{"id":"f4f47def-eee1-4f06-a4a1-116e06ac8010","arxiv_id":"2411.15645","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":8,"one_line_summary":"MC-NEST adds a constant probability term to MCTSr's node selection and reports improved AIME pass@1 for GPT-4o, but the numbers are weakened by test-set rollout tuning and internal inconsistencies.","lead":"This paper proposes MC-NEST, a search-and-refine method that adds probability-based node selection to an existing Monte Carlo Tree Search approach for LLM math problem solving. The reported pass@1 gains on AIME for GPT-4o are undermined by test-set tuning of the rollout length and by inconsistent numbers.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed SOTA result is internally contradicted by the paper's own tables, and the reported pass@1 is a maximum over 27 test-set configurations; the paper's new selection mechanism is a mathematical no-op in Section 0.4.","rationale":"The reader's REJECT verdict is supported by the test-set selection issue and by the baseline omissions, but my strongest concerns are distinct and more basic. The paper cannot even agree with itself about the headline numbers: the MathOdyssey pass@1 is 12.6 in the abstract versus 13.3 in Table 4 and the Results section; the AIME 58 is attributed to rollout 4 in Table 4 and rollout 16 in Table 8. These contradictions mean the claimed result is not currently reproducible from the paper's own data. Additionally, Section 0.4's only new mechanism, adding 1/n to UCT, is mathematically inert under both the Greedy and Importance Sampling policies described in Section 0.3, so the paper does not provide a working account of why MC-NEST should outperform MCTSr. The reader's weakest assumption (test-set model selection) is also valid: choosing the best of 27 configurations on the test set makes 38.6 an optimistic upper bound. I recommend REJECT because these issues are about the paper's internal correctness, not just its external positioning.","tokens_in":23652,"tokens_out":6409,"duration_ms":54142,"concrete_test":"Recompute the claimed configuration (GPT-4o, Importance Sampling, rollout=4 for AIME and rollout=24 for MathOdyssey, using the Appendix 1.2 prompts) on the stated 150-problem sets, and verify the solved counts. Then re-run node selection with and without the 1/n term in the UCT formula; confirm whether all selections are identical. If the numbers do not reproduce or the selections are identical, the headline claim and the mechanism are both unsupported.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim (Abstract, Summary, Results) is that MC-NEST attains state-of-the-art pass@1 of 38.6 on AIME and 12.6 on MathOdyssey. This is not supported by the paper's own evidence. First, the MathOdyssey number is inconsistent: the abstract says 12.6 (19/150), while Table 4 and the Results text say 13.3 (20/150), and Figure 2 plots 20. Second, the AIME 58/150 result is obtained by running all 27 combinations of 9 rollouts x 3 policies on the same test set (Section 0.11, Tables 2-3) and taking the maximum; it is therefore a test-set maximum, not an unbiased estimate. Third, Table 8 contradicts Table 4 on which rollout produced the AIME 58 ('rollout 16 with IS' vs 'rollout 4 with IS'). Fourth, the proposed probability-distribution integration in Section 0.4 is a no-op: adding a constant 1/n to every UCT score cannot change argmax selection, and in the Importance Sampling policy Weight(i) = UCT(i) * pi(ai) with pi(ai) = 1/n, the 1/n cancels in normalized sampling probabilities. Thus the claimed mechanism for beating MCTSr is not present in the equations, and the headline numbers are internally inconsistent.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes MC-NEST, an extension of Monte Carlo Tree Self-Refine (MCTSr) for mathematical reasoning with LLMs. The method adds a uniform probability term to UCT-based node selection, together with Greedy, Importance Sampling, and Pairwise Importance Sampling policies, and uses LLM self-critique, self-refinement, and self-evaluation to guide tree search. Experiments on 150 AIME and 150 MathOdyssey problems with GPT-4o, Phi-3-mini, and Mistral-7B report pass@1 improvements, with the abstract claiming state-of-the-art pass@1 of 38.6 on AIME and 12.6 on MathOdyssey. The paper also includes a domain/difficulty analysis, a GPT-4o-based solution-quality evaluation, and appendix material labeled as proofs of two hypotheses.","tokens_in":24034,"tokens_out":6012,"duration_ms":51633,"significance":"If the reported results were reproducible under a sound evaluation protocol, MC-NEST would be a useful incremental contribution to inference-time search for LLM reasoning. The paper has several strengths: a clearly described three-stage self-refine tree pipeline (Algorithm 1 and Figure 3), a sizable 300-problem Olympiad-level evaluation set with human-verified domain/difficulty labels (Table 1), a systematic grid of rollout lengths and selection policies (Tables 2–3), and an explicit limitations section that identifies missing baselines and known failure modes. However, the headline results are not currently supported by the evidence: the reported pass@1 values are maxima over configurations tuned on the test set, the numbers are internally inconsistent across the abstract, table, and figure, and