Multi-Agent Debate and Visual Information Extraction for SeePhys Pro: A 1st-Place Technical Report from ICML 2026 AI4Math Track 3 Challenge

This technical report presents our approach to Challenge Track~3: SeePhys Pro at the 3rd AI for Math Workshop, where the task is to answer college-level physics questions whose statement and figure may be given partly or entirely as an image. Visual physics problems become substantially harder for large language models when the decisive information resides in a figure rather than in the text, and this modality gap widens as more of the problem migrates into the image. We address the task with a two-stage framework: a visual information extraction stage that re-expresses figure content as solver-readable text to close the modality gap, and a reasoning stage that orchestrates three heterogeneous solvers through multi-agent debate. Our analysis yields two findings: the gain from orchestration comes from reliable answer selection rather than from additional debate, and the value of a figure aid scales with how much of the problem is locked inside the image. The resulting pipeline improves overall accuracy over a single-agent baseline from 0.643 to 0.802 on the public split, and won 1st place on both the public and the private leaderboard (private overall 0.743).

Semantic-aware Wasserstein Policy Regularization for Large Language Model Alignment

Large language models (LLMs) are commonly aligned with human preferences using reinforcement learning from human feedback (RLHF). In this method, LLM policies are generally optimized through reward maximization with Kullback-Leibler (KL) divergence regularization of the reference policy. However, KL and its $f$-divergence variants only compare token probabilities at identical indices, failing to capture semantic similarity. We propose Wasserstein Policy Regularization (WPR), a semantic-aware regularization for the RLHF framework based on the entropy-regularized Wasserstein distance, which incorporates the geometry of the token space. The dual formulation of the distance expresses the regularization as penalty terms applied to the reward via optimal dual variables, which yield a tractable objective compatible with standard RL algorithms. Empirically, our method outperforms KL- and $f$-divergence-based baselines, demonstrating the benefits of semantic-aware policy distances for alignment. Our code is available at https://github.com/aailab-kaist/WPR.

Reward-based Input Construction for Cross-document Relation Extraction

Relation extraction (RE) is a fundamental task in natural language processing, aiming to identify relations between target entities in text. While many RE methods are designed for a single sentence or document, cross-document RE has emerged to address relations across multiple long documents. Given the nature of long documents in cross-document RE, extracting document embeddings is challenging due to the length constraints of pre-trained language models. Therefore, we propose REward-based Input Construction (REIC), the first learning-based sentence selector for cross-document RE. REIC extracts sentences based on relational evidence, enabling the RE module to effectively infer relations. Since supervision of evidence sentences is generally unavailable, we train REIC using reinforcement learning with RE prediction scores as rewards. Experimental results demonstrate the superiority of our method over heuristic methods for different RE structures and backbones in cross-document RE. Our code is publicly available at https://github.com/aailabkaist/REIC.