Causality as a Minimum Energy Principle
Moo K. Chung, D. Vijay Anand, Anass B El-Yaagoubi, Jae-Hun Jung, Anqi Qiu + 1 more
TLDR
This paper introduces a variational causal framework that models causality as energy flow, effectively capturing cyclic and higher-order dynamics in complex networks.
Key contributions
- Introduces a novel causal framework based on a variational principle for complex networks.
- Interprets causality as directional energy flow from high- to low-energy states.
- Employs Hodge theory to decompose network flows, capturing stable cyclic interactions.
- Uncovers robust cyclic causal patterns in fMRI data, missed by conventional models.
Why it matters
Classical causal models struggle with cyclic and higher-order dynamics. This paper offers a novel variational framework that overcomes these limitations, providing a more comprehensive understanding of complex network interactions. This is crucial for fields like neuroscience, where cyclic causality is prevalent.
Original 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.
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