Related papers: Tensor Network Message Passing
In this paper we offer a solution to a long-standing problem in the study of networks. Message passing is a fundamental technique for calculations on networks and graphs. The first versions of the method appeared in the 1930s and over the…
Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it…
Spreading models capture key dynamics on networks, such as cascading failures in economic systems, (mis)information diffusion, and pathogen transmission. Here, we focus on design intervention problems -- for example, designing optimal…
We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…
Message passing neural networks have recently evolved into a state-of-the-art approach to representation learning on graphs. Existing methods perform synchronous message passing along all edges in multiple subsequent rounds and consequently…
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…
A general graph-structured neural network architecture operates on graphs through two core components: (1) complex enough message functions; (2) a fixed information aggregation process. In this paper, we present the Policy Message Passing…
Any spanning tree in a loopy interaction graph can be used for communicating the effect of the loopy interactions by introducing messages that are passed along the edges in the spanning tree. This defines an exact mapping of the problem on…
While epidemiological modeling is pivotal for informing public health strategies, a fundamental trade-off limits its predictive fidelity: exact stochastic simulations are often computationally intractable for large-scale systems, whereas…
Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning a probability distribution of energy…
Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which…
Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief…
A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…
Hypergraph networks are closer to real life because they can reflect higher-order interactions, so researchers have begun using them to build models for real-world networks. The mean-field approach is the current tool for studying the…
Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works…
We investigate the potential of tensor network based machine learning methods to scale to large image and text data sets. For that, we study how the mutual information between a subregion and its complement scales with the subsystem size…
Partitioning large networks into stable clusters of synchronized nodes is a challenging task. Recent approaches based on spectral analysis can provide exact results on specific dynamics but remain unfeasible for very large networks.…