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arXiv · 2006.14286

Implicitly Maximizing Margins with the Hinge Loss

Justin Lizama
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Abstract

A new loss function is proposed for neural networks on classification tasks which extends the hinge loss by assigning gradients to its critical points. We will show that for a linear classifier on linearly separable data with fixed step size, the margin of this modified hinge loss converges to the $\ell_2$ max-margin at the rate of $\mathcal{O}( 1/t )$. This rate is fast when compared with the $\mathcal{O}(1/\log t)$ rate of exponential losses such as the logistic loss. Furthermore, empirical results suggest that this increased convergence speed carries over to ReLU networks.

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Justin Lizama. 2020-06-25. Implicitly Maximizing Margins with the Hinge Loss. https://arxiv.org/abs/2006.14286

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