{"id":"91620024-50d9-4195-96f7-599e0c5e3818","arxiv_id":"2606.29999","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"AlgoSkill improves LLM algorithm design on programming benchmarks by framing it as verification-guided scheduling over a typed skill library with MCTS, outperforming direct generation and self-refinement.","lead":"AlgoSkill models algorithm design as sequential decision-making over a typed library of skills like abstraction and proof checking, using a learned scheduler and MCTS guided by verification feedback. A smart generalist might read it to understand structured ways to improve LLMs on complex multi-step tasks beyond direct code generation.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Verification feedback may fail to guide search if benchmark tests lack coverage of edge cases or complexity pitfalls","rationale":"The reader's weakest assumption already flags the reliability of verification feedback; the concern above simply makes that assumption concrete and testable against the experimental protocol. Because the reader's verdict was formed from the abstract alone, the full manuscript might contain the missing test-coverage details; the proposed check would settle whether the assumption holds.","tokens_in":1738,"tokens_out":314,"duration_ms":19310,"concrete_test":"Extract the exact test-generation procedure and number of stress-test cases from the experimental section; re-evaluate the top-performing AlgoSkill runs on an independently generated suite of 10× more adversarial inputs (including worst-case complexity triggers) and report whether the win rate over baselines drops by more than 15 percentage points.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim rests on MCTS over typed skills being effectively steered by verification signals (compilation, testing, stress testing, complexity analysis). This requires that the signals are both sound and sufficiently complete to distinguish correct from incorrect or suboptimal skill sequences. The abstract provides no evidence that the stress-testing regime or test suites used in the competitive-programming and combinatorial-optimization benchmarks are exhaustive; standard problem test sets frequently omit adversarial inputs or asymptotic edge cases. If those signals are incomplete, the reported gains over direct generation, CoT, self-refinement, and untyped MCTS could be artifacts of overfitting to the provided tests rather than genuine algorithmic improvement.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes AlgoSkill, which models algorithm design from natural-language statements as sequential decision-making over a typed library of skills (abstraction, constraint analysis, state design, data-structure selection, proof checking, counterexample construction, complexity refinement). A learned scheduler proposes skills and MCTS explores sequences using verification feedback from compilation, testing, stress testing, and complexity analysis. Experiments on competitive programming and combinatorial optimization benchmarks are claimed to show improvements over direct LLM generation, chain-of-thought prompting, self-refinement, and MCTS without typed skills; ablations indicate that typed skills, verification-based repair, and search-based scheduling each contribute.","tokens_in":1867,"tokens_out":456,"duration_ms":24195,"significance":"If the empirical claims are substantiated with full quantitative results and robust test coverage, the work would offer a structured alternative to one-shot LLM code generation by making algorithmic reasoning steps explicit and verifiable. The combination of typed skills with MCTS and verification feedback, together with the reported ablations, provides a reproducible experimental framework that could be extended to other synthesis tasks.","major_comments":[{"comment":"Abstract: the central empirical claim (improvements over four baselines plus positive ablations) is stated without any quantitative results, benchmark identifiers, metrics, sample sizes, or error bars. This information is load-bearing for assessing whether the data support the claim.","section":"Abstract"},{"comment":"Experiments section (and associated evaluation): the claim that verification feedback from compilation, testing, stress testing, and complexity analysis reliably steers MCTS rests on the assumption that benchmark test suites are sufficiently complete. No analysis or additional stress-test results are provided to show that the suites detect edge cases or asymptotic failures, which directly affects whether the reported gains reflect genuine algorithmic improvement rather than overfitting to the given tests.","section":"Experiments"}],"minor_comments":[{"comment":"The typed skill library is introduced in the abstract and methods; a table listing each skill with its input/output types and an example invocation would improve clarity and allow readers to assess coverage.","section":"Methods"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments, which highlight important aspects of clarity and evaluation robustness. We address each major comment below and indicate planned revisions.","responses":[{"response":"We agree that the abstract would be strengthened by including quantitative support for the claims. In the revised version, we will incorporate specific metrics (e.g., success rates on Codeforces and combinatorial optimization benchmarks), benchmark identifiers, sample sizes, and error bars from the experiments comparing AlgoSkill to direct generation, chain-of-thought, self-refinement, and MCTS without typed skills.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the central empirical claim (improvements over four baselines plus positive ablations) is stated without any quantitative results, benchmark identifiers, metrics, sample sizes, or error bars. This information is load-bearing for assessing whether the data support the claim."},{"response":"The referee raises a valid point about evaluation robustness. The manuscript does not include an explicit analysis of test suite completeness or additional stress-test results for edge cases and asymptotic failures. We will add a limitations paragraph in the experiments section discussing reliance on standard benchmark test suites and the potential for overfitting. However, we cannot provide new stress-test results without conducting additional experiments.","revision_made":"partial","referee_comment":"[Experiments] Experiments section (and associated evaluation): the claim that verification feedback from compilation, testing, stress testing, and complexity analysis reliably steers MCTS rests on the assumption that benchmark test suites are sufficiently complete. No analysis or additional stress-test results are provided to show that the suites detect edge cases or asymptotic failures, which directly affects whether the reported gains reflect genuine algorithmic improvement rather than overfitting to the given tests."