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Linearized Graph Neural Networks (GNNs) have attracted great attention in recent years for graph representation learning. Compared with nonlinear Graph Neural Network (GNN) models, linearized GNNs are much more time-efficient and can…

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…

Automated feature extraction capability and significant performance of Deep Neural Networks (DNN) make them suitable for Internet of Things (IoT) applications. However, deploying DNN on edge devices becomes prohibitive due to the colossal…

Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the…

Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…

Deep neural networks (DNNs) have achieved state-of-the-art results in various pattern recognition tasks. However, they perform poorly on out-of-distribution adversarial examples i.e. inputs that are specifically crafted by an adversary to…

Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent and thus has a slow convergence. In addition, softmax, as a decision layer, may ignore the distribution information of the data during…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

Performance of trained neural network (NN) models, in terms of testing accuracy, has improved remarkably over the past several years, especially with the advent of deep learning. However, even the most accurate NNs can be biased toward a…

Physics-informed deep learning have recently emerged as an effective tool for leveraging both observational data and available physical laws. Physics-informed neural networks (PINNs) and deep operator networks (DeepONets) are two such…

Learning in Deep Neural Networks (DNN) takes place by minimizing a non-convex high-dimensional loss function, typically by a stochastic gradient descent (SGD) strategy. The learning process is observed to be able to find good minimizers…

In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of…

Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…

In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the…

By replacing standard non-linearities with polynomial activations, Polynomial Neural Networks (PNNs) are pivotal for applications such as privacy-preserving inference via Homomorphic Encryption (HE). However, training PNNs effectively…

During training, the weights of a Deep Neural Network (DNN) are optimized from a random initialization towards a nearly optimum value minimizing a loss function. Only this final state of the weights is typically kept for testing, while the…

Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying…

Adversarial examples are perturbed inputs that are designed (from a deep learning network's (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network…

Deep neural networks (DNNs) have recently achieved a great success in computer vision and several related fields. Despite such progress, current neural architectures still suffer from catastrophic interference (a.k.a. forgetting) which…

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a…