# Partial Information Rate Decomposition

arXiv: https://arxiv.org/abs/2502.04550 · HTML: https://mlsanity.com/paper/2502.04550/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2025.

## Built on by (most cited first, 3 of 3)

- [How Vision Becomes Language: A Layer-wise Information-Theoretic Analysis of Multimodal Reasoning](https://mlsanity.com/paper/2602.15580/) (2026)
- [Consciousness as Uncommon Self-Knowledge: A Synergistic Information Framework](https://mlsanity.com/paper/2605.13884/) (2026)
- [MLLMs Hallucinate when Information Distribution Drifts in Synergy Heads](https://mlsanity.com/paper/2609.09206/) (2026)

## Abstract (arXiv)

Partial Information Decomposition (PID) is a principled and flexible method to unveil complex high-order interactions in multi-unit network systems. Though being defined exclusively for random variables, PID is ubiquitously applied to multivariate time series taken as realizations of random processes with temporal statistical structure. Here, to overcome the incorrect depiction of high-order effects by PID schemes applied to dynamic networks, we introduce the framework of Partial Information Rate Decomposition (PIRD). PIRD is first formalized applying lattice theory to decompose the information shared dynamically between a target random process and a set of source processes, and then implemented for Gaussian processes through a spectral expansion of information rates. The new framework is validated in simulated network systems and demonstrated in the practical analysis of time series from large-scale climate oscillations.