{"id":"97554d99-5480-44cf-87de-467f181da607","arxiv_id":"2505.10962","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"MPS-Prover, a stepwise Lean prover with curated training data and multi-perspective tree search, reports 75.82% on miniF2F and 32.97% on ProofNet, a new 7B-class step-level state of the art.","lead":"This paper presents MPS-Prover, a stepwise Lean theorem prover whose training-data filtering and multi-perspective search reach new state-of-the-art results on miniF2F and ProofNet within the 7B model class. If the numbers hold, it is the strongest published step-level prover at that scale and also finds markedly shorter proofs.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Figure 3's budget-equivalence comparison lacks BFS configuration; the central efficiency claim of multi-perspective search is unverified.","rationale":"The reader's weakest_assumption correctly identifies the budget-equivalence assumption in Section 3.2 as the central weakness. My stress-test concurs: the claim that multi-perspective search yields a real efficiency gain depends entirely on BFS pass@4k being an honest, same-cost baseline. The paper does not specify the BFS configuration behind Figure 3, making the comparison unfalsifiable from the text alone. No code or data is released, so the numbers cannot be independently checked. The ablation study partially supports the contribution of each heuristic, but the differences are small (3–5 problems) and at a fixed pass@64 budget, not the headline accumulative setting. The proof-length and diversity analyses use 'commonly solved problems' and therefore do not establish that MPS finds proofs BFS cannot find; they only show that when both succeed, MPS's proofs are shorter. I found no internal inconsistency or mathematical error in the method description; the concern is purely about evidence quality for the central empirical claim. Because the reader already conditioned the verdict on code/data release and clarification of the budget comparison, my concern does not shift the verdict; it reinforces the same condition. A fully specified BFS baseline and a head-to-head budget-controlled run would settle whether the efficiency advantage is real.","tokens_in":22145,"tokens_out":5073,"duration_ms":47922,"concrete_test":"Release the exact BFS configuration used in Figure 3, or run the following controlled experiment: on the same miniF2F split with the same SFT model and critic, run (a) MPS pass@k (Nperspectives=4, Nmax_iter=800, Nsamples=8) and (b) a single-perspective BFS (Nperspectives=1, same LLM, same critic, same Nmax_iter=800, same Nsamples=8, identical backtracking and accumulative rules) at pass@4k, and report per-budget solved counts and the actual total number of LLM tactic samples executed. If MPS's advantage over BFS at equal measured sample counts disappears or reverses, the multi-perspective search claim is not empirically supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's second core contribution—multi-perspective search—is supported primarily by Figure 3, which compares MPS pass@k against BFS pass@4k under 'approximately equivalent computational budgets' (Section 3.2). The load-bearing assumption is that BFS expands exactly one node per iteration with the same LLM, the same critic, the same Nmax_iter, the same Nsamples, and the same accumulative protocol, so that pass@4k equals MPS's 4× branch factor. None of these conditions are documented. The text refers to BFS from Li et al. (2024b), but Figure 3 does not state the BFS hyperparameters, whether the critic is the same model, or whether the same iteration limit (800 vs. 600 used in Table 1 baselines) applies. If BFS used a different iteration count or a weaker critic, pass@4k would not be budget-equivalent, and the observed gap (e.g., 67.62% vs. 66.39% at the lowest budget) could reflect configuration differences rather than the multi-perspective mechanism. This concern is load-bearing because the headline accuracy difference over BFS-Prover (75.82% vs. 72.54%, 8 problems) is small, and Figure 3 is the only controlled evidence isolating the search contribution. Without a fully specified BFS baseline, the efficiency and diversity advantages claimed for MPS are not established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces MPS-Prover, a stepwise Lean 4 theorem prover built on Qwen2.5-Math-7B. Its two claimed contributions are (1) a post-training data curation strategy that removes approximately 40% of expert-iteration training data by filtering short proofs and ineffective tactic steps, and (2) a multi-perspective tree search that, in addition to a learned distance-prediction critic, selects nodes using three hand-designed heuristics: tactic effectiveness scoring, minimizing case splits, and shortest state preference. On miniF2F-test the system reports 75.82% accuracy under an accumulative protocol, compared with 72.54% for BFS-Prover, and reports 32.97% on ProofNet, surpassing several 7B baselines. The paper additionally reports that MPS produces shorter proofs than whole-proof baselines (mean 3.44 steps vs 15.91 and 52.16 on 170 common miniF2F problems) and more diverse proofs than its own BFS baseline. Generated proofs are ultimately checked by the