On the Principle of Least Symmetry Breaking in Shallow ReLU Models

• URL: http://arxiv.org/abs/1912.11939v3
• Date: Thu, 28 Dec 2023 14:44:06 GMT
• Title: On the Principle of Least Symmetry Breaking in Shallow ReLU Models
• Authors: Yossi Arjevani, Michael Field
• Abstract summary: We show that the emphleast loss of symmetry with respect to the target weights may apply to a broader range of settings. Motivated by this, we conduct a series of experiments which corroborate this hypothesis for different classes of non-isotropic non-product distributions, smooth activation functions and networks with a few layers.
• Score: 13.760721677322072
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the optimization problem associated with fitting two-layer ReLU networks with respect to the squared loss, where labels are assumed to be generated by a target network. Focusing first on standard Gaussian inputs, we show that the structure of spurious local minima detected by stochastic gradient descent (SGD) is, in a well-defined sense, the \emph{least loss of symmetry} with respect to the target weights. A closer look at the analysis indicates that this principle of least symmetry breaking may apply to a broader range of settings. Motivated by this, we conduct a series of experiments which corroborate this hypothesis for different classes of non-isotropic non-product distributions, smooth activation functions and networks with a few layers.

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