Information Geometry Bridges Fisher Metric and Integrated Information in IIT — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 12, 2026 DOI: 10.5281/zenodo.21897912 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Argues that consciousness can be formally represented as integrated geometric structure in a qualia space defined by the Fisher information metric, with integrated information Phi measured as deviation from a product manifold. Proposes that the invariance and curvature properties of statistical manifolds provide a mathematical basis for linking information geometry to IIT. |
Abstract
FINDING: Information geometry provides a Riemannian metric (Fisher metric) on statistical manifolds, which IIT uses to define a "qualia space" where conscious experience corresponds to integrated geometric structure. MATH: Fisher information metric: \( g_{ij}(\theta) = \mathbb{E}_X \left[ \frac{\partial \log p(x|\theta)}{\partial \theta^i} \frac{\partial \log p(x|\theta)}{\partial \theta^j} \right] \). IIT's integrated information \(\Phi\) measures deviation from a disconnected product manifold: \(\Phi = \min_{\text{partition}} \left[ \text{distance}(p_{\text{full}}, p_{\text{partition}}) \right]\), often using the Kullback-Leibler divergence or Wasserstein distance. Qualia space is a high-dimensional manifold of probability distributions over system states. CONNECTION: The Fisher metric is invariant under reparameterization, linking to the constant curvature of statistical manifolds. For Beta/Dirichlet distributions, the Fisher metric yields constant negative curvature (hyperbolic g Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com