相关论文: Quantile and moment neural networks for learning f…

With the overwhelming success in the field of quantum information in the last decades, the "quest" for a Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. This…

In open set learning, a model must be able to generalize to novel classes when it encounters a sample that does not belong to any of the classes it has seen before. Open set learning poses a realistic learning scenario that is receiving…

Capsule networks were proposed as an alternative approach to Convolutional Neural Networks (CNNs) for learning object-centric representations, which can be leveraged for improved generalization and sample complexity. Unlike CNNs, capsule…

In this paper, we introduce a general model for jointly modelling the nodal heterogeneity and covariates in weighted or unweighted bipartite networks, which contains two different types of nodes. The model has a degree heterogeneity…

Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…

Quantum computing enables quantum neural networks (QNNs) to have great potentials to surpass artificial neural networks (ANNs). The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various…

Deep learning has received considerable empirical successes in recent years. However, while many ad hoc tricks have been discovered by practitioners, until recently, there has been a lack of theoretical understanding for tricks invented in…

In this review paper, we give a comprehensive overview of the large variety of approximation results for neural networks. Approximation rates for classical function spaces as well as benefits of deep neural networks over shallow ones for…

We study quantum neural networks made by parametric one-qubit gates and fixed two-qubit gates in the limit of infinite width, where the generated function is the expectation value of the sum of single-qubit observables over all the qubits.…

We define a neural network in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fr\'echet space $\X$ into a Banach space $\Y$. The…

Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks, and the cost functions are taken as the energy minimization…

Without large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum statistical query (QSQ) are a primary tool to study quantum algorithms for learning classical functions and search for quantum…

The global inducing point variational approximation for BNNs is based on using a set of inducing inputs to construct a series of conditional distributions that accurately approximate the conditionals of the true posterior distribution. Our…

We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a low-dimensional space, the algorithm allows us to compare…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…

In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…

In recent years, Quantum Computing witnessed massive improvements in terms of available resources and algorithms development. The ability to harness quantum phenomena to solve computational problems is a long-standing dream that has drawn…

Graph Neural Networks (GNNs) have shown expressive performance on graph representation learning by aggregating information from neighbors. Recently, some studies have discussed the importance of modeling neighborhood distribution on the…

In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…