Geodesic
On non-approximability of zero loss global $\mathcal L^2$ minimizers by gradient descent in deep learning
Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 67

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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 cannot generically 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 \cite{cheewa-2,cheewa-4}, or for gradient descent \cite{ch-7} (which assume clustering of training data).
DOI : 10.2298/TAM250121008C
Classification : 57R70, 62M45
Keywords: deep learning, underparametrization, generic training data, zero loss 
Thomas Chen; Patricia Muñoz Ewald. On non-approximability of zero loss global $\mathcal L^2$ minimizers by gradient descent in deep learning. Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 67 . doi: 10.2298/TAM250121008C
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