Lean compiler, which guards against repl-level mis-verification.","tokens_in":22274,"tokens_out":5966,"duration_ms":60171,"significance":"If the empirical claims hold, this is a strong step-level 7B result on miniF2F and ProofNet, and the data-curation finding (roughly 40% data reduction with roughly equal performance) would be practically valuable. The use of a final Lean compiler check is a clear strength, and the proof-length analysis, while confounded by the search heuristics, addresses an under-studied axis of comparison. However, the paper's main methodological claim—that multi-perspective search is more efficient than BFS under equivalent budgets—rests on an underspecified baseline, and the headline differences (8 problems on miniF2F; 1–5 problems in ablations) are reported without any uncertainty quantification. Reproducibility is currently incomplete because no code, model weights, or detailed search configurations are provided. The central benchmark numbers are plausible, but the evidence for the search-specific efficiency advantage and for the contribution of individual heuristics is not yet fully established.","major_comments":[{"comment":"The central efficiency claim—'MPS consistently outperforms BFS when allocated similar computational resources'—requires BFS pass@4k to be budget-equivalent to MPS pass@k. This equivalence demands that BFS use the same LLM backbone, the same distance critic, the same Nmax_iter and Nsamples, and the same accumulative protocol. None of these are reported for Figure 3. The BFS rows in Table 1 use the notation '2048 × 2 × 600', whereas the MPS rows use '64 × 4 × 800 × 8', so the two budget formats are not obviously comparable. Please specify the exact BFS configuration used in Figure 3, report per-budget problem counts for both methods, and state whether the same critic and iteration limits were used.","section":"Section 3.2, Figure 3"},{"comment":"The reported performance differences are small relative to the stochasticity of the sampling procedure. The headline improvement over BFS-Prover is 8 problems out of 244 (75.82% vs 72.54%), and each ablation row differs from the full method by only 1–5 problems. No repeated runs, random seeds, or confidence intervals are provided. Without these, the claim of a 'significant improvement' and the attribution of the ablations to specific heuristics are not quantitatively supported. Please report variance across multiple independent runs or otherwise demonstrate that the observed gaps exceed run-to-run noise.","section":"Section 3.1, Table 1; Section 3.3, Table 3"},{"comment":"The proof-length and diversity analyses are confounded by the MPS heuristics themselves. The 'Shortest State Preference' and 'Minimizing Case Splits' heuristics directly bias the search toward simpler and shorter states, and the 'Tactic Effectiveness Scoring' favors goal-closing and transformative tactics, so shorter and less repetitive proofs are partly by construction rather than an emergent property of multi-perspective search. Furthermore, the comparison between MPS pass@64 and BFS pass@256 does not state the BFS Nmax_iter, Nsamples, or exact total budget, and restricting the analysis to 'commonly solved problems' introduces selection bias. Please report the exact budgets, analyze the full sets of solved problems, and, if the claim is about proof efficiency, compare with a BFS baseline that is matched on the aspects not under test.","section":"Section 3.4, Figure 4"},{"comment":"The short-proof filtering threshold of 3 is selected by a grid search over {2, 3, 4, 5}. The paper does not state whether this grid search was performed on a held-out validation split or on the miniF2F test set. If the test set was used, the data-curation effectiveness claim (40% data reduction with no performance loss) could reflect selection on the evaluation benchmark. Please clarify the split used for the grid search and report the performance for the other thresholds.","section":"Section 2.2, Filtering Short Proofs"},{"comment":"Table 2 states that all models, including MPS-Prover, were evaluated under their 'respective maximum reported sampling budgets', but the actual budget used for MPS-Prover on ProofNet is not reported. Given the paper's budget formula Npass × Nperspectives × Nmax_iter × Nsamples, please report the values used for ProofNet, including whether the accumulative protocol was applied. Without this, the comparison to baselines such as DeepSeek-Prover-V2 is not fully reproducible.","section":"Section 3.1, Table 2"}],"minor_comments":[{"comment":"The word 'comfirms' should be 'confirms'.","section":"Section 5"},{"comment":"The text attributes DeepSeek-Prover-V2 to 'Guo et al. (2025)', but the reference list identifies DeepSeek-Prover-V2 as Ren et al. (2025); the citation should be corrected.","section":"Appendix A"},{"comment":"The procedure for selecting the '170 common miniF2F problems' is not described; please state how the common set was determined and whether it is the same set used in Section 3.4.","section":"Table 4"},{"comment":"Several displayed Lean proofs contain LaTeX artifacts (e.g., '\\mathbb{R}' rendered as 'R' and stray '£' characters in the DeepSeek-Prover V2 proof); these should be cleaned up for readability.","section":"Appendix D"},{"comment":"The acronym BFS is used for Best-First Search, which can be confused with breadth-first search; a footnote or parenthetical clarification at first use would help readers unfamiliar with the step-proving literature.","section":"Section 3.