相关论文: Multi-Relevance: Coexisting but Distinct Notions o…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification in a relatively small set of…
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…
Machine learning has been a fast growing field of research in several areas dealing with large datasets. We report recent attempts to use Renormalization Group (RG) ideas in the context of machine learning. We examine coarse graining…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
We develop a renormalization group (RG) description of the localization properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is induced by increasing the unit cell of subsequent commensurate approximants. Phases of…
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
Retrieval-Augmented Generation (RAG) enhances Large Language Models (LLMs) by grounding generation in external knowledge, yielding relevance responses that are aligned with factual evidence and evolving corpora. Standard RAG pipelines…
Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…
Self-similarity, where observables at different length scales exhibit similar behavior, is ubiquitous in natural systems. Such systems are typically characterized by power-law correlations and universality, and are studied using the…
Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify…
We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based…
Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method…
Recent breakthroughs in large language models (LLMs), particularly in reasoning capabilities, have propelled Retrieval-Augmented Generation (RAG) to unprecedented levels. By synergizing retrieval mechanisms with advanced reasoning, LLMs can…
Complex systems with many degrees of freedom are typically intractable, but some of their behaviors may admit simpler effective descriptions. The question of when such effective descriptions are possible remains open. The paradigmatic…
Scaling concepts and renormalization group (RG) methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by…
The renormalization group (RG) is an essential technique in statistical physics and quantum field theory, which considers scale-invariant properties of physical theories and how these theories' parameters change with scaling. Deep learning…