The learning of Transformation-Equivariant Representations (TERs), which is introduced by hinton2011transforming , has been considered as a principle to reveal visual structures under various transformations. It contains the celebrated Convolutional Neural Networks (CNNs) as a special case that only equivary to the translations. In contrast, we seek to train TERs for a generic class of transformations and train them in an unsupervised fashion. To this end, we present a novel principled method by Autoencoding Variational Transformations (AVT), compared with the conventional approach to autoencoding data. Formally, given transformed images, the AVT seeks to train the networks by maximizing the mutual information between the transformations and representations. This ensures the resultant TERs of individual images contain the intrinsic information about their visual structures that would equivary extricably under various transformations. Technically, we show that the resultant optimization problem can be efficiently solved by maximizing a variational lower-bound of the mutual information. This variational approach introduces a transformation decoder to approximate the intractable posterior of transformations, resulting in an autoencoding architecture with a pair of the representation encoder and the transformation decoder. Experiments demonstrate the proposed AVT model sets a new record for the performances on unsupervised tasks, greatly closing the performance gap to the supervised models.
Recently, @cite_34 present a novel Auto-Encoding Transformation (AET) model by learning a representation from which an input transformation can be reconstructed. This is closely related to our motivation of learning transformation equivariant representations, considering the transformation can be decoded from the learned representation of original and transformed images. On the contrary, in this paper, we approach it from an information-theoretic point of view in a more principled fashion.
@cite_34
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The success of deep neural networks often relies on a large amount of labeled examples, which can be difficult to obtain in many real scenarios. To address this challenge, unsupervised methods are strongly preferred for training neural networks without using any labeled data. In this paper, we present a novel paradigm of unsupervised representation learning by Auto-Encoding Transformation (AET) in contrast to the conventional Auto-Encoding Data (AED) approach. Given a randomly sampled transformation, AET seeks to predict it merely from the encoded features as accurately as possible at the output end. The idea is the following: as long as the unsupervised features successfully encode the essential information about the visual structures of original and transformed images, the transformation can be well predicted. We will show that this AET paradigm allows us to instantiate a large variety of transformations, from parameterized, to non-parameterized and GAN-induced ones. Our experiments show that AET greatly improves over existing unsupervised approaches, setting new state-of-the-art performances being greatly closer to the upper bounds by their fully supervised counterparts on CIFAR-10, ImageNet and Places datasets.