Continuous-Time Homeostatic Dynamics for Reentrant Inference Models

2025/12/04 by Byung Gyu Chae, Chae, Byung Gyu · 1 citation
Computer Science · Neuroscience · Physics and Astronomy · #Neural Networks and Reservoir Computing #Neural dynamics and brain function #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2512.05158

Abstract

We formulate the Fast-Weights Homeostatic Reentry Network (FHRN) as a continuous-time neural-ODE system, revealing its role as a norm-regulated reentrant dynamical process. Starting from the discrete reentry rule x_t = x_t^(ex) + γ W_r g(‖y_t-1‖) y_t-1, we derive the coupled system y=-y+f(W_ry; x, A)+g_h(y) showing that the network couples fast associative memory with global radial homeostasis. The dynamics admit bounded attractors governed by an energy functional, yielding a ring-like manifold. A Jacobian spectral analysis identifies a reflective regime in which reentry induces stable oscillatory trajectories rather than divergence or collapse. Unlike continuous-time recurrent neural networks or liquid neural networks, FHRN achieves stability through population-level gain modulation rather than fixed recurrence or neuron-local time adaptation. These results establish the reentry network as a distinct class of self-referential neural dynamics supporting recursive yet bounded computation.

Citations

• Recursive Dynamics in Fast-Weights Homeostatic Reentry Networks: Toward Reflective Intelligence
• Retentive Network: A Successor to Transformer for Large Language Models
• Emergent Analogical Reasoning in Large Language Models
• Emergent Abilities of Large Language Models
• A Modern Self-Referential Weight Matrix That Learns to Modify Itself
• 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

Cited by

• Renormalization-Group Geometry of Homeostatically Regulated Reentry Networks

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