Gradient Flow Dynamics and Implicit Bias of Diagonal Linear Networks under Infinitesimal Initialization
We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear networks and a broader class of two-layer diagonal linear networks (as defined in Definition 4.1). Specifically, we demonstrate that the training trajectories of these models can be equivalently characterized by the proposed Algorithm 1. We further prove that this algorithm converges to the solution of a modified $ \mathcal{l}_1 $ norm minimization problem. As a result, we establish that the implicit bias of both network architectures corresponds to a modified $ \...
| Authors | Jiajie Zhao, Jianxing Wang, Junjie Yang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 July 2026 |
| Last updated at source | 14 July 2026 |
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