CORE: Concept-Oriented Reinforcement for Bridging the Definition-Application Gap in Mathematical Reasoning

Researchers introduce CORE (Concept-Oriented REinforcement), a new training framework that improves large language models' mathematical reasoning by bridging the gap between memorizing definitions and applying concepts. The method uses concept-aligned quizzes and concept-primed trajectories to provide fine-grained supervision, showing consistent improvements over traditional training approaches across multiple benchmarks.

• →CORE addresses the problem where LLMs can solve math exercises but fail to apply concepts when genuine understanding is required.
• →The framework uses explicit concepts as controllable supervision signals rather than just reinforcing final answers.
• →CORE synthesizes concept-aligned quizzes and injects concept snippets during training rollouts to improve reasoning.
• →The method shows consistent gains over vanilla and supervised fine-tuning baselines on both in-domain and out-of-domain math benchmarks.
• →CORE remains algorithm- and verifier-agnostic while providing fine-grained conceptual supervision for mathematical reasoning.