On non-approximability of zero loss global ${\mathcal L}^2$ minimizers by gradient descent in Deep Learning

Thomas Chen; Patricia Muñoz Ewald

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arXiv · 2311.07065

On non-approximability of zero loss global ${\mathcal L}^2$ minimizers by gradient descent in Deep Learning

Thomas Chen·Patricia Muñoz Ewald

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Abstract

We analyze geometric aspects of the gradient descent algorithm in Deep Learning (DL), and give a detailed discussion of the circumstance that in underparametrized DL networks, zero loss minimization can generically not be attained. As a consequence, we conclude that the distribution of training inputs must necessarily be non-generic in order to produce zero loss minimizers, both for the method constructed in [Chen-Munoz Ewald 2023, 2024], or for gradient descent [Chen 2025] (which assume clustering of training data).

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BibTeX RIS

Thomas Chen, Patricia Muñoz Ewald. 2023-11-13. On non-approximability of zero loss global ${\mathcal L}^2$ minimizers by gradient descent in Deep Learning. https://arxiv.org/abs/2311.07065

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