View in EDS

GeoMIP: A Geometric-Topological and Dynamic Programming Framework for Enhanced Computational Tractability of Minimum Information Partition in Integrated Information Theory.

Saved in:
Bibliographic Details
Title: GeoMIP: A Geometric-Topological and Dynamic Programming Framework for Enhanced Computational Tractability of Minimum Information Partition in Integrated Information Theory.
Authors: Díaz-Arancibia, Jaime, Guerrero, Luz Enith, Arango-López, Jeferson, Castillo, Luis Fernando, Bustamante-Mora, Ana
Source: Applied Sciences (2076-3417); Jan2026, Vol. 16 Issue 2, p809, 46p
Subject Terms: DYNAMIC programming, COMPUTATIONAL complexity, HYPERCUBES, INFORMATION theory, HYPERGRAPHS
Abstract: The computational tractability of Integrated Information Theory (IIT) is fundamentally constrained by the exponential cost of identifying the Minimum Information Partition (MIP), which is required to quantify integrated information (Φ). Existing approaches become impractical beyond ~15–20 variables, limiting IIT analyses on realistic neural and complex systems. We introduce GeoMIP, a geometric–topological framework that recasts the MIP search as a graph-based optimization problem on the n-dimensional hypercube graph: discrete system states are modeled as graph vertices, and Hamming distance adjacency defines edges and shortest-path structures. Building on a tensor-decomposed representation of the transition probabilities, GeoMIP constructs a transition-cost (ground cost) structure by dynamic programming over graph neighborhoods and BFS-like exploration by Hamming levels, exploiting hypercube symmetries to reduce redundant evaluations. We validate GeoMIP against PyPhi, ensuring reliability of MIP identification and Φ computation. Across multiple implementations, GeoMIP achieves 165–326× speedups over PyPhi while maintaining 98–100% agreement in partition identification. Heuristic extensions further enable analyses up to ~25 variables, substantially expanding the practical IIT regime. Overall, by leveraging the hypercube's explicit graph structure (vertices, edges, shortest paths, and automorphisms), GeoMIP turns an intractable combinatorial search into a scalable graph-based procedure for IIT partitioning. [ABSTRACT FROM AUTHOR]
Copyright of Applied Sciences (2076-3417) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Complementary Index
Description
Abstract:The computational tractability of Integrated Information Theory (IIT) is fundamentally constrained by the exponential cost of identifying the Minimum Information Partition (MIP), which is required to quantify integrated information (Φ). Existing approaches become impractical beyond ~15–20 variables, limiting IIT analyses on realistic neural and complex systems. We introduce GeoMIP, a geometric–topological framework that recasts the MIP search as a graph-based optimization problem on the n-dimensional hypercube graph: discrete system states are modeled as graph vertices, and Hamming distance adjacency defines edges and shortest-path structures. Building on a tensor-decomposed representation of the transition probabilities, GeoMIP constructs a transition-cost (ground cost) structure by dynamic programming over graph neighborhoods and BFS-like exploration by Hamming levels, exploiting hypercube symmetries to reduce redundant evaluations. We validate GeoMIP against PyPhi, ensuring reliability of MIP identification and Φ computation. Across multiple implementations, GeoMIP achieves 165–326× speedups over PyPhi while maintaining 98–100% agreement in partition identification. Heuristic extensions further enable analyses up to ~25 variables, substantially expanding the practical IIT regime. Overall, by leveraging the hypercube's explicit graph structure (vertices, edges, shortest paths, and automorphisms), GeoMIP turns an intractable combinatorial search into a scalable graph-based procedure for IIT partitioning. [ABSTRACT FROM AUTHOR]
ISSN:20763417
DOI:10.3390/app16020809