Marginalized CNN: Learning Deep Invariant Representations

Training a deep neural network usually requires sufficient annotated samples. The scarcity of supervision samples in practice thus becomes the major bottleneck on performance of the network. In this work, we propose a principled method to circumvent this difficulty through marginalizing all the possible transformations over samples, termed as marginalized Convolutional Neural Network (mCNN). mCNN implicitly considers infinitely many transformed copies of the training data in every training epoch and therefore is able to learn representations invariant for transformation in an end-to-end way. We prove that such marginalization can be understood as a classic CNN with a special form of regularization and thus is efficient for implementation and not restricted to the CNN module used. Experimental results on the MNIST and affNIST digit number datasets demonstrate that mCNN can match or outperform the original CNN with much fewer training samples. Besides, mCNN also performs well for face recognition on the recently released large-scale MS-Cele-1M dataset and outperforms state-of-thearts. Moreover, compared with the traditional CNNs which use data augmentation to improve their performance, the computational cost of mCNN is reduced by a factor of 26.