Scattering Networks for Hybrid Representation Learning

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve competitive results both for supervised and unsupervised learning tasks, while making progress towards constructing more interpretable CNNs. For supervised learning, we demonstrate that the early layers of CNNs do not necessarily need to be learned, and can be replaced with a scattering network instead. Indeed, using hybrid architectures, we achieve the best results with predefined representations to-date, while being competitive with end-to-end learned CNNs. Specifically, even applying a shallow cascade of small-windowed scattering coefficients followed by 1$\times$1-convolutions results in AlexNet accuracy on the ILSVRC2012 classification task. Moreover, by combining scattering networks with deep residual networks, we achieve a single-crop top-5 error of 11.4% on ILSVRC2012. Also, we show they can yield excellent performance in the small sample regime on CIFAR-10 and STL-10 datasets, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. For unsupervised learning, scattering coefficients can be a competitive representation that permits image recovery. We use this fact to train hybrid GANs to generate images. Finally, we empirically analyze several properties related to stability and reconstruction of images from scattering coefficients.

Nonlinear Acceleration of CNNs

The Regularized Nonlinear Acceleration (RNA) algorithm is an acceleration method capable of improving the rate of convergence of many optimization schemes such as gradient descend, SAGA or SVRG. Until now, its analysis is limited to convex problems, but empirical observations shows that RNA may be extended to wider settings. In this paper, we investigate further the benefits of RNA when applied to neural networks, in particular for the task of image recognition on CIFAR10 and ImageNet. With very few modifications of exiting frameworks, RNA improves slightly the optimization process of CNNs, after training.

Nonlinear Acceleration of Deep Neural Networks

Regularized nonlinear acceleration (RNA) is a generic extrapolation scheme for optimization methods, with marginal computational overhead. It aims to improve convergence using only the iterates of simple iterative algorithms. However, so far its application to optimization was theoretically limited to gradient descent and other single-step algorithms. Here, we adapt RNA to a much broader setting including stochastic gradient with momentum and Nesterov's fast gradient. We use it to train deep neural networks, and empirically observe that extrapolated networks are more accurate, especially in the early iterations. A straightforward application of our algorithm when training ResNet-152 on ImageNet produces a top-1 test error of 20.88%, improving by 0.8% the reference classification pipeline. Furthermore, the code runs offline in this case, so it never negatively affects performance.

i-RevNet: Deep Invertible Networks

It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show via a one-to-one mapping that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build the i-RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for one, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNets learned representations suggests an alternative explanation for the success of deep networks by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by the i-RevNet we reconstruct linear interpolations between natural image representations.

Scaling the Scattering Transform: Deep Hybrid Networks

We use the scattering network as a generic and fixed ini-tialization of the first layers of a supervised hybrid deep network. We show that early layers do not necessarily need to be learned, providing the best results to-date with pre-defined representations while being competitive with Deep CNNs. Using a shallow cascade of 1 x 1 convolutions, which encodes scattering coefficients that correspond to spatial windows of very small sizes, permits to obtain AlexNet accuracy on the imagenet ILSVRC2012. We demonstrate that this local encoding explicitly learns invariance w.r.t. rotations. Combining scattering networks with a modern ResNet, we achieve a single-crop top 5 error of 11.4% on imagenet ILSVRC2012, comparable to the Resnet-18 architecture, while utilizing only 10 layers. We also find that hybrid architectures can yield excellent performance in the small sample regime, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. We demonstrate this on subsets of the CIFAR-10 dataset and on the STL-10 dataset.

Multiscale Hierarchical Convolutional Networks

Deep neural network algorithms are difficult to analyze because they lack structure allowing to understand the properties of underlying transforms and invariants. Multiscale hierarchical convolutional networks are structured deep convolutional networks where layers are indexed by progressively higher dimensional attributes, which are learned from training data. Each new layer is computed with multidimensional convolutions along spatial and attribute variables. We introduce an efficient implementation of such networks where the dimensionality is progressively reduced by averaging intermediate layers along attribute indices. Hierarchical networks are tested on CIFAR image data bases where they obtain comparable precisions to state of the art networks, with much fewer parameters. We study some properties of the attributes learned from these databases.

Building a Regular Decision Boundary with Deep Networks

In this work, we build a generic architecture of Convolutional Neural Networks to discover empirical properties of neural networks. Our first contribution is to introduce a state-of-the-art framework that depends upon few hyper parameters and to study the network when we vary them. It has no max pooling, no biases, only 13 layers, is purely convolutional and yields up to 95.4% and 79.6% accuracy respectively on CIFAR10 and CIFAR100. We show that the nonlinearity of a deep network does not need to be continuous, non expansive or point-wise, to achieve good performance. We show that increasing the width of our network permits being competitive with very deep networks. Our second contribution is an analysis of the contraction and separation properties of this network. Indeed, a 1-nearest neighbor classifier applied on deep features progressively improves with depth, which indicates that the representation is progressively more regular. Besides, we defined and analyzed local support vectors that separate classes locally. All our experiments are reproducible and code is available online, based on TensorFlow.

Deep Roto-Translation Scattering for Object Classification

Dictionary learning algorithms or supervised deep convolution networks have considerably improved the efficiency of predefined feature representations such as SIFT. We introduce a deep scattering convolution network, with predefined wavelet filters over spatial and angular variables. This representation brings an important improvement to results previously obtained with predefined features over object image databases such as Caltech and CIFAR. The resulting accuracy is comparable to results obtained with unsupervised deep learning and dictionary based representations. This shows that refining image representations by using geometric priors is a promising direction to improve image classification and its understanding.

Generic Deep Networks with Wavelet Scattering

We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables in the second layer. Numerical experiments demonstrate that this two layer convolution network, which involves no learning and no max pooling, performs efficiently on complex image data sets such as CalTech, with structural objects variability and clutter. It opens the possibility to simplify deep neural network learning by initializing the first layers with wavelet filters.