Continuous-Time Homeostatic Dynamics for Reentrant Inference Models

• URL: http://arxiv.org/abs/2512.05158v1
• Date: Thu, 04 Dec 2025 07:33:13 GMT
• Title: Continuous-Time Homeostatic Dynamics for Reentrant Inference Models
• Authors: Byung Gyu Chae,
• Abstract summary: We formulate the Fast-Weights Homeostatic Reentry Network as a continuous-time neural-ODE system.<n>The dynamics admit bounded attractors governed by an energy functional, yielding a ring-like manifold.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $x_t = x_t^{(\mathrm{ex})} + γ\, W_r\, g(\|y_{t-1}\|)\, y_{t-1}$, we derive the coupled system $\dot{y}=-y+f(W_ry;\,x,\,A)+g_{\mathrm{h}}(y)$ 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 \emph{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.

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