Continuous-Time Homeostatic Dynamics for Reentrant Inference Models

TL;DR

This paper introduces a continuous-time neural-ODE model called FHRN that combines associative memory with global homeostasis, enabling stable, recursive neural dynamics with bounded attractors and oscillatory behavior.

Contribution

It formulates a novel continuous-time reentrant neural network model, revealing its stability mechanisms and dynamic properties distinct from traditional recurrent or liquid neural networks.

Findings

FHRN exhibits bounded attractors governed by an energy functional.

The network supports stable oscillatory trajectories in a reflective regime.

Stability is achieved through population-level gain modulation, not fixed recurrence.

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 $x_t = x_t^{(\mathrm{ex})} + \gamma\, W_r\, g(\|y_{t-1}\|)\, y_{t-1}$, 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.