Causality as a Minimum Energy Principle

TL;DR

This paper introduces a novel causal modeling framework based on a variational principle, capable of capturing cyclic and higher-order dynamics in complex networks, demonstrated on fMRI data.

Contribution

It presents a new causality framework using energy flow and Hodge theory, extending beyond acyclic models to include cyclic interactions.

Findings

Revealed robust cyclic causal patterns in fMRI data

Decomposed network flows into dissipative and harmonic components

Detected causal interactions missed by traditional models

Abstract

Classical causal models, such as Granger causality and structural equation modeling, are largely restricted to acyclic interactions and struggle to represent cyclic and higher-order dynamics in complex networks. We introduce a causal framework grounded in a variational principle, interpreting causality as directional energy flow from high- to low-energy states along network connections. Using Hodge theory, network flows are decomposed into dissipative components and a persistent harmonic component that captures stable cyclic interactions. Applied to resting-state fMRI connectivity, our variational framework reveals robust cyclic causal patterns that are not detected by conventional causal models, highlighting the value of variational principles for causality.