TD-Grokking: New Framework Enables LLMs to Learn from Unsolvable Problems
Researchers have proposed TD-Grokking, a training-time decomposition framework that enables large language models to learn from 'zero-reward' problems where standard reinforcement learning fails. The method recursively breaks down intractable problems into smaller, verifiable subproblems that can generate useful training signals. This addresses a critical bottleneck in AI reasoning training, with demonstrated improvements on mathematical and medical tasks.
A new paper posted to arXiv introduces TD-Grokking, a framework designed to overcome a fundamental limitation of reinforcement learning with verifiable rewards (RLVR) in training large language models. RLVR currently fails on highly challenging 'zero-reward' problems — cases where all sampled reasoning trajectories produce failed outcomes, leaving no optimization signal for the model to learn from. TD-Grokking addresses this by recursively decomposing these intractable root problems into hierarchical trees of smaller, self-contained, and verifiable subproblems, whose solvable leaf nodes provide non-zero reward signals. The authors report that TD-Grokking outperforms vanilla GRPO (a standard reinforcement learning baseline) and all other compared approaches on both mathematical and medical reasoning benchmarks. Prior approaches to this problem, including dense process supervision, partial reward assignment, and prefix-guided exploration, are characterized by the authors as insufficient due to task constraints or incomplete capability transfer. The code and datasets have been made publicly available, facilitating reproducibility and further research.
What's missing
The paper does not report absolute performance numbers or specific benchmark/dataset names in the abstract, making it difficult to assess the magnitude of improvements. Key limitations include whether the recursive decomposition approach scales to domains beyond mathematics and medicine, how decomposition quality is ensured automatically, and whether the method introduces significant computational overhead compared to standard RLVR training. The generalizability of results to other model architectures and sizes is also unaddressed in the available abstract.
What different sources said
- arXiv cs.LGCenter
TD-Grokking: Learning from Zero-Reward Problems by Training-Time Decomposition
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