LADDER: Self-Improving LLMs Through Recursive Problem Decomposition
Authors: name: Toby Simonds, name: Akira Yoshiyama

We introduce LADDER (Learning through Autonomous Difficulty-Driven Example
Recursion), a framework which enables Large Language Models to autonomously
improve their problem-solving capabilities through self-guided learning by
recursively generating and solving progressively simpler variants of complex
problems. Unlike prior approaches that require curated datasets or human
feedback, LADDER leverages a model's own capabilities to generate easier
question variants. We demonstrate LADDER's effectiveness in the subject of
mathematical integration, improving Llama 3.2 3B's accuracy from 1% to 82% on
undergraduate-level problems and enabling Qwen2.5 7B Deepseek-R1 Distilled to
achieve 73% on the MIT Integration Bee qualifying examination. We also
introduce TTRL (Test-Time Reinforcement Learning), where we perform
reinforcement learning on variants of test problems at inference time. TTRL
enables Qwen2.5 7B Deepseek-R1 Distilled to achieve a state-of-the-art score of
90% on the MIT Integration Bee qualifying examination, surpassing OpenAI o1's
performance. These results show how self-directed strategic learning can
achieve significant capability improvements without relying on architectural
scaling or human supervision.