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is submitted as a technical report and reports benchmark results that are plausible and externally verified by the Lean compiler. The main barrier to acceptance is not the validity of the proved theorems but the reproducibility of the search-based comparisons: the BFS baseline in Figure 3 is underspecified, and the small differences in Tables 1 and 3 lack uncertainty estimates. If the authors provide the missing configuration details, error bars, and a clear statement of the ProofNet budget, the central claims could be adequately supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a legitimately engineered stepwise prover that reports strong 7B numbers on miniF2F and ProofNet. The data-curation idea—filter out proofs shorter than 4 steps and steps that don't change the state—is simple, cheap, and looks real: it cuts the training set 40% at a cost of one problem in the ablation. The multi-perspective search is a reasonable extension of BFS: keep the critic's pick plus three hand-set heuristic picks. I believe the accuracy numbers will replicate, modulo small variation.\n\nThe soft spots are concentrated around the claims that MPS is more efficient than BFS. Figure 3 compares MPS pass@k to BFS pass@4k and calls the budgets 'approximately equivalent.' But the BFS side is never specified: no iteration count, no sample count, no critic checkpoint, no mention of whether it's the same LLM. That is a load-bearing gap because the headline improvement over BFS-Prover (75.82 vs 72.54) is 8 problems, and the isolation of the search contribution depends entirely on Figure 3. Without the BFS configuration, I wouldn't buy the efficiency advantage over standard BFS.\n\nAlso: the ablations show each heuristic is worth 1-5 problems out of 244, so those effects are small; the short-proof threshold is grid-searched with no validation split mentioned; and the proof-length comparison with whole-proof provers is apples-to-oranges. A stepwise prover will naturally produce fewer Lean steps than a whole-proof generator that emits every `have` detail; that finding is interesting but not a fair contest.\n\nWhat holds up: they use the Lean compiler for final verification, which guards against repl mis-verification, and the data-curation numbers are concrete. The limitation appendix is honest about stepwise provers' trouble with `have` and nested sub-proofs.\n\nVerdict: this deserves a serious referee, not a desk reject. I'd ask the authors for code/data and for a fully specified BFS baseline before signing off on the efficiency claim. The core accuracy results are likely real and useful to the ATP community.","headline":"Engineered stepwise prover with a plausible data-curation recipe, but the multi-perspective search efficiency claim needs the BFS baseline fully specified before it can be trusted.","tokens_in":22947,"tokens_out":4078,"would_cite":false,"duration_ms":34956,"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":"The paper claims that a stepwise Lean prover using multi-perspective search reaches 75.82% on miniF2F and beats all 7B baselines on ProofNet.","keywords":["automated theorem proving","Lean 4","stepwise proof search","best-first search","multi-perspective search","expert iteration","data curation","formal mathematics"],"falsifier":"Run the same 7B model and the same critic in a pure best-first search with a total tactic-candidate budget $B$, and run MPS with the same sampling and iteration settings at a budget $B/4$; if BFS at pass@$4k$ matches or exceeds MPS at pass@$k$ on miniF2F, the central efficiency claim fails.","tokens_in":21820,"feed_emoji":"🧮","tokens_out":5965,"duration_ms":55787,"temperature":0.7,"pith_summary":"The paper argues that stepwise theorem proving in Lean can be made substantially stronger by fixing two weaknesses of existing search-based provers: reliance on a single learned critic and indiscriminate reuse of expert-iteration data. It claims that a multi-perspective tree search, which keeps one critic-chosen node and three heuristic-chosen nodes per expansion, plus a curation step that drops roughly 40% of short or low-value training proofs, raises the success rate to 75.82% on miniF2F (185 of 244 problems) and 32.97% on ProofNet with a 7-billion-parameter model. A careful reader would care because the proofs are machine-checked by the Lean compiler, and because the same search also finds materially shorter proofs (mean 3.44 steps versus 15.91 and 52.16 for two whole-proof provers on 170 shared problems).","feed_headline":"Stepwise prover cracks 75.8% of miniF2F with multi-perspective search","feed_subtitle":"A 7B Lean theorem prover beats prior 7B provers on ProofNet and produces proofs a fraction as long.","key_machinery":"The load-bearing mechanism is the multi-perspective tree search. In each expansion the system samples tactic candidates and retains up to four next states: one selected by a learned critic