Related papers: Critical Behavior and Universality Classes for an …

We study the creep response of solids to a constant external load in the framework of a novel fiber bundle model introduced. Analytical and numerical calculations showed that increasing the external load on a specimen a transition takes…

With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that…

Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis…

We present microscopic models of spin ladders which exhibit continuous critical surfaces whose properties and existence, unusually, cannot be inferred from those of the flanking phases. These models exhibit either `multiversality' -- the…

A {\em universal 1-bit compressive sensing (CS)} scheme consists of a measurement matrix $A$ such that all signals $x$ belonging to a particular class can be approximately recovered from $\textrm{sign}(Ax)$. 1-bit CS models extreme…

Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The…

The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the…

We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the…

This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming…

The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…

Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on…

We present a novel quantum high-dimensional linear regression algorithm with an $\ell_1$-penalty based on the classical LARS (Least Angle Regression) pathwise algorithm. Similarly to available classical algorithms for Lasso, our quantum…

We study quantum sparse recovery in non-orthogonal, overcomplete dictionaries: given coherent quantum access to a state and a dictionary of vectors, the goal is to reconstruct the state up to $\ell_2$ error using as few vectors as possible.…

Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…

We use the epsilon expansion to explore a new universality class of second order quantum phase transitions associated with a four-dimensional Yukawa field theory coupled to a traceless Hermitean matrix scalar field. We argue that this class…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular…

We determine the scaling equation of state of the three-dimensional O(N) universality class, for N=5, 6, 32, 64. The N=5 model is relevant for the SO(5) theory of high-T_c superconductivity, while the N=6 model is relevant for the chiral…