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Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…

Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network…

Large-scale deep neural networks (DNN) have been successfully used in a number of tasks from image recognition to natural language processing. They are trained using large training sets on large models, making them computationally and…

Deep neural networks (DNNs) have been deployed in myriad machine learning applications. However, advances in their accuracy are often achieved with increasingly complex and deep network architectures. These large, deep models are often…

The (inverse) discrete Fourier transform (DFT/IDFT) is often perceived as essential to orthogonal frequency-division multiplexing (OFDM) systems. In this paper, a deep complex-valued convolutional network (DCCN) is developed to recover bits…

As Deep Learning (DL) systems are widely deployed for mission-critical applications, debugging such systems becomes essential. Most existing works identify and repair suspicious neurons on the trained Deep Neural Network (DNN), which,…

Size-based separation of bioparticles/cells is crucial to a variety of biomedical processing steps for applications such as exosomes and DNA isolation. Design and improvement of such microfluidic devices is a challenge to best answer the…

The remarkable performance of overparameterized deep neural networks (DNNs) must arise from an interplay between network architecture, training algorithms, and structure in the data. To disentangle these three components, we apply a…

High-dimensional depth separation results for neural networks show that certain functions can be efficiently approximated by two-hidden-layer networks but not by one-hidden-layer ones in high-dimensions $d$. Existing results of this type…

Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies amongst the spatial and temporal components of a wide variety of dynamical…

Q-learning played a foundational role in the field reinforcement learning (RL). However, TD algorithms with off-policy data, such as Q-learning, or nonlinear function approximation like deep neural networks require several additional tricks…

Linear canonical transforms (LCTs) are of importance in many areas of science and engineering with many applications. Therefore a satisfactory discrete implementation is of considerable interest. Although there are methods that link the…

In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically…

Recently, with the advent of deep convolutional neural networks (DCNN), the improvements in visual saliency prediction research are impressive. One possible direction to approach the next improvement is to fully characterize the multi-scale…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Dense prediction tasks typically employ encoder-decoder architectures, but the prevalent convolutions in the decoder are not image-adaptive and can lead to boundary artifacts. Different generalized convolution operations have been…

Diagonal linear networks (DLNs) are a toy simplification of artificial neural networks; they consist in a quadratic reparametrization of linear regression inducing a sparse implicit regularization. In this paper, we describe the trajectory…

There currently exist two extreme viewpoints for neural network feature learning -- (i) Neural networks simply implement a kernel method (a la NTK) and hence no features are learned (ii) Neural networks can represent (and hence learn)…

Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and…