# Continuous-Time Homeostatic Dynamics for Reentrant Inference Models

arXiv: https://arxiv.org/abs/2512.05158 · HTML: https://mlsanity.com/paper/2512.05158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Emergent Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2212.09196/) (2022)
- [Using Fast Weights to Attend to the Recent Past](https://mlsanity.com/paper/1610.06258/) (2016)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [A Modern Self-Referential Weight Matrix That Learns to Modify Itself](https://mlsanity.com/paper/2202.05780/) (2022)
- [Biophysical models of intrinsic homeostasis: Firing rates and beyond](https://mlsanity.com/paper/2203.14870/) (2022)
- [Recursive Dynamics in Fast-Weights Homeostatic Reentry Networks: Toward Reflective Intelligence](https://mlsanity.com/paper/2511.06798/) (2025)

## Abstract (arXiv)

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 xt = xt(ex) + γ, Wr, g(|yt-1|), yt-1, we derive the coupled system doty=-y+f(Wry;,x,,A)+gh(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 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.