HOLOGRAPH: LLM-Guided Causal Discovery with Sheaf Theory

This paper introduces HOLOGRAPH, a novel framework for causal discovery that leverages Large Language Models (LLMs) and formalizes the process using sheaf theory. It addresses the limitations of observational data in causal discovery by incorporating prior causal knowledge from LLMs. The use of sheaf theory provides a rigorous mathematical foundation, allowing for a more principled approach to integrating LLM priors. The paper's key contribution lies in its theoretical grounding and the development of methods like Algebraic Latent Projection and Natural Gradient Descent for optimization. The experiments demonstrate competitive performance on causal discovery tasks.