Abstract:This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models with fully connected and convolutional neural networks, we introduce auxiliary variables associated with hidden layer outputs and construct corresponding layer separation models, which decompose the original deeply nested optimization problem into a sequence of more manageable subproblems. We also conduct theoretical analyses, proving that the new layer separation loss provides an upper bound for the original cross-entropy loss. Moreover, we design alternating minimization algorithms and prove that, under appropriate conditions, these algorithms exhibit decreasing properties of the loss function. Numerical experiments validate the effectiveness of the proposed methods and indicate improved optimization behavior, especially for fully connected and convolutional neural networks.
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC) |
| MSC classes: | 65K10, 68T07, 90C30 |
| Cite as: | arXiv:2604.23225 [cs.LG] |
| (or arXiv:2604.23225v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.23225 arXiv-issued DOI via DataCite (pending registration) |
From: Yaru Liu [view email]
[v1]
Sat, 25 Apr 2026 09:33:24 UTC (2,803 KB)
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