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Image-matched nonseparable wavelets can find potential use in many applications including image classification, segmen- tation, compressive sensing, etc. This paper proposes a novel design methodology that utilizes convolutional neural net-…
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…
With the usage of appropriate inductive biases, Counterfactual Generative Networks (CGNs) can generate novel images from random combinations of shape, texture, and background manifolds. These images can be utilized to train an invariant…
Graph neural networks (GNNs), consisting of a cascade of layers applying a graph convolution followed by a pointwise nonlinearity, have become a powerful architecture to process signals supported on graphs. Graph convolutions (and thus,…
Deep Convolutional Neural Network (CNN) is a special type of Neural Networks, which has shown exemplary performance on several competitions related to Computer Vision and Image Processing. Some of the exciting application areas of CNN…
Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…
We introduce the \emph{Symplectic Generative Network (SGN)}, a deep generative model that leverages Hamiltonian mechanics to construct an invertible, volume-preserving mapping between a latent space and the data space. By endowing the…
Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…
Graph Neural Networks (GNNs) have recently received significant research attention due to their superior performance on a variety of graph-related learning tasks. Most of the current works focus on either static or dynamic graph settings,…
Over the last few years, we have witnessed the availability of an increasing data generated from non-Euclidean domains, which are usually represented as graphs with complex relationships, and Graph Neural Networks (GNN) have gained a high…
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…
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…
Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited.…
Graph Neural Networks (GNNs) are exemplary deep models designed for graph data. Message passing mechanism enables GNNs to effectively capture graph topology and push the performance boundaries across various graph tasks. However, the trend…
This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN)…
Deep neural networks (DNNs) in the infinite width/channel limit have received much attention recently, as they provide a clear analytical window to deep learning via mappings to Gaussian Processes (GPs). Despite its theoretical appeal, this…
Convolutional Neural Networks (CNNs) have proven to be highly effective in solving a broad spectrum of computer vision tasks, such as classification, identification, and segmentation. These methods can be deployed in both centralized and…
The ability of deep neural networks (DNNs) to represent phonotactic generalizations derived from lexical learning remains an open question. This study (1) investigates the lexically-invariant generalization capacity of generative…
The goal of exemplar-based texture synthesis is to generate texture images that are visually similar to a given exemplar. Recently, promising results have been reported by methods relying on convolutional neural networks (ConvNets)…
Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. However, the locality assumption of GNNs, which limits information exchange to neighboring nodes, hampers their ability to capture…