Related papers: Scattering Networks on Noncommutative Finite Group…
We present a scattering theory for the efficient transmission of an excitation across a finite network with designed disorder. We show that the presence of randomly positioned networks sites allows to significantly accelerate the excitation…
We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with…
In this paper, we apply the scattering transform (ST), a nonlinear map based off of a convolutional neural network (CNN), to classification of underwater objects using sonar signals. The ST formalizes the observation that the filters…
Extracting information from stochastic fields or textures is a ubiquitous task in science, from exploratory data analysis to classification and parameter estimation. From physics to biology, it tends to be done either through a power…
Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain of the data is commonly encountered manifolds such as the…
We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa). The main difficulty of using a…
Leveraging the symmetries inherent to specific data domains for the construction of equivariant neural networks has lead to remarkable improvements in terms of data efficiency and generalization. However, most existing research focuses on…
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire…
We study the first-order scattering transform as a candidate for reducing the signal processed by a convolutional neural network (CNN). We show theoretical and empirical evidence that in the case of natural images and sufficiently small…
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…
The purpose of this short and simple note is to clarify a common misconception about convolutional neural networks (CNNs). CNNs are made up of convolutional layers which are shift equivariant due to weight sharing. However, convolutional…
We propose a novel spectral convolutional neural network (CNN) model on graph structured data, namely Distributed Feedback-Looped Networks (DFNets). This model is incorporated with a robust class of spectral graph filters, called…
Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to…
Convolutional Neural Networks(CNN) are inherently equivariant under translations, however, they do not have an equivalent embedded mechanism to handle other transformations such as rotations and change in scale. Several approaches exist…
3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on…
Wavelets are well known for data compression, yet have rarely been applied to the compression of neural networks. This paper shows how the fast wavelet transform can be used to compress linear layers in neural networks. Linear layers still…
We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined. The model incorporates the…
Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…
Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These…