arXiv subjects

V. Ros

Publications and source records attributed to V. Ros.

6 recordsLinked to original sources

arXiv2025

Class Imbalance in Anomaly Detection: Learning from an Exactly Solvable Model

Class imbalance (CI) is a longstanding problem in machine learning, slowing down training and reducing performances. Although empirical remedies exist, it is often unclear which ones work best and when, due to the lack of an overarching theory. We address a common case of imbalance, that of anomaly (or outlier) detection. We provide a theoretical framework to analyze, interpret and address CI. It is based on an exact solution of the teacher-student perceptron model, through replica theory. Within this framework, one can distinguish several sources of CI: either intrinsic, train or test imbalance. Our analysis reveals that the optimal train imbalance is generally different from 50%, with a non trivial dependence on the intrinsic imbalance, the abundance of data and on the noise in the learning. Moreover, there is a crossover between a small noise training regime where results are independent of the noise level to a high noise regime where performances quickly degrade with noise. Our results challenge some of the conventional wisdom on CI and offer practical guidelines to address it.

cs.LG↗

arXiv2020

Dynamical Instantons and Activated Processes in Mean-Field Glass Models

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

cond-mat.dis-nn↗

arXiv2016

Review: Local Integrals of Motion in Many-Body Localized systems

We review the current (as of Fall 2016) status of the studies on the emergent integrability in many-body localized models. We start by explaining how the phenomenology of fully many-body localized systems can be recovered if one assumes the existence of a complete set of (quasi)local operators which commute with the Hamiltonian (local integrals of motion, or LIOMs). We describe the evolution of this idea from the initial conjecture, to the perturbative constructions, to the mathematical proof given for a disordered spin chain. We discuss the proposed numerical algorithms for the construction of LIOMs and the status of the debate on the existence and nature of such operators in systems with a many-body mobility edge, and in dimensions larger than one.

cond-mat.dis-nn↗

arXiv2016

Remanent magnetization: signature of Many-Body Localization in quantum antiferromagnets

We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains, initialized in a fully magnetized state. Its long time limit is an order parameter for the localization transition, which is readily accessible by standard experimental probes in magnets. We analytically calculate its value in the strong-disorder regime exploiting the explicit construction of quasi-local conserved quantities of the localized phase. We discuss analogies in cold atomic systems.

cond-mat.dis-nn↗

arXiv2015

Localized systems coupled to small baths: from A$_{nderson}$ to Z$_{eno}$

We investigate what happens if an Anderson localized system is coupled to a small bath, with a discrete spectrum, when the coupling between system and bath is specially chosen so as to never localize the bath. We find that the effect of the bath on localization in the system is a non-monotonic function of the coupling between system and bath. At weak couplings, the bath facilitates transport by allowing the system to 'borrow' energy from the bath. But above a certain coupling the bath produces localization, because of an orthogonality catastrophe, whereby the bath 'dresses' the system and hence suppresses the hopping matrix element. We call this last regime the regime of "Zeno-localization", since the physics of this regime is akin to the quantum Zeno effect, where frequent measurements of the position of a particle impede its motion. We confirm our results by numerical exact diagonalization.

cond-mat.dis-nn↗

arXiv2015

Integrals of motion in the Many-Body localized phase

We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $\{0,1\}$, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.

cond-mat.dis-nn↗