Related papers: Loop Series Expansions for Tensor Networks

Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…

We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already…

Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspond to sum-product neural networks with a sparse connectivity…

We begin with an exact expression for the entropy of a system of hard spheres within the Hamming space. This entropy relies on probability marginals, which are determined by an extended set of Belief Propagation (BP) equations. The BP…

Interpreting complex neural networks is crucial for understanding their decision-making processes, particularly in applications where transparency and accountability are essential. This proposed method addresses this need by focusing on…

Governments across the world are planning to increase the share of renewables in their energy systems. The siting of new wind and solar power plants requires close coordination with grid planning, and hence co-optimization of investment in…

Independence-based (IB) assignments to Bayesian belief networks were originally proposed as abductive explanations. IB assignments assign fewer variables in abductive explanations than do schemes assigning values to all evidentially…

To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without…

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of…

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or…

While neural networks have acted as a strong unifying force in the design of modern AI systems, the neural network architectures themselves remain highly heterogeneous due to the variety of tasks to be solved. In this chapter, we explore…

This paper investigates the computational complexity of sparse label propagation which has been proposed recently for processing network structured data. Sparse label propagation amounts to a convex optimization problem and might be…

A fault-tolerant approach to reliable quantum memory is essential for scalable quantum computing, as physical qubits are susceptible to noise. Quantum error correction (QEC) must be continuously performed to prolong the memory lifetime. In…

We define and study an inference algorithm based on "belief propagation" (BP) and the Bethe approximation. The idea is to encode into a graph an a priori information composed of correlations or marginal probabilities of variables, and to…

Message-passing algorithms based on the Belief Propagation (BP) equations constitute a well-known distributed computational scheme. It is exact on tree-like graphical models and has also proven to be effective in many problems defined on…

The spatial correlations in transmitter node locations introduced by common multiple access protocols makes the analysis of interference, outage, and other related metrics in a wireless network extremely difficult. Most works therefore…

A graphical model is a structured representation of locally dependent random variables. A traditional method to reason over these random variables is to perform inference using belief propagation. When provided with the true data generating…

It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…

Near optimal decoding of good error control codes is generally a difficult task. However, for a certain type of (sufficiently) good codes an efficient decoding algorithm with near optimal performance exists. These codes are defined via a…

Real-world applications such as the internet of things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems are typically modeled as network structures. Network…