that predicts distance-to-completion, and three selected by hand-designed heuristics: a tactic-effectiveness score favoring transformative tactics, minimizing the number of case splits, and preferring shorter Lean state strings. A separate data-curation pass supports the model by removing proofs of three or fewer steps and steps whose tactics produce no state change, cutting about 40% of training data with little effect on accuracy.","core_discovery":"The central claim, stated on the paper's own terms, is that MPS-Prover is the strongest published 7B stepwise prover on miniF2F and ProofNet. It proves 185 of 244 miniF2F problems under an accumulative search, a gain over the previous stepwise best (BFS-Prover at 72.54%), and reaches 32.97% on ProofNet, ahead of all 7B baselines including a CoT-distilled model. Under approximately matched computational budgets, MPS at pass@k is reported to beat BFS at pass@4k, with the gap widening as the budget grows. It also finds shorter and more tactic-diverse proofs than both the BFS baseline and whole-proof provers, which the paper attributes to combining multiple selection perspectives rather than trusting a single critic's bias.","pith_inferences":["If the budget-equivalence comparison holds under closer scrutiny, the same multi-perspective principle could be applied to other sparse tree searches to reduce wasted expansion.","The heuristic scoring table is manually tuned for Lean; a learned or automatically fitted version of these scores could transfer the idea to other proof assistants, but the paper does not test that.","The authors' hybrid-system suggestion implies a testable extension: feed MPS-Prover's short proof skeletons as high-level plans to a whole-proof generator."],"forward_implications":["Within the 7B model class, a natively trained stepwise prover can beat whole-proof baselines, including a CoT-distilled one, on ProofNet.","Under the paper's budget-equivalence assumption, spending the same compute on multi-perspective expansion rather than more BFS trials yields higher accuracy at every budget tested.","About 40% of expert-iteration training data can be dropped without hurting proof-finding performance, making training cheaper.","Stepwise search produces dramatically shorter proofs, which are easier to inspect and verify, while whole-proof systems generate longer scripts on the same theorems."],"supporting_citations":[{"why":"Supplies the miniF2F benchmark whose test set is the primary accuracy yardstick.","marker":"Zheng et al. (2022)"},{"why":"Supplies the ProofNet benchmark used for the 7B-model comparison.","marker":"Azerbayev et al. (2023)"},{"why":"Defines the BFS-Prover baseline that MPS-Prover must beat and provides the accumulative search protocol.","marker":"Xin et al. (2025)"},{"why":"Contributes the tree-based distance critic model and BFS methodology that multi-perspective search extends.","marker":"Li et al. (2024b)"},{"why":"One of the stepwise baselines and source of the expert-iteration style training approach.","marker":"Wu et al. (2024)"},{"why":"Whole-proof baseline (DeepSeek-Prover-V2) compared on ProofNet and in proof-length analysis.","marker":"Ren et al. (2025)"},{"why":"Whole-proof baseline (Kimina-Prover) compared on proof-length and miniF2F.","marker":"Wang et al. (2025)"},{"why":"Introduces the expert-iteration loop from which the data-curation pipeline derives.","marker":"Polu & Sutskever (2020)"}],"fun_headline_variants":["MPS-Prover: 7B stepwise prover tops miniF2F with multi-perspective search","Multi-perspective search and data pruning give 7B prover SOTA results","MPS-Prover: shorter proofs via multi-perspective search and 40% data cut","Lean prover's multi-perspective search beats 7B baselines and shortens proofs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that comparing MPS at pass@k with BFS at pass@4k really does compare roughly equal computational budgets; the paper does not specify the BFS baseline's configuration, so if BFS was run with different trials, iteration counts, or sampling, the claimed efficiency gain could be an artifact.","fun_headline_variants_meta":{"raw":{"variants":["MPS-Prover: 7B stepwise prover tops miniF2F with multi-perspective search","Multi-perspective search and data pruning give 7B prover SOTA results","MPS-Prover: shorter proofs via multi-perspective search and 40% data cut","Lean prover's multi-perspective search beats 7B baselines and shortens proofs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000878,"raw_usage":{"total_tokens":3810,"prompt_tokens":970,"completion_tokens":2840,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":586,"completion_tokens_details":{"reasoning_tokens":2739}},"tokens_in":586,"tokens_out":2840,"duration_ms":19428,"temperature":1.0,"reasoning_tokens":2739,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:00:25.383364+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same 7B model and the same critic in a pure best-first search with a total tactic-candidate budget $B$, and run MPS with the same sampling and iteration settings at a budget $B/4$; if BFS at pass@$4k$ matches or exceeds MPS at pass@$k$ on miniF2F, the central efficiency claim fails.","supporting_citations":[],"review_version":1}