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Graph Neural Networks (GNNs) have emerged as fundamental tools for a wide range of prediction tasks on graph-structured data. Recent studies have drawn analogies between GNN feature propagation and diffusion processes, which can be…

Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…

Despite their impressive performance, Deep Neural Networks (DNNs) typically underperform Gradient Boosting Trees (GBTs) on many tabular-dataset learning tasks. We propose that applying a different regularization coefficient to each weight…

One practice of employing deep neural networks is to apply the same architecture to all the input instances. However, a fixed architecture may not be representative enough for data with high diversity. To promote the model capacity,…

Discontinuous motion which is a motion composed of multiple continuous motions with sudden change in direction or velocity in between, can be seen in state-aware robotic tasks. Such robotic tasks are often coordinated with sensor…

Recently many first and second order variants of SGD have been proposed to facilitate training of Deep Neural Networks (DNNs). A common limitation of these works stem from the fact that they use the same learning rate across all instances…

Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field…

An ongoing challenge in neural information processing is: how do neurons adjust their connectivity to improve task performance over time (i.e., actualize learning)? It is widely believed that there is a consistent, synaptic-level learning…

A connectional brain template (CBT) is a normalized graph-based representation of a population of brain networks also regarded as an average connectome. CBTs are powerful tools for creating representative maps of brain connectivity in…

In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt…

Dynamical Mean-Field Theory (DMFT) has established itself as a reliable and well-controlled approximation to study correlation effects in bulk solids and also two-dimensional systems. In combination with standard density-functional theory…

Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…

Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…

Training Deep Neural Networks relies on the model converging on a high-dimensional, non-convex loss landscape toward a good minimum. Yet, much of the phenomenology of training remains ill understood. We focus on three seemingly disparate…

In this paper, the problem of optimal gradient lossless compression in Deep Neural Network (DNN) training is considered. Gradient compression is relevant in many distributed DNN training scenarios, including the recently popular federated…

We develop a framework for the analysis of deep neural networks and neural ODE models that are trained with stochastic gradient algorithms. We do that by identifying the connections between control theory, deep learning and theory of…

Quantum mechanical methods like Density Functional Theory (DFT) are used with great success alongside efficient search algorithms for studying kinetics of reactive systems. However, DFT is prohibitively expensive for large scale…

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by…