DIPHINE: Diffusion-based $Φ$-ID Neural Estimator
This work enables ΦID analysis for continuous non-Gaussian dynamical systems, addressing a key limitation that previously restricted such analysis to Gaussian or discrete systems.
DIPHINE is the first neural estimator for Integrated Information Decomposition (ΦID) that uses score-based diffusion models to estimate all required mutual information terms from a single amortized network, enabling application to continuous non-Gaussian systems. It accurately recovers ground-truth atoms on synthetic benchmarks and extracts physiologically interpretable structure from real data without distributional assumptions.
Uncovering the true informational architecture of real-world complex systems requires disentangling how their components uniquely store, redundantly share, and synergistically integrate information over time. Integrated Information Decomposition ($Φ$ID) is a framework for decomposing the information dynamics of multivariate systems into sixteen non-overlapping atoms that characterize redundant, unique, and synergistic modes of information storage, transfer, and integration. Existing methods to compute $Φ$ID are restricted to Gaussian or discrete systems, preventing its application to continuous non-Gaussian dynamical systems. We address this limitation by proposing DIPHINE (Diffusion-based $Φ$-ID Neural Estimator), the first neural estimator that leverages score-based diffusion models to jointly estimate all the mutual information terms required by $Φ$ID from a single amortized network, recovering the sixteen atoms through Möbius inversion. We provide a theoretical analysis of error propagation through the inversion, showing that the Jacobian of the mapping from mutual informations to atoms is integer-valued and that the synergy-to-synergy atom is provably the hardest to estimate. We demonstrate accurate recovery of ground-truth atoms on synthetic benchmarks, superior performance compared to established mutual information estimators, and the ability to extract physiologically interpretable information-dynamic structure on an application involving real data without any distributional assumptions.