Think beyond Instances: Abstraction as Modeling for Mathematical Reasoning

Mathematical reasoning is a fundamental capability of large language models (LLMs), requiring multi-step deduction and precise symbolic manipulation. Existing training-based and inference-time approaches improve reasoning performance but often rely on instance-specific solution traces, overlooking reusable computational structures shared across related problems and thereby limiting reasoning generalization. To address this limitation, we propose Think beyond Instances, a process-level reasoning abstraction framework that transforms instance-specific solutions into reusable logic-card chains. Our framework integrates multi-expert reasoning, logic-preserving reasoning abstraction that disentangles reusable logic from instance-specific realizations at each step, and chain-level validation to ensure global reasoning consistency before applying the validated chain to solve the original query. Experiments on six mathematical reasoning benchmarks demonstrate consistent improvements over competitive baselines. On Qwen3.5-9B, our framework achieves an average accuracy of 54.72%, outperforming the strongest baseline by 3.69 percentage points. Further analyses validate the effectiveness, transferability, and scalability of our framework. Our code is publicly available at an anonymous link https://anonymous.4open.science/r/Think-beyond-Instances-123-3E7C.