Related papers: Renormalization of tensor networks using graph ind…

Graph Neural Networks (GNNs) have shown to be powerful tools for graph analytics. The key idea is to recursively propagate and aggregate information along edges of the given graph. Despite their success, however, the existing GNNs are…

Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…

Recently a novel real-space RG algorithm was introduced, identifying the relevant degrees of freedom of a system by maximizing an information-theoretic quantity, the real-space mutual information (RSMI), with machine learning methods.…

We apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to…

Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…

This paper investigates the problem of recovering hyperspectral (HS) images from single RGB images. To tackle such a severely ill-posed problem, we propose a physically-interpretable, compact, efficient, and end-to-end learning-based…

Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…

Predicting the ground-state 3D molecular conformations from 2D molecular graphs is critical in computational chemistry due to its profound impact on molecular properties. Deep learning (DL) approaches have recently emerged as promising…

Recent research has tried to extend the concept of renormalization, which is naturally defined for geometric objects, to more general networks with arbitrary topology. The current attempts do not naturally apply to directed networks, for…

Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

Building upon previous $2D$ studies, this research focuses on describing $3D$ tensor renormalisation group (RG) flows for lattice spin systems, such as the Ising model. We present a novel RG map, which operates on tensors with…

This paper presents a novel approach to neural network pruning by integrating a graph-based observation space into an AutoML framework to address the limitations of existing methods. Traditional pruning approaches often depend on…

The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…

We explore how minimal neural networks can invert the renormalization group (RG) coarse-graining procedure in the two-dimensional Ising model, effectively ``dreaming up'' microscopic configurations from coarse-grained states. This task -…

In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…

Scalability of graph neural networks remains one of the major challenges in graph machine learning. Since the representation of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes…

The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential…

We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian…

The tensor-network renormalization group (TNRG) is an accurate numerical real-space renormalization group method for studying phase transitions in both quantum and classical systems. Continuous phase transitions, as an important class of…