DIPHINE: Diffusion-based $Φ$-ID Neural Estimator

2026-06-17

AI Summary

Existing methods struggle to fully estimate the sixteen information atoms required for Integrated Information Decomposition (ΦID) in continuous non-Gaussian dynamical systems. This work proposes a diffusion model–based neural estimator that jointly approximates all mutual information terms via a single amortized network and accurately recovers the complete set of information atoms through Möbius inversion. To our knowledge, this is the first approach enabling full ΦID computation in continuous non-Gaussian settings. Theoretical analysis elucidates the error propagation mechanism from mutual information estimates to information atoms, identifying synergy-to-synergy atoms as the most challenging to estimate. Experiments demonstrate that the method accurately reconstructs ground-truth information structures on synthetic data, substantially outperforming existing mutual information estimators, and successfully uncovers interpretable information dynamics in real physiological data without assuming any specific distribution.

Abstract

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.

Problem

• Integrated Information Decomposition
• non-Gaussian dynamical systems
• mutual information estimation
• information dynamics
• continuous systems

Innovation

• Diffusion models
• Integrated Information Decomposition
• Neural estimation
• Mutual information
• Non-Gaussian systems