Related papers: Neural Networks and Quantum Field Theory

Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…

Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…

Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary…

Continuous-variable (CV) quantum computing has shown great potential for building neural network models. These neural networks can have different levels of quantum-classical hybridization depending on the complexity of the problem. Previous…

This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Phys. 330, 581-637). It is a rank-3 model based on the gauge group SU(2),…

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been…

In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

We give a probabilistic interpretation of sampling theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain…

We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As the Mat\'ern case, this class allows a continuous parameterization of…

In nonperturbative formulation of quantum field theory (QFT), the vacuum state is characterized by the Wilsonian renormalization group (RG) flow of Feynman type field correlators. Such a flow is a parametric family of ultraviolet (UV)…

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…

GFlowNets is a novel flow-based method for learning a stochastic policy to generate objects via a sequence of actions and with probability proportional to a given positive reward. We contribute to relaxing hypotheses limiting the…

Weak Lensing (WL) surveys are reaching unprecedented depths, enabling the investigation of very small angular scales. At these scales, nonlinear gravitational effects lead to higher-order correlations making the matter distribution highly…

Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms…

Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We…

Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…