Self-Organized Criticality from Protected Mean-Field Dynamics: Loop Stability and Internal Renormalization in Reflective Neural Systems

2026/01/07 by Byung Gyu Chae · 1 voice
Physics and Astronomy · #nlin.AO #physics.comp-ph

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arxiv published 2026/01/07 · arxiv updated 2026/01/12

Abstract

The reflective homeostatic dynamics provides a minimal mechanism for self-organized criticality in neural systems. Starting from a reduced stochastic description, we demonstrate within the MSRJD field-theoretic framework that fluctuation effects do not destabilize the critical manifold. Instead, loop corrections are dynamically regularized by homeostatic curvature, yielding a protected mean-field critical surface that remains marginally stable under coarse-graining. Beyond robustness, we show that response-driven structural adaptation generates intrinsic parameter flows that attract the system toward this surface without external fine tuning. Together, these results unify loop renormalization and adaptive response in a single framework and establish a concrete route to autonomous criticality in reentrant neural dynamics.

Citations

• Renormalization-Group Geometry of Homeostatically Regulated Reentry Networks
• Continuous-Time Homeostatic Dynamics for Reentrant Inference Models
• Recursive Dynamics in Fast-Weights Homeostatic Reentry Networks: Toward Reflective Intelligence
• Linear Transformers Are Secretly Fast Weight Programmers
• Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention
• Liquid Time-constant Networks
• Using Fast Weights to Attend to the Recent Past
• Thermodynamics with continuous information flow
• Stochastic thermodynamics, fluctuation theorems and molecular machines
• Emergent complex neural dynamics
• Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics
• Paths to self-organized criticality
• On the Dynamics of Small Continuous-Time Recurrent Neural Networks
• Simplified neuron model as a principal component analyzer

Discussions

• Byung Gyu Chae: Self-Organized Criticality from Protected Mean-Field Dynamics: Loop Stability and Internal Renormalization in Reflective Neural Systems https://arxiv.org/abs/2601.04450 https://arxiv.o [bsky, 0 points, 0 comments]

Related

• Renormalization-Group Geometry of Homeostatically Regulated Reentry Networks
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• Self-tuned criticality: Controlling a neuron near its bifurcation point via temporal correlations
• Continuous-Time Homeostatic Dynamics for Reentrant Inference Models