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Graph Neural Networks (GNNs) are deep-learning architectures designed for graph-type data, where understanding relationships among individual observations is crucial. However, achieving promising GNN performance, especially on unseen data,…

A new computationally simple method of imposing hard convex constraints on the neural network output values is proposed. The key idea behind the method is to map a vector of hidden parameters of the network to a point that is guaranteed to…

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

In this work we study the problem of network morphism, an effective learning scheme to morph a well-trained neural network to a new one with the network function completely preserved. Different from existing work where basic morphing types…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…

The interpretation of reasoning by Deep Neural Networks (DNN) is still challenging due to their perceived black-box nature. Therefore, deploying DNNs in several real-world tasks is restricted by the lack of transparency of these models. We…

This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying…

Several significant models have been developed that enable the study of diffusion of signals across biological, social and engineered networks. Within these established frameworks, the inverse problem of identifying the source of the…

We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph…

Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence…

Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…

It is widely perceived that leveraging the success of modern machine learning techniques to mobile devices and wireless networks has the potential of enabling important new services. This, however, poses significant challenges, essentially…

Diffusion dynamics in multiplex networks can model a diverse number of real-world processes. In some specific configurations of these systems, the super-diffusion phenomenon arises, in which the diffusion is faster in the multiplex network…

The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…

This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…

In the mid-twentieth century, mathematician and polymath John von Neumann created a computational system on an array of cells as a simple model of the human brain, where each cell had one of a finite set of roles or states that he predicted…