Self-Evidencing Through Hierarchical Gradient Decomposition: A Dissipative System That Maintains Non-Equilibrium Steady-State by Minimizing Variational Free Energy

TL;DR

This paper introduces a hierarchical gradient decomposition system that minimizes variational free energy, enabling self-organization, robustness, and efficient learning through biologically plausible local rules.

Contribution

It provides a constructive proof that the Free Energy Principle can be implemented via exact local credit assignment mechanisms at multiple hierarchical levels.

Findings

TFM achieves 0.9693 correlation with oracle gradients

System retains 98.6% after task interference

Enables autonomous recovery and efficient reinforcement learning

Abstract

The Free Energy Principle (FEP) states that self-organizing systems must minimize variational free energy to persist, but the path from principle to implementable algorithm has remained unclear. We present a constructive proof that the FEP can be realized through exact local credit assignment. The system decomposes gradient computation hierarchically: spatial credit via feedback alignment, temporal credit via eligibility traces, and structural credit via a Trophic Field Map (TFM) that estimates expected gradient magnitude for each connection block. We prove these mechanisms are exact at their respective levels and validate the central claim empirically: the TFM achieves 0.9693 Pearson correlation with oracle gradients. This exactness produces emergent capabilities including 98.6% retention after task interference, autonomous recovery from 75% structural damage, self-organized criticality (spectral radius p ~= 1.0$), and sample-efficient reinforcement learning on continuous control tasks without replay buffers. The architecture unifies Prigogine's dissipative structures, Friston's free energy minimization, and Hopfield's attractor dynamics, demonstrating that exact hierarchical inference over network topology can be implemented with local, biologically plausible rules.