Zero loss guarantees and explicit minimizers for generic overparametrized Deep Learning networks

Fuente: arXiv
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Main Authors: Chen, Thomas, Moore, Andrew G.
Format: Preprint
Published: 2025
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author Chen, Thomas
Moore, Andrew G.
author_facet Chen, Thomas
Moore, Andrew G.
contents We determine sufficient conditions for overparametrized deep learning (DL) networks to guarantee the attainability of zero loss in the context of supervised learning, for the $\mathcal{L}^2$ cost and {\em generic} training data. We present an explicit construction of the zero loss minimizers without invoking gradient descent. On the other hand, we point out that increase of depth can deteriorate the efficiency of cost minimization using a gradient descent algorithm by analyzing the conditions for rank loss of the training Jacobian. Our results clarify key aspects on the dichotomy between zero loss reachability in underparametrized versus overparametrized DL.
format Preprint
id arxiv_https___arxiv_org_abs_2502_14114
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Zero loss guarantees and explicit minimizers for generic overparametrized Deep Learning networks
Chen, Thomas
Moore, Andrew G.
Machine Learning
Artificial Intelligence
Analysis of PDEs
Optimization and Control
57R70, 62M45
We determine sufficient conditions for overparametrized deep learning (DL) networks to guarantee the attainability of zero loss in the context of supervised learning, for the $\mathcal{L}^2$ cost and {\em generic} training data. We present an explicit construction of the zero loss minimizers without invoking gradient descent. On the other hand, we point out that increase of depth can deteriorate the efficiency of cost minimization using a gradient descent algorithm by analyzing the conditions for rank loss of the training Jacobian. Our results clarify key aspects on the dichotomy between zero loss reachability in underparametrized versus overparametrized DL.
title Zero loss guarantees and explicit minimizers for generic overparametrized Deep Learning networks
topic Machine Learning
Artificial Intelligence
Analysis of PDEs
Optimization and Control
57R70, 62M45
url https://arxiv.org/abs/2502.14114