Continuous-Time Homeostatic Dynamics for Reentrant Inference Models
This work addresses the challenge of stability in self-referential neural systems for researchers in computational neuroscience and machine learning, though it appears incremental as it builds on existing reentry models.
The paper tackled the problem of achieving stable, bounded computation in reentrant neural networks by formulating a continuous-time homeostatic dynamics model, which revealed a reflective regime enabling stable oscillatory trajectories without divergence or collapse.
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.