Deep Learning using Linear Support Vector Machines

TL;DR

Replacing the softmax layer with a linear support vector machine in deep neural networks consistently improves performance across multiple standard datasets.

Contribution

Demonstrates that substituting softmax with linear SVMs in deep learning models yields significant accuracy gains on benchmark datasets.

Findings

Significant accuracy improvements on MNIST, CIFAR-10, and face expression recognition datasets.

Linear SVMs outperform softmax layers in deep neural network classifiers.

Simple replacement of softmax with SVMs enhances model performance.

Abstract

Recently, fully-connected and convolutional neural networks have been trained to achieve state-of-the-art performance on a wide variety of tasks such as speech recognition, image classification, natural language processing, and bioinformatics. For classification tasks, most of these "deep learning" models employ the softmax activation function for prediction and minimize cross-entropy loss. In this paper, we demonstrate a small but consistent advantage of replacing the softmax layer with a linear support vector machine. Learning minimizes a margin-based loss instead of the cross-entropy loss. While there have been various combinations of neural nets and SVMs in prior art, our results using L2-SVMs show that by simply replacing softmax with linear SVMs gives significant gains on popular deep learning datasets MNIST, CIFAR-10, and the ICML 2013 Representation Learning Workshop's face expression recognition challenge.