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arXiv Machine Learning By Eric Regis, Sinho Chewi

Unifying Central Flow, Rod Flow, and the Edge Coupling

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The paper introduces the edge coupling, a functional whose critical points correspond to the fixed points and period‑two orbits of gradient descent. It shows that both central flow and rod flow—previous continuous‑time models for the edge of stability—can be derived from this edge coupling, with rod flow coarse‑graining only the fastest time scale and central flow coarse‑graining both fast and intermediate scales. The authors extend these derivations to momentum methods such as heavy ball and Adam, and experimentally confirm that the resulting flows track discrete iterates across all training phases, including the transition to the edge of stability.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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