Abstract
Causal discovery from observational data remains fundamentally limited by identifiability constraints. Recent work has explored leveraging Large Language Models (LLMs) as sources of prior causal knowledge, but existing approaches rely on heuristic integration that lacks theoretical grounding. We introduce HOLOGRAPH, a framework that formalizes LLM-guided causal discovery through sheaf theory--representing local causal beliefs as sections of a presheaf over variable subsets. Our key insight is that coherent global causal structure corresponds to the existence of a global section, while topological obstructions manifest as non-vanishing sheaf cohomology. We propose the Algebraic Latent Projection to handle hidden confounders and Natural Gradient Descent on the belief manifold for principled optimization. Experiments on synthetic and real-world benchmarks demonstrate that HOLOGRAPH provides rigorous mathematical foundations while achieving competitive performance on causal discovery tasks with 50-100 variables. Our sheaf-theoretic analysis reveals that while Identity, Transitivity, and Gluing axioms are satisfied to numerical precision (<10^{-6}), the Locality axiom fails for larger graphs, suggesting fundamental non-local coupling in latent variable projections. Code is available at [this https URL](this https URL).
Abstract (translated)
从观测数据中进行因果发现的根本限制在于识别性约束。最近的研究探索了利用大型语言模型（LLMs）作为先验因果知识来源的可能性，但现有的方法依赖于缺乏理论依据的启发式集成方式。我们提出了HOLOGRAPH框架，该框架通过层叠理论（sheaf theory）将基于LLM的因果发现形式化——表示局部因果信念为变量子集上的预层截面。我们的关键洞察是：一致的整体因果结构对应于全局截面的存在，而拓扑障碍则表现为非消失的层上同调。 我们提出代数潜在投影来处理隐藏混淆因素，并在信念流形上采用自然梯度下降进行原则性优化。在合成数据和真实世界基准上的实验表明，HOLOGRAPH提供了严格的数学基础，在涉及50到100个变量的因果发现任务中表现出竞争性的性能。 我们的层叠理论分析揭示了同一性、传递性和粘合公理以数值精度（<10^{-6}）被满足，而局部性公理在更大的图上失败，这表明潜在变量投影中的根本非局部耦合。代码可在[此链接](this https URL)获取。
URL
https://arxiv.org/abs/2512.24478