}],"tokens_in":1362,"tokens_out":400,"duration_ms":17095,"standing_objections":["Additional stress-test results demonstrating benchmark test suite completeness for edge cases and asymptotic failures"]},"desk_editor":{"model":"grok-4.3","letter":"The core of this paper is a system that treats algorithm design as picking from a fixed set of typed skills—abstraction, constraint analysis, state design, and so on—then uses a learned scheduler plus MCTS to explore sequences, steered by compilation, test, and complexity feedback. It reports better results than direct generation, CoT, self-refinement, and plain MCTS on competitive programming and combinatorial optimization tasks, with ablations backing the individual pieces.\n\nWhat stands out is the explicit decomposition into human-like steps rather than hoping the model figures them out implicitly. That framing is a reasonable extension of existing search-plus-LLM work, and the choice to keep the skill library typed and reusable looks practical for reuse across problems.\n\nThe main limitation is that the abstract gives no numbers, no error bars, and no description of the test suites or how exhaustive the stress testing actually was. If the benchmarks rely on standard problem sets that miss adversarial inputs or asymptotic cases, the verification signals could be steering the search toward solutions that pass the given tests without being robust. The paper would be stronger with a clearer account of how the test coverage was validated and whether the gains survive on held-out or harder instances.\n\nThis is aimed at researchers building LLM agents for code and algorithm tasks. Someone already working on search-augmented generation or structured prompting would find the concrete scheduler and skill typing useful to compare against. It is coherent on its own terms and engages the right baselines, so it clears the bar for peer review even if the evaluation needs tightening.","headline":"AlgoSkill adds a typed skill library and verification-guided MCTS scheduler to LLM algorithm design, with claimed gains on programming benchmarks, but the evidence details are thin.","tokens_in":2368,"tokens_out":390,"would_cite":false,"duration_ms":18047,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"AlgoSkill models algorithm design as scheduling a typed library of skills like abstraction and constraint analysis, guided by verification feedback.","keywords":["algorithm design","large language models","skill scheduling","monte carlo tree search","verification feedback","competitive programming","combinatorial optimization"],"falsifier":"Running the same competitive-programming and combinatorial-optimization benchmarks with direct LLM generation or MCTS without the typed skills and finding no performance gap would falsify the central claim.","tokens_in":2627,"feed_emoji":"🛠️","tokens_out":562,"duration_ms":9623,"temperature":0.7,"pith_summary":"The paper claims that turning algorithm design into explicit sequential choices over a fixed set of human-like skills, scheduled by a learned policy and explored with MCTS, yields better code than one-shot LLM generation or generic refinement. The skills include abstraction, constraint analysis, state design, data-structure selection, proof checking, counterexample construction, and complexity refinement. Verification from compilation, tests, and complexity analysis supplies the signal that steers the search. A reader would care if this decomposition makes automatic design more reliable on problems where direct prompting fails.","feed_headline":"Skill scheduling with verification beats direct LLM code generation","feed_subtitle":"Typed steps for abstraction, state design and proof checking plus test-guided search raise results on programming and optimization benchmark","key_machinery":"The typed library of algorithmic skills together with verification-guided MCTS scheduling over skill sequences.","core_discovery":"AlgoSkill models algorithm design as sequential decision-making over a typed library of algorithmic skills. A learned scheduler proposes skills from the current state while an MCTS controller explores sequences, using feedback from compilation, testing, stress testing, and complexity analysis to repair and refine.","pith_inferences":["The same skill-scheduling pattern might transfer to other domains that require stepwise construction and verification, such as theorem proving or circuit design.","Explicit skill libraries could make LLM outputs more auditable by exposing which reasoning step produced each code fragment.","If the skill set proves incomplete for some problem classes, the method would need either new skills or a way to learn additional ones."],"forward_implications":["Performance gains appear on both competitive programming and combinatorial optimization tasks.","Removing typed skills, verification-based repair, or search-based scheduling each reduces results.","The approach replaces implicit one-shot generation with explicit, verifiable steps."],"fun_headline_variants":["Skill scheduling with typed library and verification beats direct LLM generation","MCTS explores sequences of abstraction state design and proof skills with feedback","Learned scheduler and MCTS controller schedule skills for algorithm design tasks","Verification feedback from tests guides skill scheduling in algorithm synthesis"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The listed skills cover the essential steps needed to design algorithms from natural language and that test and complexity feedback is reliable enough to steer the search productively.","fun_headline_variants_meta":{"raw":{"variants":["Skill scheduling with typed library and verification beats direct LLM generation","MCTS explores sequences of abstraction state design and proof skills with feedback","Learned scheduler and MCTS controller schedule skills for algorithm design tasks","Verification feedback from tests guides skill scheduling in algorithm synthesis"]},"model":"grok-4.3","cost_usd":0.007211,"raw_usage":{"total_tokens":3298,"prompt_tokens":612,"num_sources_used":0,"completion_tokens":68,"cost_in_usd_ticks":72112000,"prompt_tokens_details":{"text_tokens":612,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2618,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":612,"tokens_out":68,"duration_ms":21584,"temperature":1.0,"reasoning_tokens":2618,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T06:07:42.451788+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Running the same competitive-programming and combinatorial-optimization benchmarks with direct LLM generation or MCTS without the typed skills and finding no performance gap would falsify the central claim.","supporting_citations":[],"review_version":1}