Related papers: Mean-Field Networks

Bayesian neural networks (BNNs) combine the expressive power of deep learning with the advantages of Bayesian formalism. In recent years, the analysis of wide, deep BNNs has provided theoretical insight into their priors and posteriors.…

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential…

Graph neural networks (GNNs) are a class of deep models that operate on data with arbitrary topology represented as graphs. We introduce an efficient memory layer for GNNs that can jointly learn node representations and coarsen the graph.…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…

Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the…

Fake news on social media is increasingly regarded as one of the most concerning issues. Low cost, simple accessibility via social platforms, and a plethora of low-budget online news sources are some of the factors that contribute to the…

In the study of network synchronization, an outstanding question of both theoretical and practical significance is how to allocate a given set of heterogenous oscillators on a complex network in order for improving the synchronization…

It is widely believed that deep neural networks contain layer specialization, wherein neural networks extract hierarchical features representing edges and patterns in shallow layers and complete objects in deeper layers. Unlike common…

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…

This paper addresses semantic image segmentation by incorporating rich information into Markov Random Field (MRF), including high-order relations and mixture of label contexts. Unlike previous works that optimized MRFs using iterative…

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower…

Convolutional neural networks (CNNs) have achieved superior accuracy in many visual related tasks. However, the inference process through intermediate layers is opaque, making it difficult to interpret such networks or develop trust in…

The generative adversarial network (GAN) is one of the most widely used deep generative models for synthesizing high-quality images with the same statistics as the training set. Finite element method (FEM) based property prediction often…

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This…

We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's widths increase, the network's learning trajectory is shown to be well captured by a meaningful and dynamically…

Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome…

Deep learning techniques are increasingly applied to scientific problems, where the precision of networks is crucial. Despite being deemed as universal function approximators, neural networks, in practice, struggle to reduce the prediction…