences is informative, but the magnitude claims need statistical support.","section":"Table 1 and Table 2"},{"comment":"The training data used for the CoT and Self-Refine baselines is not described: no query counts, rationale counts, or sampling procedure are given. Since the PBT pipeline synthesizes a large corpus (234k rationales), the PBT-vs-CoT comparison could conflate the prejudge format with data volume. Please report the dataset sizes for all baselines and add a data-matched control (identical query set and rationale count, plain CoT format); the 'w. CoT' row in Table 1 suggests such controls are feasible.","section":"§4.3"}],"minor_comments":[{"comment":"Section 4.3 cites the Self-Refine baseline as '(Kumar et al., 2024)', but the described behavior (iterative refinement with feedback) is the Self-Refine method of (Madaan et al., 2023); the reference list's Kumar et al. (2024) entry is a different method. Please correct the attribution.","section":"§4.3 / References"},{"comment":"The Abstract states that the work 'construct[s] 234k data', while the body reports approximately 39k Phase-1 and 195k Phase-2 rationales and Table 4's #Train query counts sum to about 110k. Please state explicitly that 234k refers to rationales rather than queries, and clarify how the #Search/#Train query counts relate to the final rationale counts.","section":"Abstract / Table 4"},{"comment":"Section 5.3 does not state whether the five sets D_k (k=1,...,5) contain the same queries with k prejudge hints or contain different sampled queries. If the queries differ across sets, the upward trend in Figure 4 may reflect query difficulty rather than hint count; please clarify the construction and report run-level variance for the SFT accuracies.","section":"§5.3"},{"comment":"The sentence '...the more likely the model will make prejudges, which can better guide the model to make incorrect prejudges before thinking' appears garbled; the intended meaning is presumably that more prejudge hints guide the model to avoid the anticipated mistakes.","section":"§5.3"},{"comment":"Please fix the typos: 'Monto Carlo Tree Search' should be 'Monte Carlo Tree Search' (Introduction), and 'prejudge before use' (Introduction and Section 5.4) should be 'prejudge before think' to match the title.","section":"§1, §5.4"},{"comment":"State explicitly whether the LLM-as-a-judger inside the dynamic tree search is the same Qwen2.5-14B-Instruct model used for the other three roles, with Qwen2.5-72B-Instruct used only for final benchmark evaluation; this would make the Abstract's 'requires only one LLM' claim precise and reproducible.","section":"§4.2 / Figure 5"},{"comment":"Define Pass@N precisely (empirical fraction correct at N sampled completions versus a pass@k estimator), and report the completion temperature, the seed, and the variance across the 2,000 queries for the curves in Figure 3.","section":"§5.2 / Figure 3"},{"comment":"The symbol N denotes the number of repeated samples per layer in tree search (Section 2.2) and also the self-consistency count (N=32) in Phase 2 (Section 4.1); please use distinct symbols for these two quantities to avoid confusion.","section":"§2.2 / §4.1"},{"comment":"Please report the total compute of the data-synthesis pipeline (e.g., GPU-hours for the 21k-query tree search and the Phase-2 distillation), since the per-query cost ('about 5 minutes') alone does not allow cost-based comparison with existing self-training methods.","section":"Limitations"}],"recommendation":"major_revision","confidential_remarks":"The SVAMP training/evaluation overlap is the most consequential issue; I recommend verifying against the released code and data whether the 700 training queries were excluded from evaluation, as this affects one of the eight benchmarks in the headline comparison. The Self-Refine citation mismatch in §4.3 (Kumar et al. 2024 for a method that is Madaan et al. 2023) may reflect broader attribution sloppiness worth checking during revision. The paper fits the journal's scope and the core idea is publishable if the budget-relative 'dead-end' labels and the statistical support are addressed. I did not find a circularity problem: the benchmark judgments use external ground truth, and the Phase-2 self-distillation is a standard self-training step, though its biases should be discussed in the revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the prejudge-node idea is new and the pipeline is clearly described, but the evaluation is muddier than the abstract claims. The paper defines a prejudge node as a step with a child that has no path to the correct answer, then uses tree search to find such nodes, generate hints, verify them, and distill the rationales into SFT and RL. That mechanism is not in the prior self-refine/verification literature, and the single-LLM dynamic tree-search pipeline is a legitimate engineering contribution. The code and data release helps reproducibility.\n\nWhat is good: the method beats CoT and Self-Refine on average by 3.5 and 2.4 points (7B/32B), and the w/o Verify ablation points to the verification component mattering. The two-phase SFT+RL scaling is standard but executed cleanly. The case studies look plausible.