Related papers: Scattering Networks on Noncommutative Finite Group…

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…

Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called…

Scattering often limits the controlled delivery of light in applications such as biomedical imaging, optogenetics, optical trapping, and fiber-optic communication or imaging. Such scattering can be controlled by appropriately shaping the…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…

Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing…

Deep convolutional neural networks accuracy is heavily impacted by rotations of the input data. In this paper, we propose a convolutional predictor that is invariant to rotations in the input. This architecture is capable of predicting the…

We show the universality of depth-2 group convolutional neural networks (GCNNs) in a unified and constructive manner based on the ridgelet theory. Despite widespread use in applications, the approximation property of (G)CNNs has not been…

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where…

We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering…

A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus…

The success of convolutional networks in learning problems involving planar signals such as images is due to their ability to exploit the translation symmetry of the data distribution through weight sharing. Many areas of science and…

An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…

Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…

This paper introduces a Deep Scattering network that utilizes Dual-Tree complex wavelets to extract translation invariant representations from an input signal. The computationally efficient Dual-Tree wavelets decompose the input signal into…

A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…

Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…

Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper, we advocate performing this task using the scattering transform, a statistical tool sharing ideas with…

Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we…

Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a…