Continuous Limits of Coupled Flows in Representation Learning
While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these discrete dynamics on continuous data manifolds remain theoretically unresolved, notoriously suffering from parameter explosion. We bridge this gap by formalizing decentralized learning as a coupled slow-fast dynamical system on Riemannian manifolds. First, using measure-theoretic limits, we prove that the discrete spatial transitions converge uniformly to an overdamped Langevin stochastic differential equation. Second, via the Itô-Poisson resolvent and a stoch...
| Authors | Zilin Li, Weiwei Xu, Xuchun Tong et al. |
|---|---|
| Primary category | cs.LG |
| Published | 18 April 2026 |
| Last updated at source | 18 April 2026 |
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