\n\nThe soft spots are real. First and most important: the benchmark suite is largely contaminated. GSM8K, MATH-500, AQuA, SVAMP, and AIME-2024 all come from the same sources used to build the training data (Table 4). So those columns are not independent. The only clean benchmarks are TheoremQA, GAOKAO-2023, and GPQA-Diamond; gains there are smaller but still mostly positive. Second, the 'consistently outperforms Self-Refine' claim in Section 4.4 is factually wrong: 7B SVAMP 90.3 vs 90.7, 32B GSM8K 92.4 vs 92.6, and 32B GAOKAO 78.6 vs 79.4 all go the other direction. It is a 3-of-16-cell point, but the text overstates. Third, the dead-end labels in Eq. 1-2 are sampled under a fixed 1024-path/14-step budget with a 14B generator; a child marked v=0 may be under-searched, not genuinely dead. No sensitivity analysis is provided, so the prejudge nodes could be partly spurious. That is a moderate concern, not fatal, because the method still seems to help. Fourth, the main ablations are length-confounded: removing verify shortens rationales, and increasing prejudge count lengthens them, so the 'prejudge helps' conclusion is entangled with test-time compute.\n\nMy take: the mechanism is worth a serious look, but the current evaluation does not establish that the gains come from prejudging per se rather than longer rationales and contaminated training overlap. A referee should ask for a held-out evaluation on non-overlapping benchmarks, error bars or at least variance across seeds, and an ablation that controls for rationale length. This paper deserves a revise-and-resubmit, not a desk reject.","headline":"A genuinely new data-synthesis mechanism for inserting 'prejudge' hints into reasoning trajectories, with consistent but partly contaminated empirical support.","tokens_in":20495,"tokens_out":3609,"would_cite":false,"duration_ms":29802,"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":"Inserting 'prejudge' warnings about upcoming errors into a reasoning chain lifts LLM accuracy on eight competition-level math and logic benchmarks, with average gains of 3.5 and 2.4 points for a 7B and a 32B model.","keywords":["process prejudge","prejudge node","dynamic tree search","LLM reasoning","test-time reasoning","reinforcement learning","chain-of-thought","self-correction"],"falsifier":"Take a sample of the synthesized prejudge trajectories, re-run the tree search with a much larger sampling budget (e.g., tens of thousands of paths per node instead of 1024), and measure how often a child that was marked $v=0$ actually leads to a correct answer. If a substantial fraction of 'dead-end' children are resurrected, the prejudge-node definition is flagging sampling artifacts rather than genuine errors, and the training signal is largely noise.","tokens_in":19360,"feed_emoji":"⚠️","tokens_out":9891,"duration_ms":72825,"temperature":0.7,"pith_summary":"The paper claims that a language model can be taught to 'prejudge before thinking': to pause at a reasoning step, anticipate the error a later step is about to make, and insert a short warning hint before proceeding. The authors build an automated pipeline that locates these pauses—called prejudge nodes—by tree search, generates the hint with a critic, verifies it with a second search, and then fine-tunes the model on the resulting rationales. On eight competition-level benchmarks, the resulting model beats chain-of-thought and self-refine baselines for both a 7B and a 32B backbone, by 3.5 and 2.4 average points, with further gains from reinforcement learning. The point of the exercise is to show that anticipatory error avoidance, not just trial-and-error correction, is a learnable and transferable reasoning skill for LLMs.","feed_headline":"LLMs that prejudge before thinking beat chain-of-thought on 8 tests","feed_subtitle":"Training on rationales with built-in 'prejudge' warnings lifts average accuracy by 3.5 points.","key_machinery":"The central object is the 'prejudge node': a reasoning step $z_i$ that is itself on a correct path ($v(z_i)=1$) but has at least one sampled child that is a dead end ($\\min_j v(z_{i+1}^j)=0$). The prejudge value $v_p(z_i)=v(z_i)\\cdot \\mathbf{1}(\\min_j v(z_{i+1}^j)=0)$ identifies these nodes. Around this definition the paper builds a one-LLM dynamic tree search that estimates node values with an LLM-as-judger using hard estimation, produces error analysis and a prejudge hint through an LLM-as-critic, re-searches with the hint to confirm it leads to a correct completion, and writes accepted trajectories with \"<|think|>\", \"<|verify|>\", and \"<|prejudge|>\" boundary tags. That data then feeds a two-phase post-training scheme: cold-start SFT on about 39k searched rationales, distillation to about 195k rationales, and then GRPO or DPO reinforcement learning.","core_discovery":"The central claim is that a reasoning model trained on rationales that contain prejudge hints—short self-oriented warnings such as 'the denominator cannot be 0' placed just before the step that would otherwise commit the error—learns to foresee and sidestep mistakes, and that this transferable 'prejudge before think' behavior improves test-time accuracy beyond what chain-of-thought or self-corrective pipelines achieve. The paper operationalizes the claim as follows: with the same backbone, PBT#1 outperforms CoT and Self-Refine on all eight benchmarks, with average gains of 