# Non-Parametric Structural Priors for Geometry Theorem Prediction

arXiv: https://arxiv.org/abs/2603.04852 · HTML: https://mlsanity.com/paper/2603.04852/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [RAPTOR: Recursive Abstractive Processing for Tree-Organized Retrieval](https://mlsanity.com/paper/2401.18059/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [On the Planning Abilities of Large Language Models : A Critical Investigation](https://mlsanity.com/paper/2305.15771/) (2023)
- [HippoRAG: Neurobiologically Inspired Long-Term Memory for Large Language Models](https://mlsanity.com/paper/2405.14831/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [DeepMath - Deep Sequence Models for Premise Selection](https://mlsanity.com/paper/1606.04442/) (2016)
- [jina-embeddings-v4: Universal Embeddings for Multimodal Multilingual Retrieval](https://mlsanity.com/paper/2506.18902/) (2025)
- [What Makes Multimodal In-Context Learning Work?](https://mlsanity.com/paper/2404.15736/) (2024)
- [LANS: A Layout-Aware Neural Solver for Plane Geometry Problem](https://mlsanity.com/paper/2311.16476/) (2023)
- [GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training](https://mlsanity.com/paper/2412.11863/) (2024)
- [A Symbolic Character-Aware Model for Solving Geometry Problems](https://mlsanity.com/paper/2308.02823/) (2023)
- [AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning](https://mlsanity.com/paper/2505.23381/) (2025)
- [FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network](https://mlsanity.com/paper/2402.11461/) (2024)
- [Logic-RAG: Augmenting Large Multimodal Models with Visual-Spatial Knowledge for Road Scene Understanding](https://mlsanity.com/paper/2503.12663/) (2025)
- [FGeo-DRL: Deductive Reasoning for Geometric Problems through Deep Reinforcement Learning](https://mlsanity.com/paper/2402.09051/) (2024)

## Built on by (most cited first, 1 of 1)

- [Beyond Symbolic Solving: Multi Chain-of-Thought Voting for Geometric Reasoning in Large Language Models](https://mlsanity.com/paper/2604.00890/) (2026)

## Abstract (arXiv)

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.