Implicit Bias of Mirror Flow in Homogeneous Neural Networks: Sparse and Dense Feature Learning
We study the max-margin solutions reached by mirror flow in deep neural networks with homogeneous activation functions. Extending classical results on gradient flow, we derive a novel balance equation for mirror flow from convex duality, enabling a characterization of the horizon function governing the induced margin. We further establish max-margin characterizations together with convergence rates and norm growth estimates. Finally, we support our theory through experiments on synthetic datasets and standard vision tasks. Concretely, we show that: (1) distinct non-homogeneous mirror maps can induce the same max-margin solution; (2) convergence can be extremely slow, including exponential...
| Authors | Tom Jacobs, Guido Montufar |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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