Incremental Learning in Mirror Flows
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.
| Authors | Raphaël Berthier, Loucas Pillaud-Vivien |
|---|---|
| Primary category | math.OC |
| Published | 22 June 2026 |
| Last updated at source | 25 August 2026 |
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