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Incremental Learning in Mirror Flows
[Submitted on 22 Jun 2026] · 2026-06-23 · via stat updates on arXiv.org

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Abstract:We study mirror flows generated by a convex quadratic loss and a general convex lower semicontinuous mirror potential. We show that, when initialized near the boundary of the domain of the mirror potential, their rescaled trajectories converge to a limiting mirror flow whose potential is the indicator function of the domain. In this limit, the primal variable minimizes the loss over a time-dependent hypothesis set: the subdifferential of the support function of the domain, evaluated at the dual variable. This characterization provides a general mechanism for incremental learning in mirror flows.

Submission history

From: Raphaël Berthier [view email]
[v1] Mon, 22 Jun 2026 11:46:06 UTC (4,389 KB)