Information-Geometric Neural Granger Causality

Discovering causal relationships from time series data is fundamental across scientific domains. While neural networks have advanced time series analysis, neural approaches to Granger causality lack theoretical foundations—particularly recent methods that achieve strong empirical performance without explanatory theory. We introduce Information-Geometric Neural Granger Causality (IG-NGC), a framework revealing how neural networks discover causal relationships through learning statistical manifolds. Our key insight is that causality manifests as directional information flow measured by the Fisher metric on these manifolds. This geometric perspective provides a theoretical framework that connects neural causality methods: we prove that causal influences emerge as information-geometric properties and demonstrate how existing approaches can be interpreted as approximations of our Information-Geometric Granger Causality (IGGC) measure, with exact equivalence established under Gaussian assumptions. Our framework yields theoretical guarantees including consistency, finite-sample complexity bounds, and scale consistency. Experiments on synthetic and real-world datasets confirm our theoretical predictions, transforming neural causality from empirical techniques into theoretically grounded methodologies.