iit-fep-maxcaliber-bridge

name

iit-fep-maxcaliber-bridge

description

Maximum-Caliber Deviation framework bridging Integrated Information Theory (IIT) with the Free Energy Principle (FEP). Defines information as deviation from constrained maximum-caliber path ensembles, re-derives IIT cause/effect repertoires from variational principles, connects to active inference. Activation: iit fep bridge, maximum caliber, integrated information theory free energy, consciousness framework, constrained entropy maximization.

Information as Maximum-Caliber Deviation: Bridging IIT and FEP

A mathematical framework defining information as deviation from constrained maximum-caliber path ensembles, enabling re-derivation of IIT 3.0 cause/effect repertoires from variational principles and establishing a bridge to active inference.

Metadata

• Source: arXiv:2605.12536
• Author: Alexander Kearney (Mathematical Institute, University of Oxford)
• Published: 2026-05-03
• Length: 84 pages, 10 figures, 2 tables (Extended Master's thesis)
• Subjects: Neurons and Cognition (q-bio.NC); Artificial Intelligence (cs.AI); Information Theory (cs.IT)

Core Methodology

Key Innovation

Defines information as the deviation ψ of realized dynamics from a constrained maximum-caliber (MaxCal) path ensemble over a finite time horizon. Under this definition, IIT 3.0's cause/effect repertoires emerge directly from MaxCal variational principles — allowing IIT's phenomenological calculus to be re-derived from Constrained Entropy Maximization over Paths (CMEP).

Technical Framework

1. Information as Maximum-Caliber Deviation

• Realized dynamics deviate from a constrained MaxCal path ensemble
• Deviation ψ quantifies information content
• Applies over finite time horizons
• Bridges trajectory-level statistics with causal structure

2. Re-deriving IIT from Variational Principles

• IIT 3.0 cause/effect repertoires derived from CMEP (Constrained Maximum-Entropy over Paths)
• Eliminates need for IIT's axiomatic starting point
• Provides physically grounded basis for integrated information (Φ)
• Connects consciousness calculus to thermodynamic entropy maximization

3. Bridge to Active Inference

• Active inference is mathematically dual to CMEP under Langevin dynamics
• Provides principled route for extending IIT to new dynamical regimes
• Unifies predictive processing with integrated information theory

4. Connection to Predictive Coding

• Under Central Limit Theorem for Markov chains and Large Deviations Theory (LDT) applied to Ising models:
  • Information ψ is equivalent to prediction error under predictive coding models
• Explains "hill-shaped trajectory" of Φ observed in neuronal cultures adapting to sensory inputs

5. Thermodynamic Framework of Cognition

• Grounds consciousness in violations of the Fluctuation-Dissipation Theorem (FDT)
• Connects FEP, IIT, and thermodynamic frameworks of cognition

Mathematical Components

MaxCal Path Ensemble

• Path entropy maximization subject to constraints
• Realized trajectory deviation from ensemble quantified as ψ
• Finite time horizon formulation

CMEP (Constrained Maximum-Entropy over Paths)

• Variational principle generating IIT cause/effect repertoires
• Provides physical grounding for Φ (integrated information)
• Dual to active inference under Langevin dynamics

LDT Application to Ising Models

• Large Deviations Theory applied to network models
• Connects information deviation to prediction error
• Links to observable neuronal culture dynamics

Applications

• Consciousness research: Unified mathematical framework for IIT and FEP
• Neural adaptation: Explaining Φ trajectories in adapting neuronal cultures
• Active inference systems: Extending IIT to dynamical regimes
• AI safety: Understanding information processing in artificial systems
• Theoretical neuroscience: Bridging thermodynamic and information-theoretic approaches

Related Skills

• iit-critical-review
• spiking-free-energy-control
• neuro-grounded-foundation-models
• neural-emulator-theory
• thermodynamic-brain-connectivity
• nonequilibrium-brain-dynamics
• nonequilibrium-brain-dynamics-physics
• abstraction-fallacy-ai-consciousness
• ctm-ai-consciousness-blueprint

Pitfalls

• Theoretical synthesis: This is a mathematical bridge proposal, not yet experimentally validated
• Computational complexity: MaxCal path ensembles over finite horizons may be intractable for large systems
• IIT assumptions: Inherits all debates around IIT's foundational axioms
• Oxford Master's thesis: Extended academic work — 84 pages, may contain speculative extensions beyond core claims
• FDT violations: The consciousness-FDT connection is proposed but not proven

Implementation Notes

• Framework is primarily theoretical/mathematical
• Key equations involve path entropy maximization and variational calculus
• For practical applications, start with simple Ising model implementations
• LDT + CLT for Markov chains provide concrete testable predictions