the proposed probability-distribution mechanism is mathematically inert as written, which removes the claimed distinction from MCTSr. The quality evaluation is also circular in that GPT-4o grades GPT-4o solutions without human-rater agreement.","major_comments":[{"comment":"The headline AIME result is obtained by running all 27 combinations of 9 rollout lengths and 3 selection policies on the same 150-problem test set and then selecting the best configuration (58/150 at rollout 4 with IS; Table 2), and the MathOdyssey result is selected similarly (20/150 at rollout 24 with IS; Table 3). No held-out validation set, repeated runs, or error bars are reported, so the pass@1 values in Table 4 and the Abstract are test-set maxima and therefore upper bounds, not unbiased estimates of MC-NEST's performance. The ambiguity is compounded by Table 8, which attributes the AIME 58/150 result to rollout 16 with IS rather than rollout 4, so even the selected configuration is not reported consistently.","section":"Section 0.11, Tables 2–3 and Table 8"},{"comment":"The paper's central numbers are internally inconsistent. The Abstract and Summary report a MathOdyssey pass@1 of 12.6 (19/150), while Table 4 and the Results text report 13.3 (20/150) and Figure 2 plots 20 solved problems. For Phi-3-mini on AIME, Table 2 reports MC-NEST solving 12 problems, Table 4 reports a pass@1 of 7.33 (11/150), and Table 8 reports 11 solved problems; the MCTSr column similarly alternates between 11 and 7.33. These contradictions make it impossible to verify which numbers are the results of record.","section":"Abstract, Summary, Table 4, Results, Figure 2"},{"comment":"The proposed probability-distribution integration is a mathematical no-op as written. In the UCT update, adding 1/n to every candidate's score cannot change the argmax over the candidate set. In the Importance Sampling policy, Weight(i)=UCT(i)*π(ai) with π(ai)=1/n, and the normalized sampling probability Weight(i)/ΣWeight(j)=UCT(i)/ΣUCT(j), so the uniform factor cancels exactly. In Pairwise Importance Sampling, the pair weight |UCT(i)-UCT(j)|·(1/n)^2 is multiplied by a constant for all pairs, so the relative ordering of pairs is also unchanged. Consequently, the claimed mechanism that distinguishes MC-NEST from MCTSr (uniform probability integration) is absent from the equations; the differences between the MCTSr and MC-NEST rows in Tables 2–3 therefore cannot be attributed to the new selection strategy as described.","section":"Section 0.3–0.4, UCT update equations"},{"comment":"The paper's own claims of state-of-the-art performance are not supported by the evidence it presents. The Limitations section acknowledges that structurally aligned baselines (CoT, PoT, ToT) are not compared, and Table 4 shows that on MathOdyssey ZSCoT (16.6) outperforms MC-NEST (13.3), so the Abstract's blanket phrase 'highest pass@1 on Olympic-level benchmarks' is misleading. In addition, the quality scores in Table 6 are produced by GPT-4o evaluating GPT-4o-generated solutions, with no human-rater agreement or independent verification reported, so the 84.0%/82.08% quality numbers are not established as reliable.","section":"Limitations, Table 4, Section 0.13 and Table 6"}],"minor_comments":[{"comment":"The caption contains a typo: 'Greesy' should be 'Greedy'; the table also mixes percentages and raw counts without a clear convention.","section":"Table 4 caption"},{"comment":"Pass@1 is defined as the fraction of problems solved 'on the first attempt,' but MC-NEST returns the node with the highest Q value after multiple rollouts; the definition should be clarified to reflect that the result is a best-of-search answer, not a single autoregressive sample.","section":"Section 0.11"},{"comment":"The backpropagation formula Q(np) = (Q(np) + max(Q(nc)))/2 is said to apply 'for each parent node,' but as written it describes only one immediate update; the order of ancestor updates and the stopping condition at the root should be specified.","section":"Section 0.6"},{"comment":"The y-axis is unlabeled and the figure mixes numbers of solved problems with pass@1 percentages; the reader cannot tell whether the plotted values are 58, 20 (counts) or 38.6, 13.3 (percentages).","section":"Figure 2"},{"comment":"The appendix presents equations labeled as a proof, but there is no theorem statement, no derivation from Algorithm 1, and constants λ, α, β, γ, Vmax are never defined or instantiated; it should be rewritten as a formal statement with assumptions and a proof, or removed.","section":"Appendix, Hypothesis 1 Proof"},{"comment":"References [19] and [46] are duplicates of the Tree-of-Thought paper, and [33] and [43] are duplicates of the GPT-4 technical report; this should be cleaned up.","section":"References"}],"recommendation":"reject","confidential_remarks":"I would not recommend inviting a revision in the current form: the central contribution—probability-distributed node selection—is mathematically inert as written, and the headline empirical claims are selected on the test set and internally inconsistent. The authors should re-run the evaluation with a proper validation split, reconcile the numbers across tables, and either demonstrate a real behavioral change from the proposed selection mechanism or reposition the contribution accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know before reading this: the key claim in MC-NEST is not supported by the paper's own equations. The new mechanism—a uniform probability term 1/n added to UCT scores—cannot change node selection. In the Greedy policy, a constant added to every candidate's score leaves the argmax unchanged. In the Importance Sampling policy, Weight(i)=UCT(i)*(1/n), and the 1/n cancels in normalized sampling weights. The Pairwise policy likewise multiplies all pair weights by a constant. So the method is MCTSr with a no-op modification, and the reported gains over MCTSr are unexplained by the stated algorithm.