Cumulative Reasoning with Large Language Models
Large language models (LLMs) remain constrained in complex logical and mathematical reasoning. This paper introduces Cumulative Reasoning (CR), a novel framework that emulates human incremental thinking by decomposing problems into subtasks and iteratively accumulating and reusing intermediate propositions and execution results—without external retrieval or internet access. CR integrates symbolic reasoning chain construction, iterative prompt engineering, and an internal code execution environment to enable pure model-intrinsic reasoning leaps. Experiments demonstrate substantial gains: 98.04% accuracy on FOLIO (+9.3%), 98% on Game of 24 (+24%), +4.2% overall on MATH and up to +43% on its hardest subset. A code-only CR variant achieves 72.2%, significantly outperforming PAL and PoT (+38.8%). This work is the first to systematically propose and empirically validate an intrinsic, cumulative, iterative reasoning paradigm.