Related papers: Mean-Field Networks
Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true…
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…
A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas…
In this paper we propose an improved mean-field inference algorithm for the fully connected paired CRFs model. The improved method Message Passing operation is changed from the original linear convolution to the present graph attention…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing…
Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
Deep learning models have achieved state-of-the-art performance in many classification tasks. However, most of them cannot provide an interpretation for their classification results. Machine learning models that are interpretable are…
Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…
The Mean Field Approximation (MFA), or continuum method, is often used in courses on Networks to derive the degree distribution of preferential attachment networks. This method is simple and the outcome is close to the correct answer.…
In intractable, undirected graphical models, an intuitive way of creating structured mean field approximations is to select an acyclic tractable subgraph. We show that the hardness of computing the objective function and gradient of the…
Two of the most popular modelling paradigms in computer vision are feed-forward neural networks (FFNs) and probabilistic graphical models (GMs). Various connections between the two have been studied in recent works, such as e.g. expressing…
Compressing large Neural Networks (NN) by quantizing the parameters, while maintaining the performance is highly desirable due to reduced memory and time complexity. In this work, we cast NN quantization as a discrete labelling problem, and…
Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in…
Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…
A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous…
In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). Our filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and…