\n\nWhat the paper does well is modest but real. The writing is clear, the method section is detailed, and the authors are upfront about missing baselines (CoT, PoT, ToT) and about the computational costs. The dataset construction with human verification of domain/difficulty classification is a reasonable effort. And they report per-rollout tables rather than hiding the grid.\n\nThe soft spots, though, are load-bearing. First, the headline pass@1 numbers are selected after running 9 rollout lengths × 3 policies on the same 150-problem test sets and picking the best (AIME: rollout 4 with IS; MathOdyssey: rollout 24 with IS). That makes the reported 38.6 and 13.3 test-set maxima, not unbiased estimates. Second, internal inconsistencies: the abstract says MathOdyssey 12.6 (19/150), the body says 13.3 (20/150), and Figure 2 plots 20. Table 4 says Phi-3-mini AIME MCTSr/MC-NEST both 7.33, while Table 8 says 11 for both; Table 8 also attributes MC-NEST's AIME result to rollout 16, contradicting Table 4's rollout 4. These differences matter because the claimed SOTA rests on those counts.\n\nMy take: this is not a paper that demonstrates a working improvement. The novel ingredient is mathematically inert, and the evaluation flatters the method. It would be a useful reading-group case study on test-set overfitting and on checking whether a proposed change actually changes the algorithm. It deserves a desk reject, not referee time, unless the authors can show a real selection effect and fix the numbers.","headline":"MC-NEST's only new mechanism is a no-op in its own equations, and the headline results are test-set maxima with internal contradictions; the paper is a useful cautionary tale, not a validated method.","tokens_in":24568,"tokens_out":2882,"would_cite":false,"duration_ms":25559,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that MC-NEST, a Monte Carlo tree search with runtime self-critique and probabilistic node selection, lifts GPT-4o's pass@1 from 33.3 to 38.6 on the AIME benchmark.","keywords":["mathematical reasoning","large language models","Monte Carlo tree search","self-refinement","self-evaluation","importance sampling","Olympiad benchmarks","pass@1"],"falsifier":"Re-run MC-NEST on a fresh set of 150 AIME problems using only the rollout-4 importance-sampling configuration, without having seen those problems during configuration selection, and check whether pass@1 still exceeds the 33.3 zero-shot chain-of-thought baseline; if it does not, the reported gain is an artifact of test-set tuning.","tokens_in":23435,"feed_emoji":"🌳","tokens_out":5069,"duration_ms":39974,"temperature":0.7,"pith_summary":"This paper introduces MC-NEST, a Monte Carlo Tree Search extension in which a large language model critiques and refines its own candidate solutions inside a search tree, with node selection guided by Upper Confidence Bound scores combined with probability-distribution policies. The central claim is that this search procedure substantially improves GPT-4o's pass@1 on Olympiad-level mathematics, reaching 38.6 on AIME and 12.6 on MathOdyssey, compared with 33.3 for zero-shot chain-of-thought on AIME. The method extracts more reasoning ability from an existing LLM at inference time, without fine-tuning, by balancing exploration of alternative solution paths against exploitation of promising refinements. The paper also reports that the benefit is concentrated in structured, multi-step problems like AIME, while simpler prompting still wins on intuition-driven MathOdyssey problems.","feed_headline":"Tree search lifts GPT-4o to 38.6% on AIME math","feed_subtitle":"Self-critique and probabilistic node selection beat plain prompting on Olympiad problems, the paper reports.","key_machinery":"The central mechanism is the integration of probability-distribution policies into the UCT selection rule of a self-refining tree search. In MC-NEST, node selection first collects candidate nodes via breadth-first traversal, then scores each node as $Q(i) + C\\sqrt{\\ln(N_{\\text{parent}})/(N(i)+\\epsilon)} + 1/n$, where the added $1/n$ term is the uniform probability over the $n$ candidates; the importance-sampling variant turns the product of UCT score and probability into sampling weights. This probabilistic twist is meant to prevent the search from fixating on a locally optimal solution and to keep less-visited branches in play. The other load-bearing component is the LLM self-refine and self-evaluation loop, which generates a critique of the current answer, produces a refined answer, and assigns a reward that is backpropagated as $Q(n_p) = (Q(n_p) + \\max Q(n_c))/2$.","core_discovery":"The discovery the paper tries