Akira Yoshiyama

Toby Simonds, 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.

Toby Simonds, Kevin Lopez, Akira Yoshiyama et al.

Large language models can generate solutions to complex problems, but training them with reinforcement learning typically requires verifiable rewards that are expensive to create and not possible for all domains. We demonstrate that LLMs can effectively self-improve through self-judging without reference solutions, leveraging the inherent asymmetry between generating and verifying solutions. Our experiments show that models can provide reliable reward signals without ground truth answers, enabling reinforcement learning in domains where verifiable rewards are impractical. By implementing self-judging across Countdown puzzles and integration problems, we achieve performance comparable to formal verification without ground truth solutions. Most notably, Qwen 2.5 7B DeepSeek Distilled trained with self-rewards qualifies for the prestigious MIT Integration Bee competition, performance through self-supervised improvement. When combined with synthetic question generation, we establish a complete self-improvement loop where models generate practice problems, solve them, and evaluate their own performance without any external validation. Our findings demonstrate that LLM judges can provide effective reward signals for training, unlocking reinforcement learning in countless domains previously limited by reward engineering challenges. This work represents a significant step toward autonomous AI systems that continuously improve through self-directed learning rather than human-guided training, potentially accelerating progress across domains where training data is scarce or evaluation is complex.