Toby Simonds

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

We present Entropy Adaptive Decoding (EAD), a novel approach for efficient language model inference that dynamically switches between different-sized models based on prediction uncertainty. By monitoring rolling entropy in model logit distributions, our method identifies text regions where a smaller model suffices and switches to a larger model only when prediction uncertainty exceeds a threshold. Unlike speculative decoding approaches that maintain perfect output fidelity through verification, EAD accepts controlled output divergence in exchange for computational efficiency. Our experiments on the MATH benchmark demonstrate remarkable efficiency gains across different model families. Using the LLaMA family, we maintain 96.7\% of the 11B model's performance (50.4\% vs 52.1\%) while using it for only 43\% of tokens, decreasing computational cost by 41.5\%. These gains become more pronounced with larger size differentials in the Qwen family, where we achieve 92.9\% of the 14B model's performance (74.3\% vs 80.0\%) while using it for just 25\% of tokens, decreasing computational cost by 67\%. The consistency of these results across model pairs suggests that language model computation can be significantly optimized by selectively deploying model capacity based on local generation complexity. Our findings indicate that current approaches to model inference may be unnecessarily conservative in their pursuit of perfect output fidelity, and that accepting minor performance trade-offs can enable dramatic reductions in computational costs.

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.

Toby Simonds, Jey Han Lau, Chaithanya Bandi

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.