Related papers: Higher-order Laplacian Renormalization
By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…
In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is…
Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its two-dimensional real-space Hamiltonian. Furthermore, we describe a "renormalization-group" (RG)…
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…
Deep learning is a broad set of techniques that uses multiple layers of representation to automatically learn relevant features directly from structured data. Recently, such techniques have yielded record-breaking results on a diverse set…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
Nowadays, scaling methods for general large-scale complex networks have been developed. We proposed a new scaling scheme called "two-site scaling". This scheme was applied iteratively to various networks, and we observed how the degree…
We develop a multiscale approach to estimate high-dimensional probability distributions from a dataset of physical fields or configurations observed in experiments or simulations. In this way we can estimate energy functions (or…
Traditionally, interaction systems have been described as networks, where links encode information on the pairwise influences among the nodes. Yet, in many systems, interactions take place in larger groups. Recent work has shown that…
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 -…
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.…
Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based…
Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are…
We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…
Many complex systems are organized around complementary roles and naturally described as bipartite networks. Unveiling their multiscale structure presents a fundamental challenge because coarse-graining procedures must preserve role…
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics,…
Building on the Renormalization Group (RG) method the beam-beam interaction in circular colliders is studied. A regularized symplectic RG beam-beam map, that describes successfully the long-time asymptotic behavior of the original system…
We formally introduce a class of models inspired by renormalization group (RG) theory, built on additive hierarchical expansions analogous to those appearing in functional ANOVA and mixed-effects models. Like ReLU convolutional neural…