QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first large-scale dual-rubric alignment benchmark to systematically measure alignment with human experts on university-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix (7 judges x 5 solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude Opus 4.5, DeepSeek-V3, Qwen 2.5 Max, and Llama 4 Maverick exhibit significant positive bias (up to +0.18, +0.20, +0.30, +0.36 mean score inflation, respectively). Furthermore, we uncover a critical reasoning gap in the discrete domain: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 average human evaluation score), other reasoning models like GPT-5 Pro and Claude Sonnet 4.5 see their performance significantly degrade in discrete domains. Specifically, their average human evaluation scores drop to 0.72 and 0.63 in Discrete Math, and to 0.74 and 0.50 in Graph Theory. In addition to these research results, we also release QEDBench as a public benchmark for evaluating and improving AI judges. Our benchmark is publicly published at https://github.com/qqliu/Yale-QEDBench.

Dueling Optimization with a Monotone Adversary

We introduce and study the problem of dueling optimization with a monotone adversary, which is a generalization of (noiseless) dueling convex optimization. The goal is to design an online algorithm to find a minimizer $\mathbf{x}^{*}$ for a function $f\colon X \to \mathbb{R}$, where $X \subseteq \mathbb{R}^d$. In each round, the algorithm submits a pair of guesses, i.e., $\mathbf{x}^{(1)}$ and $\mathbf{x}^{(2)}$, and the adversary responds with any point in the space that is at least as good as both guesses. The cost of each query is the suboptimality of the worse of the two guesses; i.e., ${\max} \left( f(\mathbf{x}^{(1)}), f(\mathbf{x}^{(2)}) \right) - f(\mathbf{x}^{*})$. The goal is to minimize the number of iterations required to find an $\varepsilon$-optimal point and to minimize the total cost (regret) of the guesses over many rounds. Our main result is an efficient randomized algorithm for several natural choices of the function $f$ and set $X$ that incurs cost $O(d)$ and iteration complexity $O(d\log(1/\varepsilon)^2)$. Moreover, our dependence on $d$ is asymptotically optimal, as we show examples in which any randomized algorithm for this problem must incur $\Omega(d)$ cost and iteration complexity.