提出一种新型神经网络动态机制，实现稳定递归计算。
Continuous-Time Homeostatic Dynamics for Reentrant Inference Models
- 将快速权重与自稳态反馈结合，构建连续时间神经动力系统
- 揭示网络存在受能量函数约束的环状吸引子，支持稳定振荡
- 适用于需要长期稳定递归处理的任务，如时序建模
我们将快速权重自稳态重入网络（FHRN）建模为连续时间神经-微分方程系统，揭示其作为规范调控型重入动力过程的本质。从离散重入规则 $x_t = x_t^{( ext{ex})} + γackslash W_rackslash g(ackslash\|y_{t-1}\|)ackslash y_{t-1}$ 出发，推导出耦合系统 $ackslashdot{y}=-y+f(W_ry;ackslash x,ackslash A)+g_{ ext{h}}(y)$，表明网络将快速联想记忆与全局径向自稳态相耦合。该动力学具有受能量泛函控制的有界吸引子，形成环状流形。雅可比谱分析识别出一种‘反射区’，在此区间内重入引发稳定振荡轨迹而非发散或坍缩。不同于连续时间循环神经网络或液体神经网络，FHRN通过群体层级增益调制实现稳定性，而非依赖固定递归或神经元局部时间适应。这些结果确立了重入网络作为一类支持递归但有界的自我指涉神经动力的新类别。
原文摘要 · Abstract (English)
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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