Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational sciences, sensor communications, functional brain imaging, regulatory genetics, and meshed surfaces computer graphics. In many applications, such geometric are large complex (in the case of networks, on scale billions), natural targets for machine learning techniques. particular, we would like to use deep neural which have recently proven be...

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability exploit the local translational invariance of signal classes over domain. In this paper we consider possible generalizations CNNs signals defined on more general domains without action a translation group. particular, propose two constructions, one based upon hierarchical clustering domain, another spectrum graph Laplacian. We show through experiments that for...

A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades transform convolutions with nonlinear modulus averaging operators. The first layer outputs SIFT-type descriptors, whereas the next layers provide complementary that improves mathematical analysis of networks explains important properties deep convolution stationary processes incorporates higher order...

Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity multi-scale compositional structure, that allows expressing long range interactions in terms shorter, localized interactions. However, there exist other important examples, such as text documents or bioinformatic data, may lack some all these strong regularities. In this paper we consider general question how...

We present techniques for speeding up the test-time evaluation of large convolutional networks, designed object recognition tasks. These models deliver impressive accuracy but each image requires millions floating point operations, making their deployment on smartphones and Internet-scale clusters problematic. The computation is dominated by convolution operations in lower layers model. exploit linear structure within filters to derive approximations that significantly reduce required...

We propose to study the problem of few-shot learning with prism inference on a partially observed graphical model, constructed from collection input images whose label can be either or not. By assimilating generic message-passing algorithms their neural-network counterparts, we define graph neural network architecture that generalizes several recently proposed models. Besides providing improved numerical performance, our framework is easily extended variants learning, such as semi-supervised...

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding are fact feasible with appropriate computational scale. Remarkably, the essence of is built from two simple algorithmic principles: first, notion representation feature whereby adapted, often hierarchical, features capture...

Inverse problems in image and audio, super-resolution particular, can be seen as high-dimensional structured prediction problems, where the goal is to characterize conditional distribution of a high-resolution output given its low-resolution corrupted observation. When scaling ratio small, point estimates achieve impressive performance, but soon they suffer from regression-to-the-mean problem, result their inability capture multi-modality this distribution. Modeling audio distributions hard...

We propose a strong baseline model for unsupervised feature learning using video data. By to predict missing frames or extrapolate future from an input sequence, the discovers both spatial and temporal correlations which are useful represent complex deformations motion patterns. The models we largely borrowed language modeling literature, adapted vision domain by quantizing space of image patches into large dictionary. demonstrate approach on filling generation task. For first time, show...

Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consist cascade layers, each which applies convolution, followed by pointwise nonlinearity. In this work, we study the impact that changes underlying topology on output GNN. First, show are permutation equivariant, implies they effectively exploit internal symmetries topology. Then,...

The reconstruction of a discrete surface from point cloud is fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use deep neural network as geometric prior reconstruction. Specifically, we overfit representing local chart parameterization to part an input using Wasserstein distance measure approximation. By jointly fitting such networks overlapping parts cloud, while enforcing consistency condition, compute manifold atlas....

Deep neural networks are highly expressive models that have recently achieved state of the art performance on speech and visual recognition tasks. While their expressiveness is reason they succeed, it also causes them to learn uninterpretable solutions could counter-intuitive properties. In this paper we report two such First, find there no distinction between individual high level units random linear combinations units, according various methods unit analysis. It suggests space, rather than...

Current state-of-the-art classification and detection algorithms train deep convolutional networks using labeled data. In this work we study unsupervised feature learning with in the context of temporally coherent unlabeled We focus on from video data, assumption that adjacent frames contain semantically similar information. This is exploited to a pooling auto-encoder regularized by slowness sparsity priors. establish connection between slow metric learning. Using define "temporal coherence"...

A scattering vector is a local descriptor including multiscale and multi-direction co-occurrence information. It computed with cascade of wavelet decompositions complex modulus. This representation locally translation invariant linearizes deformations. supervised classification algorithm PCA model selection on vectors. State the art results are obtained for handwritten digit recognition texture classification.

The availability of large labeled datasets has allowed Convolutional Network models to achieve impressive recognition results. However, in many settings manual annotation the data is impractical; instead our noisy labels, i.e. there some freely available label for each image which may or not be accurate. In this paper, we explore performance discriminatively-trained Convnets when trained on such data. We introduce an extra noise layer into network adapts outputs match distribution....

Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there been increasing interests in studying their expressive power. One line work studies the capability GNNs to approximate permutation-invariant functions graphs, and another focuses power as tests for graph isomorphism. Our connects these two perspectives proves equivalence. We further develop a framework that incorporates both viewpoints using language sigma-algebra, through which we...

Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing task using the scattering transform, statistical tool sharing ideas convolutional neural networks (CNNs) but requiring no training nor tuning. It generates compact set of coefficients, which can be used as robust summary statistics for information. especially suited presenting localized structures hierarchical clustering, such cosmological...