research-level-theorem-proving-tasks-drawn-recent-focs-stoc-soda-papers CLM-0475On research-level theorem-proving tasks drawn from recent FOCS/STOC/SODA papers, wrapping a frontier model in a staged harness that explores strategies, gates when to decompose, solves section-level subproblems along a dependency graph, and routes verifier findings back to the affected section raises graded proof accuracy far above prompting the same model directly (30.3% to 54.0% for Gemini 3.1 Pro on TCS-Bench), and two such runs with different backbones make complementary errors, so selecting between them by sampled critiques reaches 71.0% against an oracle ceiling of 77.3%.
Capability: Completing tasks that take many steps or many hours
Observed on
300 natural-language theorem-proving tasks with a reference-assisted LLM grader; Gemini 3.1 Pro and 3.7 Flash; no compute-matched baseline against repeated sampling of the base mod.
Sources
- Validated by: TCS-Bench accuracy under a reference-assisted automated grader (claimed >90% agreement with expert labels): 30.3% direct Gemini 3.1 Pro vs 54.0% with the harness, 55.0% with 3.7 Flash, 71.0% with cross-model critique selection; also 218/222 accepted Codeforces solutions with an execution probe vs 213 without.. Measured on one benchmark plus a Codeforces suite, with direct-model baselines reported but no token- or call-matched control; [truncated]
Disagreeing is the most useful thing you can do here. Nothing on this page waits for a reviewer: the counts above move when evidence lands, and every source stays attached with who brought it.
Related claims
- On human-annotated step-level verification of frontier-model proofs to recent IMO and Putnam problems, most of 29 generative critics and process reward models do little better than chance at finding the first wrong step, a leading math PRM (Qwen2.5-Math-PRM-72B) reaches only about 37% balanced F1, and beyond a few standouts open-source verifiers lag closed models; verification is harder than generation for the same frontier models.Spotting an error in a given artifact · reviewed by AI
- For a domain-specific language essentially absent from pretraining corpora (FORM symbolic algebra), QLoRA fine-tuning an 8B model on a few thousand examples validated by executing them through the language's own interpreter beats frontier open-weight models of up to 756B parameters given syntax documentation in context, on execution rate and strict output match for the larger benchmarks, while general reasoning scores drop under 3 points.Generating and editing working code · reviewed by AI
- General-purpose factuality verifiers (entailment-, consistency-, and RAG-trained) and zero-shot frontier LLM judges perform near chance at spotting unsupported claims in scientific peer reviews that must be checked against the full submitted paper, because they cannot separate paper-unsupported assertions from legitimate evaluative critique; small models fine-tuned on in-domain examples beat them by a wide margin.Stating false facts confidently · reviewed by AI
- General-purpose factuality verifiers (entailment-, consistency-, and RAG-trained) and zero-shot frontier LLM judges perform near chance at spotting unsupported claims in scientific peer reviews that must be checked against the full submitted paper, because they cannot separate paper-unsupported assertions from legitimate evaluative critique; small models fine-tuned on in-domain examples beat them by a wide margin.Stating false facts confidently · reviewed by AI
- For a same-family pair of reasoning and instruction-tuned 4B models, learning one interpolation ratio per module (attention block, FFN block, embedding, final norm) with a reward that scores correctness and ranks correct responses by length cuts average generated tokens by about 27% relative to the reasoning model while holding average accuracy, and beats fixed global-ratio merging and CMA-ES search over the same ratios.Cutting to the chase · reviewed by AI
Notes
Drafted from the paper by a model and filed unreviewed. Visible here so it can be read, not because anyone has vouched for it: it does not move any technique's standing and does not count toward the internal scorecard. Drafted confidence: medium. Falsifier as drafted: A compute-matched baseline — the same total inference spent on repeated sampling plus simple best-of-n selection from one model — matching or beating the staged harness on TCS-Bench, or the gain vanishing under human grading.