aiqbench analysis
This research addresses the "Structural Drift" bottleneck in in-context learning by introducing Theorem Precedence Graphs to enforce topological constraints without gradient-based optimization. By encoding historical solution traces into directed graphs, the method enables LLMs to function as structured planners, achieving 89.29% accuracy on the FormalGeo7k benchmark while matching supervised state-of-the-art models. The approach demonstrates that explicit structural priors significantly improve scalability for multi-step symbolic reasoning tasks.
Non-Parametric Structural Priors for Geometry Theorem Prediction
arXiv:2603.04852v2 Announce Type: replace Abstract: Multi-step theorem prediction is a central challenge in geometry problem solving. Existing neural-symbolic approaches rely heavily on supervised parametric models, which exhibit limited generalization to evolving theorem libraries. In this work, we explore training-free theorem prediction through the lens of in-context learning (ICL). We identify a critical scalability bottleneck, termed Structural Drift: as reasoning depth increases, the performance of vanilla ICL degrades sharply, often collapsing to near zero. We attribute this failure to the LLM's inability to recover latent topological dependencies, leading to unstructured exploration. To address this issue, we propose Theorem Precedence Graphs, which encode temporal dependencies from historical solution traces as directed graphs, and impose explicit topological constraints that effectively prune the search space during inference. Coupled with retrieval-augmented graph construction and a stepwise symbolic executor, our approach enables LLMs to act as structured planners without any gradient-based optimization. Experiments on the FormalGeo7k benchmark show that our method achieves 89.29% accuracy, substantially outperforming ICL baselines and matching state-of-the-art supervised models. These results indicate that explicit structural priors offer a promising direction for scaling LLM-based symbolic reasoning.
Abstract:Multi-step theorem prediction is a central challenge in geometry problem solving. Existing neural-symbolic approaches rely heavily on supervised parametric models, which exhibit limited generalization to evolving theorem libraries. In this work, we explore training-free theorem prediction through the lens of in-context learning (ICL). We identify a critical scalability bottleneck, termed Structural Drift: as reasoning depth increases, the performance of vanilla ICL degrades sharply, often collapsing to near zero. We attribute this failure to the LLM's inability to recover latent topological dependencies, leading to unstructured exploration. To address this issue, we propose Theorem Precedence Graphs, which encode temporal dependencies from historical solution traces as directed graphs, and impose explicit topological constraints that effectively prune the search space during inference. Coupled with retrieval-augmented graph construction and a stepwise symbolic executor, our approach enables LLMs to act as structured planners without any gradient-based optimization. Experiments on the FormalGeo7k benchmark show that our method achieves 89.29% accuracy, substantially outperforming ICL baselines and matching state-of-the-art supervised models. These results indicate that explicit structural priors offer a promising direction for scaling LLM-based symbolic reasoning.
Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV)
arXiv:2603.04852 [cs.AI]
(or arXiv:2603.04852v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2603.04852 Focus to learn more arXiv-issued DOI via DataCite
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