![[2602.14885] Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.14885] Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks
Summary
The paper introduces Drift-Diffusion Matching, a framework for training recurrent neural networks (RNNs) to model complex stochastic dynamics in low-dimensional spaces, emphasizing the role of asymmetric connectivity in enhancing network behavior.
Why It Matters
This research provides insights into how RNNs can better emulate biological neural networks, which often exhibit asymmetric connectivity. By extending attractor neural network theory, it opens new avenues for understanding complex dynamical systems and their applications in fields like neuroscience and machine learning.
Key Takeaways
- Introduces a new framework for training RNNs with asymmetric connectivity.
- Demonstrates how RNNs can represent complex stochastic dynamics.
- Extends existing theories of neural networks to include nonequilibrium dynamics.
- Provides applications for modeling associative and episodic memory.
- Highlights the significance of time-irreversibility in network dynamics.
Condensed Matter > Disordered Systems and Neural Networks arXiv:2602.14885 (cond-mat) [Submitted on 16 Feb 2026] Title:Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks Authors:Ramón Nartallo-Kaluarachchi, Renaud Lambiotte, Alain Goriely View a PDF of the paper titled Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks, by Ram\'on Nartallo-Kaluarachchi and Renaud Lambiotte and Alain Goriely View PDF HTML (experimental) Abstract:Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows. In contrast, biological networks support rich time-dependent behaviour facilitated by their asymmetry. Here we introduce a general framework, which we term drift-diffusion matching, for training continuous-time RNNs to represent arbitrary stochastic dynamical systems within a low-dimensional latent subspace. Allowing asymmetric connectivity, we show that RNNs can faithfully embed the drift and diffusion of a given stochastic differential equation, including nonlinear and nonequilibrium dynamics such as chaotic attractors. As an application, we construct RNN realisations of stochastic systems that transiently explore various attractors through both input-driven switching and autonomous...
