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We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…
Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized…
Deep neural networks have seen enormous success in various real-world applications. Beyond their predictions as point estimates, increasing attention has been focused on quantifying the uncertainty of their predictions. In this review, we…
Time Series Classification (TSC) is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed. Among these methods, only a few have considered Deep…
This paper proposes a new mean-field framework for over-parameterized deep neural networks (DNNs), which can be used to analyze neural network training. In this framework, a DNN is represented by probability measures and functions over its…
Tree tensor networks (TTNs) offer powerful models for image classification. While these TTN image classifiers already show excellent performance on classical hardware, embedding them into quantum neural networks (QNNs) may further improve…
Deep neural networks (DNNs), trained with gradient-based optimization and backpropagation, are currently the primary tool in modern artificial intelligence, machine learning, and data science. In many applications, DNNs are trained offline,…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…
The ability to train Deep Neural Networks (DNNs) with constraints is instrumental in improving the fairness of modern machine-learning models. Many algorithms have been analysed in recent years, and yet there is no standard, widely accepted…
Deep neural networks are known to be difficult to train due to the instability of back-propagation. A deep \emph{residual network} (ResNet) with identity loops remedies this by stabilizing gradient computations. We prove a boosting theory…
Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a…
Training deep neural networks (DNNs) in large-cluster computing environments is increasingly necessary, as networks grow in size and complexity. Local memory and processing limitations require robust data and model parallelism for crossing…
Using machine learning, we explore the utility of various deep neural networks (NN) when applied to high harmonic generation (HHG) scenarios. First, we train the NNs to predict the time-dependent dipole and spectra of HHG emission from…
Communication by rare, binary spikes is a key factor for the energy efficiency of biological brains. However, it is harder to train biologically-inspired spiking neural networks (SNNs) than artificial neural networks (ANNs). This is…
Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…
Deep neural networks (DNNs) have become increasingly important due to their excellent empirical performance on a wide range of problems. However, regularization is generally achieved by indirect means, largely due to the complex set of…
Recently, data-driven approaches motivated by modern deep learning have been applied to optical communications in place of traditional model-based counterparts. The application of deep neural networks (DNN) allows flexible statistical…
Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…
There exists continuous demand of improved turbulence models for the closure of Reynolds Averaged Navier-Stokes (RANS) simulations. Machine Learning (ML) offers effective tools for establishing advanced empirical Reynolds stress closures on…
Currently, deep neural networks are deployed on low-power portable devices by first training a full-precision model using powerful hardware, and then deriving a corresponding low-precision model for efficient inference on such systems.…