# LADDER: Self-Improving LLMs Through Recursive Problem Decomposition

arXiv: https://arxiv.org/abs/2503.00735 · HTML: https://mlsanity.com/paper/2503.00735/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Synthetic reasoning data and bootstrapping, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 6 of its 9 references that are in the map.
- First posted on arXiv 2 Mar 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 6 of 6)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [On Reinforcement Learning and Distribution Matching for Fine-Tuning Language Models with no Catastrophic Forgetting](https://mlsanity.com/paper/2206.00761/) (2022)

## Built on by (most cited first, 25 of 25)

- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [Learning to Reason for Long-Form Story Generation](https://mlsanity.com/paper/2503.22828/) (2025)
- [RLSR: Reinforcement Learning from Self Reward](https://mlsanity.com/paper/2505.08827/) (2025)
- [DISCOVER: Automated Curricula for Sparse-Reward Reinforcement Learning](https://mlsanity.com/paper/2505.19850/) (2025)
- [Local Mixtures of Experts: Essentially Free Test-Time Training via Model Merging](https://mlsanity.com/paper/2505.14136/) (2025)
- [Recursive Experiential-Working Memory Evolution for Long-Horizon Agent Harnesses](https://mlsanity.com/paper/2608.24876/) (2026)
- [Test-time Scaling Techniques in Theoretical Physics -- A Comparison of Methods on the TPBench Dataset](https://mlsanity.com/paper/2506.20729/) (2025)
- [Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning](https://mlsanity.com/paper/2512.10534/) (2025)
- [Detecting and Mitigating the Correct-Answer Extinction Window in Test-Time Reinforcement Learning with Majority Voting](https://mlsanity.com/paper/2605.19444/) (2026)
- [A quantum semantic framework for natural language processing](https://mlsanity.com/paper/2506.10077/) (2025)
- [Self-Improvement of Large Language Models: A Technical Overview and Future Outlook](https://mlsanity.com/paper/2603.25681/) (2026)
- [Training LLMs for Divide-and-Conquer Reasoning Elevates Test-Time Scalability](https://mlsanity.com/paper/2602.02477/) (2026)
- [When Your Own Output Becomes Your Training Data: Noise-to-Meaning Loops and a Formal RSI Trigger](https://mlsanity.com/paper/2505.02888/) (2025)
- [Amplification Effects in Test-Time Reinforcement Learning: Safety and Reasoning Vulnerabilities](https://mlsanity.com/paper/2603.15417/) (2026)
- [SCOPE-RL: Optimizing Reasoning Paths Before and After Success](https://mlsanity.com/paper/2607.11506/) (2026)
- [Knowledge Conceptualization Impacts RAG Efficacy](https://mlsanity.com/paper/2507.09389/) (2025)
- [ReLAPSe: Reinforcement-Learning-trained Adversarial Prompt Search for Erased concepts in unlearned diffusion models](https://mlsanity.com/paper/2602.00350/) (2026)
- [VERIFY-RL: Verifiable Recursive Decomposition for Reinforcement Learning in Mathematical Reasoning](https://mlsanity.com/paper/2602.07559/) (2026)
- [RVLM: Recursive Vision-Language Models with Adaptive Depth](https://mlsanity.com/paper/2603.24224/) (2026)
- [Be Your Own Teacher: Steering Protein Language Models via Unsupervised Reward Optimization](https://mlsanity.com/paper/2606.18961/) (2026)
- [Ladders of Thought: A Self-Evolving Curriculum of Progressively Simplified Reasoning Traces](https://mlsanity.com/paper/2609.25643/) (2026)
- [Variance-Optimal State Resampling for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2610.15888/) (2026)

## Abstract (arXiv)

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.