On the Loss Landscape Geometry of Regularized Deep Matrix Factorization: Uniqueness and Sharpness
Weight decay is ubiquitous in training deep neural network architectures. Its empirical success is often attributed to capacity control; nonetheless, our theoretical understanding of its effect on the loss landscape and the set of minimizers remains limited. In this paper, we show that $\ell^2$-regularized deep matrix factorization/deep linear network training problems with squared-error loss admit a unique end-to-end minimizer for all target matrices subject to factorization, except for a set of Lebesgue measure zero formed by the depth and the regularization parameter. This observation reveals fundamental properties of the loss landscape of regularized deep matrix factorization problems...
| Authors | Anil Kamber, Rahul Parhi |
|---|---|
| Primary category | stat.ML |
| Published | 28 March 2026 |
| Last updated at source | 28 March 2026 |
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