Shunkai Zhang
Publications
MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling
We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series. M3 first trains three proof-oriented capabilities -- proof generation, proof verification, and critique-conditioned proof repair -- using a defense-in-depth generative verifier engineered for low false-positive rate. These capabilities are merged into a single released M3 model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searches over a population of candidate proofs, and returns one final proof through tournament selection. With MaxProof test-time scaling, the M3 model reaches 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.
ComBench: A Benchmark for Rigorous Proof Reasoning and Constructive Realization in Olympiad-Level Combinatorics
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 large language models. 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.
$π$-Bench: Evaluating Proactive Personal Assistant Agents in Long-Horizon Workflows
The rise of personal assistant agents, e.g., OpenClaw, highlights the growing potential of large language models to support users across everyday life and work. A core challenge in these settings is proactive assistance, since users often begin with underspecified requests and leave important needs, constraints, or preferences unstated. However, existing benchmarks rarely evaluate whether agents can identify and act on such hidden intents before they are explicitly stated, especially in sustained multi-turn interactions where user needs emerge gradually. To address this gap, we introduce $π$-Bench, a benchmark for proactive assistance comprising 100 multi-turn tasks across 5 domain-specific user personas. By incorporating hidden user intents, inter-task dependencies, and cross-session continuity, $π$-Bench evaluates agents' ability to anticipate and address user needs over extended interactions, jointly measuring proactivity and task completion in long-horizon trajectories that better reflect real-world use. Experiments show (1) proactive assistance remains challenging, (2) a clear distinction between task completion and proactivity, and (3) the value of prior interaction for proactive intent resolution in later tasks.