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The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks. It is common belief that the optimizer dynamics, network…

Neural-network quantum states (NQS) has emerged as a powerful application of quantum-inspired deep learning for variational Monte Carlo methods, offering a competitive alternative to existing techniques for identifying ground states of…

We study the properties of nonparametric least squares regression using deep neural networks. We derive non-asymptotic upper bounds for the prediction error of the empirical risk minimizer of feedforward deep neural regression. Our error…

This work introduces the quantum-inspired variational convolution (QiVC) framework, a novel learning paradigm that integrates principles of probabilistic inference, variational optimization, and quantum-inspired transformations within…

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived…

Uncertainty quantification is crucial in time series prediction, and quantile regression offers a valuable mechanism for uncertainty quantification which is useful for extreme value forecasting. Although deep learning models have been…

Recently, convolutional neural networks (CNN) have demonstrated impressive performance in various computer vision tasks. However, high performance hardware is typically indispensable for the application of CNN models due to the high…

At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans…

Quantum neural networks (QNNs) are a framework for creating quantum algorithms that promises to combine the speedups of quantum computation with the widespread successes of machine learning. A major challenge in QNN development is a…

This note presents a simple way to add a count (or quantile) constraint to a regression neural net, such that given $n$ samples in the training set it guarantees that the prediction of $m<n$ samples will be larger than the actual value (the…

Intrusion Detection Systems (IDSs) must maintain high detection sensitivity while operating under strict false-positive constraints, a challenge intensified by class imbalance and heterogeneous IoT traffic. This work investigates whether…

Quantile regression (QR) is now widely used to analyze the effect of covariates on the conditional distribution of a response variable. It provides a more comprehensive picture of the relationship between a response and covariates compared…

The rapid development of quantum computers promises transformative impacts across diverse fields of science and technology. Quantum neural networks (QNNs), as a forefront application, hold substantial potential. Despite the multitude of…

While Quantum Convolutional Neural Networks (QCNNs) offer a theoretical paradigm for quantum machine learning, their practical implementation is severely bottlenecked by barren plateaus -- the exponential vanishing of gradients -- and poor…

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…

Convolutional Neural Networks (CNNs) have shown impressive performance in computer vision tasks such as image classification, detection, and segmentation. Moreover, recent work in Generative Adversarial Networks (GANs) has highlighted the…

Identifying high-quality and easily accessible annotated samples poses a notable challenge in medical image analysis. Transfer learning techniques, leveraging pre-training data, offer a flexible solution to this issue. However, the impact…

In the last decade, Convolutional Neural Network with a multi-layer architecture has advanced rapidly. However, training its complex network is very space-consuming, since a lot of intermediate data are preserved across layers, especially…

Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography…

The paper contains approximation guarantees for neural networks that are trained with gradient flow, with error measured in the continuous $L_2(\mathbb{S}^{d-1})$-norm on the $d$-dimensional unit sphere and targets that are Sobolev smooth.…