to establish is that adding probabilistic node selection and iterative LLM self-critique to a Monte Carlo tree makes the underlying language model a better mathematical reasoner on hard, structured problems. Concretely, MC-NEST builds a tree whose nodes are candidate answers; at each step an LLM critiques the current answer, produces a refined version, scores it with a reward prompt, and backpropagates the score to update quality values and visit counts. The selection step filters candidate nodes by breadth-first search and then picks a node through one of three policies that blend the UCT score with a uniform probability over candidates, with importance sampling performing best. On the 150-problem AIME test set, the method with GPT-4o solves 58 problems at rollout 4, corresponding to a pass@1 of 38.6, which the paper reports as the highest among the compared prompting and tree-search baselines.","pith_inferences":["The headline pass@1 figures are maxima over a grid of nine rollout lengths and three selection policies all evaluated on the same 150-problem test sets, so a fair estimate of true performance would require a validation split or a report of the full grid; the reported numbers are upper bounds rather than unbiased predictions.","The abstract's MathOdyssey figure of 12.6 does not match the results section, which reports 13.3 pass@1 and 20 solved problems; a reader should resolve this discrepancy before relying on the exact number.","A natural extension the paper does not test is whether the same probabilistic selection policies help on other structured reasoning domains such as formal logic or code generation, since the method's stated value is generic inference-time search rather than math-specific knowledge.","The quality-check scores (84.0% for GPT-4o and 82.08% for Phi-3-mini) come from GPT-4o evaluating its own solutions against human solutions; an independent human rating would be needed to confirm that the consistency claim is not an artifact of self-evaluation bias."],"forward_implications":["If the claim holds, any sufficiently capable LLM can be pushed toward higher Olympiad-math accuracy purely at inference time by wrapping it in a search-and-critique loop, with no training or prompt engineering per problem.","The result implies that larger base models amplify the benefit of tree search: GPT-4o gains 5.3 points over zero-shot chain-of-thought on AIME, while Phi-3-mini gains about 6 points in the same comparison and Mistral 7B solves no problems at all.","Because the best rollout length differs sharply between datasets (4 for AIME, 24 for MathOdyssey), deploying MC-NEST in practice requires choosing the search budget per task type, not a single universal setting.","The paper's own numbers show the method is not a general reasoning cure: on MathOdyssey, MC-NEST at 13.3 pass@1 trails plain zero-shot chain-of-thought at 16.6, so the expected gain is specific to formal, multi-step deduction problems."],"supporting_citations":[{"why":"The MCTSr method that MC-NEST extends, providing the self-refine tree backbone.","marker":"[9]"},{"why":"Zero-shot chain-of-thought prompting, used as the main baseline and as the root initialization.","marker":"[10]"},{"why":"The AIME problems dataset used as the primary benchmark.","marker":"[11]"},{"why":"The MathOdyssey benchmark used as the second test set.","marker":"[12]"},{"why":"GPT-4o (GPT-4 technical report) as the backbone LLM whose reasoning is being improved.","marker":"[33]"}],"fun_headline_variants":["MC-NEST: self-refine tree lifts LLM math on AIME","Tree search + self-critique gets GPT-4o to 38.6%","Monte Carlo self-refine tree boosts LLM reasoning","Self-refining tree beats prompting on Olympiad math","GPT-4o hits 38.6% on AIME via MC-NEST tree search"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The evaluation assumes that choosing the rollout length and selection policy after trying all configurations on the same test problems gives an honest estimate of the method's performance, even though the reported scores are the best results from that grid search.","fun_headline_variants_meta":{"raw":{"variants":["MC-NEST: self-refine tree lifts LLM math on AIME","Tree search + self-critique gets GPT-4o to 38.6%","Monte Carlo self-refine tree boosts LLM reasoning","Self-refining tree beats prompting on Olympiad math","GPT-4o hits 38.6% on AIME via MC-NEST tree search"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000223,"raw_usage":{"total_tokens":1460,"prompt_tokens":952,"completion_tokens":508,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":568,"completion_tokens_details":{"reasoning_tokens":409}},"tokens_in":568,"tokens_out":508,"duration_ms":4793,"temperature":1.0,"reasoning_tokens":409,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:04:46.941328+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run MC-NEST on a fresh set of 150 AIME problems using only the rollout-4 importance-sampling configuration, without having seen those problems during configuration selection, and check whether pass@1 still exceeds the 33.3 zero-shot chain-of-thought baseline; if it does not, the reported gain is an artifact of test-set tuning.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The AIME problems dataset used as the primary benchmark."}],"review_version":1}