Haoran Zhang
Publications
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.
The Last Harness You'll Ever Build
AI agents are increasingly deployed on complex, domain-specific workflows -- navigating enterprise web applications that require dozens of clicks and form fills, orchestrating multi-step research pipelines that span search, extraction, and synthesis, automating code review across unfamiliar repositories, and handling customer escalations that demand nuanced domain knowledge. \textbf{Each new task domain requires painstaking, expert-driven harness engineering}: designing the prompts, tools, orchestration logic, and evaluation criteria that make a foundation model effective. We present a two-level framework that automates this process. At the first level, the \textbf{Harness Evolution Loop} optimizes a worker agent's harness $\mathcal{H}$ for a single task: a Worker Agent $W_{\mathcal{H}}$ executes the task, an Evaluator Agent $V$ adversarially diagnoses failures and scores performance, and an Evolution Agent $E$ modifies the harness based on the full history of prior attempts. At the second level, the \textbf{Meta-Evolution Loop} optimizes the evolution protocol $Λ= (W_{\mathcal{H}}, \mathcal{H}^{(0)}, V, E)$ itself across diverse tasks, \textbf{learning a protocol $Λ^{(\text{best})}$ that enables rapid harness convergence on any new task -- so that adapting an agent to a novel domain requires no human harness engineering at all.} We formalize the correspondence to meta-learning and present both algorithms. The framework \textbf{shifts manual harness engineering into automated harness engineering}, and takes one step further -- \textbf{automating the design of the automation itself}.