3.5% and 2.4% for Qwen2.5-7B and Qwen2.5-32B respectively; adding GRPO reinforcement learning raises the 7B average from 59.0% to 63.9%. The authors also show that removing the verification component degrades performance, that prejudge hints improve pass@N by about 3% in a thought-completion task, and that mixing prejudge data with long-CoT (o1-style) data is compatible and often additive.","pith_inferences":["If the effect is real, it suggests that part of chain-of-thought's value is anticipatory error avoidance rather than merely more tokens; a testable extension is ablating the specificity of hints (generic warnings vs. problem-specific ones) to isolate what the model learns.","Because the dead-end labels come from a bounded tree search, a natural stress test is measuring how much of the training signal is an artifact of undersampling; the paper's own reported search limits (1024 paths, 14 steps) make this the empirical hinge of the method.","The same 'prejudge node + hint + verify' template could transfer to other verifiable step-structured domains, such as code generation or theorem proving, where a hint before a risky operation can be generated and checked automatically.","The paper's stated limitation (about 5 minutes per query for search) points to a practical next step: distilling the prejudge-hint generation itself into a lightweight model that can emit hints at inference time without search."],"forward_implications":["Across all eight benchmarks, PBT#1 beats both CoT training and Self-Refine for Qwen2.5-7B and Qwen2.5-32B; removing the verification step degrades results, so verification is load-bearing for the prejudge recipe.","Adding GRPO reinforcement learning after SFT raises the 7B average from 59.0% to 63.9%, outperforming DPO by about 2 points.","Increasing the number of prejudge hints per rationale improves accuracy on GSM8K and MATH-500, and prejudge hints improve pass@N by about 3% in the thought-completion test.","Mixing prejudge data with o1-style LIMO data keeps or improves most benchmarks, suggesting the prejudge mode is compatible with existing long-chain reasoning styles."],"supporting_citations":[{"why":"Supplies the hard estimation procedure used to assign value scores to tree nodes during prejudge detection.","marker":"(Wang et al., 2024e)"},{"why":"Establishes the LLM-as-critic pattern that the paper adapts to generate error analysis and prejudge hints.","marker":"(Shinn et al., 2023)"},{"why":"Provides the GRPO reinforcement learning algorithm used in the two-phase post-training.","marker":"(Shao et al., 2024)"},{"why":"Defines the long-chain slow-thinking paradigm that PBT is compared against and blended with in the o1-style experiment.","marker":"(Guo et al., 2025)"},{"why":"Supplies the Monte Carlo tree search formulation that the dynamic tree-searching strategy is modeled on.","marker":"(Kocsis and Szepesvári, 2006)"},{"why":"Supplies the MATH-500 benchmark used in evaluation and the process-supervision perspective behind the prejudge verification.","marker":"(Lightman et al., 2024)"},{"why":"Provides the LIMO o1-style training data used in the compatibility experiment.","marker":"(Ye et al., 2025)"}],"fun_headline_variants":["Prejudge-before-think boosts LLM reasoning on all 8 benchmarks","LLMs that prejudge errors outperform chain-of-thought by 3.5%","Process prejudge: LLMs learn to foresee mistakes, top CoT on 8 tests","Self-warning rationales lift LLM accuracy 3.5 points on average","Train LLMs to prejudge before thinking: +3.5% accuracy on 8 benchmarks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The pipeline assumes that a node marked as a dead end by the LLM-as-judger inside the truncated tree search (at most 1024 paths and 14 steps) truly has no path to the correct answer; if a dead-end child is merely undersampled, then the prejudge positions and hints are built on a false premise and the training data contains misleading prejudge positions.","fun_headline_variants_meta":{"raw":{"variants":["Prejudge-before-think boosts LLM reasoning on all 8 benchmarks","LLMs that prejudge errors outperform chain-of-thought by 3.5%","Process prejudge: LLMs learn to foresee mistakes, top CoT on 8 tests","Self-warning rationales lift LLM accuracy 3.5 points on average","Train LLMs to prejudge before thinking: +3.5% accuracy on 8 benchmarks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000888,"raw_usage":{"total_tokens":3859,"prompt_tokens":1002,"completion_tokens":2857,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":618,"completion_tokens_details":{"reasoning_tokens":2745}},"tokens_in":618,"tokens_out":2857,"duration_ms":18662,"temperature":1.0,"reasoning_tokens":2745,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T12:07:01.255182+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a sample of the synthesized prejudge trajectories, re-run the tree search with a much larger sampling budget (e.g., tens of thousands of paths per node instead of 1024), and measure how often a child that was marked $v=0$ actually leads to a correct answer. If a substantial fraction of 'dead-end' children are resurrected, the prejudge-node definition is flagging sampling artifacts rather than genuine errors, and the training signal is largely noise.","supporting_citations":[],"review_version":1}