In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equivariance under translations and rotations by design. The proposed architecture employs steerable filters to efficiently compute orientation dependent responses for many orientations without suffering interpolation artifacts from filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize He's weight initialization scheme to filters which are defined as a linear combination of a system of atomic filters. Numerical experiments show a substantial enhancement of the sample complexity with a growing number of sampled filter orientations and confirm that the network generalizes learned patterns over orientations. The proposed approach achieves state-of-the-art on the rotated MNIST benchmark and on the ISBI 2012 2D EM segmentation challenge.
A priori knowledge about transformation-invariance of images can be exploited in manifold ways. A commonly utilized technique is data augmentation, see e.g. @cite_0 . The basic idea is to enrich the training set by transformed samples. Augmenting datasets allows to train larger models and is easily applicable without modifying the network architectures. When the augmenting transformations form a group @math the additional images @math lie on the orbit @math . In contrast to equivariant models the hypothesis space is not restricted to the quotient space @math under the utilized symmetry group but the equivariance needs to be learned explicitly by the network. This demands for a high learning capacity which makes the network prone to overfitting.
@cite_0
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Effective training of neural networks requires much data. In the low-data regime, parameters are underdetermined, and learnt networks generalise poorly. Data Augmentation krizhevsky2012imagenet alleviates this by using existing data more effectively. However standard data augmentation produces only limited plausible alternative data. Given there is potential to generate a much broader set of augmentations, we design and train a generative model to do data augmentation. The model, based on image conditional Generative Adversarial Networks, takes data from a source domain and learns to take any data item and generalise it to generate other within-class data items. As this generative process does not depend on the classes themselves, it can be applied to novel unseen classes of data. We show that a Data Augmentation Generative Adversarial Network (DAGAN) augments standard vanilla classifiers well. We also show a DAGAN can enhance few-shot learning systems such as Matching Networks. We demonstrate these approaches on Omniglot, on EMNIST having learnt the DAGAN on Omniglot, and VGG-Face data. In our experiments we can see over 13 increase in accuracy in the low-data regime experiments in Omniglot (from 69 to 82 ), EMNIST (73.9 to 76 ) and VGG-Face (4.5 to 12 ); in Matching Networks for Omniglot we observe an increase of 0.5 (from 96.9 to 97.4 ) and an increase of 1.8 in EMNIST (from 59.5 to 61.3 ). In this paper we present a deep neural network topology that incorporates a simple to implement transformationinvariant pooling operator (TI-POOLING). This operator is able to efficiently handle prior knowledge on nuisance variations in the data, such as rotation or scale changes. Most current methods usually make use of dataset augmentation to address this issue, but this requires larger number of model parameters and more training data, and results in significantly increased training time and larger chance of under-or overfitting. The main reason for these drawbacks is that that the learned model needs to capture adequate features for all the possible transformations of the input. On the other hand, we formulate features in convolutional neural networks to be transformation-invariant. We achieve that using parallel siamese architectures for the considered transformation set and applying the TI-POOLING operator on their outputs before the fully-connected layers. We show that this topology internally finds the most optimal "canonical" instance of the input image for training and therefore limits the redundancy in learned features. This more efficient use of training data results in better performance on popular benchmark datasets with smaller number of parameters when comparing to standard convolutional neural networks with dataset augmentation and to other baselines. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method. In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equivariance under translations and rotations by design. The proposed architecture employs steerable filters to efficiently compute orientation dependent responses for many orientations without suffering interpolation artifacts from filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize He's weight initialization scheme to filters which are defined as a linear combination of a system of atomic filters. Numerical experiments show a substantial enhancement of the sample complexity with a growing number of sampled filter orientations and confirm that the network generalizes learned patterns over orientations. The proposed approach achieves state-of-the-art on the rotated MNIST benchmark and on the ISBI 2012 2D EM segmentation challenge.