title: LADDER: Self-Improving LLMs Through Recursive Problem Decomposition
summary: 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.
paper_authors._id: 67c7dc0c9ad085d8f8ffc0cd
paper_authors.name: Toby Simonds
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-03-05T10:11:10.920Z
paper_authors._id: 649e1f4d2ccae3ea1f2b6a7f
paper_authors.avatarUrl: /avatars/04657fb53bde660dafb743da4273325f.svg
paper_authors.fullname: Toby Simonds
paper_authors.type: user
paper_authors.user: TamasSimonds
paper_authors._id: 67c7dc0c9ad085d8f8ffc0ce
paper_authors.name: Akira Yoshiyama
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-03-05T10:11:12.944Z
paper_authors._id: 667b8f5f09faa9d48cf82d2c
paper_authors.avatarUrl: /avatars/ca6c009ff73cedf4585ef8fea018443b.svg
paper_authors.fullname: Akira Yoshiyama
paper_authors.type: user
paper_authors.user: akiray1
paper_title: LADDER: Self-Improving LLMs Through Recursive Problem Decomposition
paper_summary: 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.
paper_ai_keywords: LADDER (Learning through Autonomous Difficulty-Driven Example Recursion) Large Language Models self-guided learning recursive generation simpler variants complex problems TTRL (Test-Time Reinforcement Learning) undergraduate-level problems Qwen2.5 7B Deepseek-R1 Distilled MIT Integration Bee qualifying examination self-directed strategic learning