S-DAG: A Subject-Based Directed Acyclic Graph for Multi-Agent Heterogeneous Reasoning

Abstract: LLMs have achieved impressive performance in complex reasoning problems. Their effectiveness highly depends on the specific nature of the task, especially the required domain knowledge. Existing approaches, such as mixture-of-experts, typically operate at the task level; they are too coarse to effectively solve the heterogeneous problems involving multiple subjects. This work proposes a novel framework that performs fine-grained analysis at subject level equipped with a designated multi-agent collaboration strategy for addressing heterogeneous problem reasoning. Specifically, given an input query, we first employ a Graph Neural Network to identify the relevant subjects and infer their interdependencies to generate an \textit{Subject-based Directed Acyclic Graph} (S-DAG), where nodes represent subjects and edges encode information flow. Then we profile the LLM models by assigning each model a subject-specific expertise score, and select the top-performing one for matching corresponding subject of the S-DAG. Such subject-model matching enables graph-structured multi-agent collaboration where information flows from the starting model to the ending model over S-DAG. We curate and release multi-subject subsets of standard benchmarks (MMLU-Pro, GPQA, MedMCQA) to better reflect complex, real-world reasoning tasks. Extensive experiments show that our approach significantly outperforms existing task-level model selection and multi-agent collaboration baselines in accuracy and efficiency. These results highlight the effectiveness of subject-aware reasoning and structured collaboration in addressing complex and multi-subject problems.