A Principled Infotheoretic \phi-like Measure

TL;DR

This paper introduces a new measure, ψ, for quantifying irreducibility in integrated information theory, addressing limitations of the traditional φ measure with a more rigorous and computationally efficient approach.

Contribution

The paper proposes a revised irreducibility measure, ψ, grounded in Partial Information Decomposition, improving upon φ in theory and computational speed.

Findings

ψ is rigorously grounded in Partial Information Decomposition

ψ addresses key concerns about φ's limitations

ψ is faster to compute than φ

Abstract

Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $\phi$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we pinpoint three concerns about $\phi$ and propose a revised measure, $\psi$, which addresses them. Our measure $\psi$ is rigorously grounded in Partial Information Decomposition and is faster to compute than $\phi$.