TD-Grokking: New Framework Enables LLMs to Learn from Unsolvable Problems
Researchers propose TD-Grokking, a training method that breaks down impossible problems into solvable subproblems to help large language models learn from zero-reward scenarios. Current reinforcement learning approaches fail when all attempted solutions fail, providing no learning signal. The framework could improve LLM reasoning on challenging mathematical and medical tasks.
A new preprint on arXiv presents TD-Grokking, a training-time decomposition framework designed to address a fundamental limitation in reinforcement learning for large language models: the inability to learn from problems where all attempted solutions fail. The method recursively breaks down intractable root problems into smaller, self-contained subproblems organized in hierarchical trees, where solvable leaf nodes provide non-zero rewards that can guide model improvement. The authors evaluated TD-Grokking on mathematical and medical reasoning tasks, finding it outperformed vanilla GRPO and other baseline approaches. The framework converts zero-reward examples into usable training signals, enabling consistent performance gains. Code and datasets have been made available for reproducibility.
What's missing
The preprint does not discuss potential limitations of the decomposition approach, such as cases where problems may not decompose cleanly into verifiable subproblems, or computational overhead of the hierarchical decomposition process. Generalization to domains beyond mathematics and medicine is not addressed.
What different sources said
- arXiv cs.LGCenter
TD-Grokking: Learning from Zero-Reward Problems by Training-Time Decomposition
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