ComBench: A Benchmark for Rigorous Proof Reasoning and Constructive Realization in Olympiad-Level Combinatorics
Quick Answer
ComBench is a new benchmark for evaluating combinatorial reasoning in large language models, revealing a performance gap in Olympiad-level problems.
Quick Take
The strongest model, Kimi-K2.6, scores 65.4% overall, while GPT-5.5 excels in analysis but not in construction tasks. This highlights distinct capabilities in rigorous proof reasoning versus constructive realization.
Key Points
- ComBench includes 100 human-annotated Olympiad-level combinatorial problems.
- Problems are divided into analysis-centric and construction-centric categories.
- Evaluation combines proof grading with deterministic construction verification.
- Kimi-K2.6 outperforms GPT-5.5 in construction tasks but lags in proof grading.
- Existence and Construction problems are consistently the hardest across models.
Paper Resources
Article Content
From source RSS / original summaryarXiv:2606. 10479v1 Announce Type: new Abstract: Combinatorics is central to Olympiad-level mathematical problem solving, requiring deep discrete reasoning, creative constructions, and rigorous structural insight. Recent evidence suggests that even today's strongest frontier models remain uneven on Olympiad combinatorics, revealing a gap in creative mathematical reasoning.
We introduce ComBench, an Olympiad-level combinatorics benchmark for evaluating and diagnosing the combinatorial reasoning capabilities of . ComBench contains 100 human-annotated competition-level problems organized around two complementary settings: analysis-centric problems, which primarily require rigorous mathematical arguments, and construction-centric problems, which require explicit constructions in addition to correctness justifications.
The evaluation protocol combines rubric-guided proof grading with deterministic construction verification, exposing cases where proof quality and construction validity diverge. Experiments on frontier open- and closed-source models show that ComBench is far from saturated: the strongest model reaches 65. 4% overall Avg. and 75. 3% overall Best@4. We further find that Rigorous Proof Reasoning and Constructive Realization are distinct capabilities: Kimi-K2. 6 trails GPT-5.
5 on analysis-centric proof grading but surpasses it on construction-centric Best@4, while Existence and Construction problems remain consistently hardest across representative frontier models.
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