# LADDER: Self-Improving LLMs Through Recursive Problem Decomposition

**Authors:** Toby Simonds, Akira Yoshiyama  
**arXiv:** [2503.00735](https://arxiv.org/abs/2503.00735)  
**Date:** 2025-03-02  
**Summary page:** https://www.summarizepaper.com/en/paper/2503.00735v1/

## Key points

- Authors Toby Simonds and Akira Yoshiyama introduce the LADDER framework for Large Language Models (LLMs)
- LADDER enables models to enhance problem-solving abilities autonomously through self-guided learning
- The framework iteratively generates and solves simpler versions of complex problems, leading to reinforcement learning for tackling more challenging tasks
- LADDER relies on verifiable reward signals for self-improvement, eliminating the need for curated datasets or human feedback
- Effectiveness demonstrated in mathematical integration tasks with significant accuracy improvements in model performance
- Introduction of Test-Time Reinforcement Learning (TTRL) method further enhances performance by generating problem variants during inference
- TTRL enables models to achieve outstanding scores by continuously creating and solving related problems during testing
- Strategic self-directed learning in AI systems showcases potential for substantial capability improvements without architectural scaling or human supervision

## Summary

, , , , 

In their paper titled "LADDER: Self-Improving LLMs Through Recursive Problem Decomposition," authors Toby Simonds and Akira Yoshiyama introduce a groundbreaking framework called LADDER (Learning through Autonomous Difficulty-Driven Example Recursion). This framework empowers Large Language Models (LLMs) to enhance their problem-solving abilities autonomously through self-guided learning. By iteratively generating and solving simpler versions of complex problems, LADDER enables models to progressively learn how to tackle more challenging tasks through reinforcement learning. The unique aspect of LADDER is its reliance on verifiable reward signals for guiding the model's self-improvement process, eliminating the need for curated datasets or human feedback. The model leverages its own capabilities to navigate through easier variants of sample questions, leading to significant advancements in problem-solving proficiency. The effectiveness of LADDER is demonstrated in mathematical integration tasks, where it substantially boosts the accuracy of a Llama 3B model from 1% to an impressive 82% on undergraduate-level problems. Additionally, a 7B parameter model achieves state-of-the-art performance (70%) on the prestigious MIT Integration Bee examination for its model size. Furthermore, the authors introduce Test-Time Reinforcement Learning (TTRL), a method that generates problem variants during inference and applies reinforcement learning to further enhance performance. By continuously creating and solving related problems during testing, TTRL enables the 7B model to achieve an outstanding score of 85%, surpassing previous benchmarks. Overall, these results highlight the potential of strategic self-directed learning in AI systems, showcasing how recursive problem decomposition and solution verification can lead to substantial capability improvements without relying on architectural scaling or human supervision. This innovative approach opens up new avenues for developing autonomous AI systems capable of extending their own capabilities in various domains.