{"ID":2832865,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.05158","arxiv_id":"2512.05158","title":"Continuous-Time Homeostatic Dynamics for Reentrant Inference Models","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.","short_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+...","url_abs":"https://arxiv.org/abs/2512.05158","url_pdf":"https://arxiv.org/pdf/2512.05158v1","authors":"[\"Byung Gyu Chae\"]","published":"2025-12-04T07:33:13Z","proceeding":"math.DS","tasks":"[\"math.DS\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}