Related papers: Universal Approximation Theorem and error bounds f…

Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called…

We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…

Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

It is well understood that neural networks with carefully hand-picked weights provide powerful function approximation and that they can be successfully trained in over-parametrized regimes. Since over-parametrization ensures zero training…

In this paper, we develop a wavelet-based theoretical framework for analyzing the universal approximation capabilities of neural networks over a wide range of activation functions. Leveraging wavelet frame theory on the spaces of…

Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on…

Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…

The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…

This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The results most commonly found in the literature prove that neural…

The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…

In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We…

Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

Most of the weights in a Lightweight Neural Network have a value of zero, while the remaining ones are either +1 or -1. These universal approximators require approximately 1.1 bits/weight of storage, posses a quick forward pass and achieve…

Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper…

Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate…

Quantum artificial intelligence is a frontier of artificial intelligence research, pioneering quantum AI-powered circuits to address problems beyond the reach of deep learning with classical architectures. This work implements a large-scale…

We present a constructive approximation framework for analyzing the expressive power of Fourier residual networks in approximating a broad class of one-dimensional functions. Our study covers both piecewise continuous functions -- including…