arXiv subjects

Fabrizio Antenucci

Publications and source records attributed to Fabrizio Antenucci.

14 recordsLinked to original sources

arXiv2021

Exact results on high-dimensional linear regression via statistical physics

It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation techniques, that call for rigorous results against which they can be tested. In this context, the simplest case of high-dimensional linear regression has acquired significant new relevance and attention. In this paper we use the statistical physics perspective on inference to derive a number of new exact results for linear regression in the high-dimensional regime.

math.ST↗

arXiv2021

Glassiness and Lack of Equipartition in Random Lasers: the common roots of Ergodicity Breaking in Disordered and Non-linear Systems

We present here for the first time a unifying perspective for the lack of equipartition in non-linear ordered systems and the low temperature phase-space fragmentation in disordered systems. We demonstrate that they are just two manifestation of the same underlying phenomenon: ergodicity breaking. Inspired by recent experiments, suggesting that lasing in optically active disordered media is related to an ergodicity-breaking transition, we studied numerically a statistical mechanics model for the nonlinearly coupled light modes in a disordered medium under external pumping. Their collective behavior appears to be akin to the one displayed around the ergodicity-breaking transition in glasses, as we show measuring the glass order parameter of the replica-symmetry-breaking theory. Most remarkably, we also find that at the same critical point a breakdown of energy equipartition among light modes occurs, the typical signature of ergodicity breaking in non-linear systems as the celebrated Fermi-Pasta-Ulam model. The crucial ingredient of our system which allows us to find equipartition breakdown together with replica symmetry breaking is that the amplitudes of light modes are locally unbounded, i.e., they are only subject to a global constraint. The physics of random lasers appears thus as a unique test-bed to develop under a unifying perspective the study of ergodicity breaking in statistical disordered systems and non-linear ordered ones.

cond-mat.stat-mech↗

arXiv2019

Self-starting nonlinear mode-locking in random lasers

In ultra-fast multi-mode lasers, mode-locking is implemented by means of ad hoc devices, like saturable absorbers or modulators, allowing for very short pulses. This comes about because of nonlinear interactions induced among modes at different, well equispaced, frequencies. Theory predicts that the same locking of modes would occur in random lasers but, in absence of any device, its detection is unfeasible so far. Because of the general interest in the phenomenology and understanding of random lasers and, moreover, because it is a first example of self-starting mode-locking we devise and test a way to measure such peculiar non-linear coupling. Through a detailed analysis of multi-mode correlations we provide clear evidence for the occurrence of nonlinear mode-coupling in the cavity-less random laser made of a powder of GaAs crystals and its self-starting mode-locking nature. The behavior of multi-point correlations among intensity peaks is tested against the nonlinear frequency matching condition equivalent to the one underlying phase-locking in ordered ultrafast lasers. Non-trivially large multi-point correlations are clearly observed for spatially overlapping resonances and turn out to sensitively depend on the frequency matching being satisfied, eventually demonstrating the occurrence of non-linear mode-locked mode-coupling.

physics.optics↗

arXiv2019

Glassy nature of the hard phase in inference problems

An algorithmically hard phase was described in a range of inference problems: even if the signal can be reconstructed with a small error from an information theoretic point of view, known algorithms fail unless the noise-to-signal ratio is sufficiently small. This hard phase is typically understood as a metastable branch of the dynamical evolution of message passing algorithms. In this work we study the metastable branch for a prototypical inference problem, the low-rank matrix factorization, that presents a hard phase. We show that for noise-to-signal ratios that are below the information theoretic threshold, the posterior measure is composed of an exponential number of metastable glassy states and we compute their entropy, called the complexity. We show that this glassiness extends even slightly below the algorithmic threshold below which the well-known approximate message passing (AMP) algorithm is able to closely reconstruct the signal. Counter-intuitively, we find that the performance of the AMP algorithm is not improved by taking into account the glassy nature of the hard phase. This result provides further evidence that the hard phase in inference problems is algorithmically impenetrable for some deep computational reasons that remain to be uncovered.

cond-mat.dis-nn↗

arXiv2018

Approximate Survey Propagation for Statistical Inference

Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this algorithm as the approximate survey propagation (ASP) and derive it for a class of low-rank matrix estimation problems. We derive the state evolution for the ASP algorithm and prove that it reproduces the one-step replica symmetry breaking (1RSB) fixed-point equations, well-known in physics of disordered systems. Our derivation thus gives a concrete algorithmic meaning to the 1RSB equations that is of independent interest. We characterize the performance of ASP in terms of convergence and mean-squared error as a function of the free Parisi parameter s. We conclude that when there is a model mismatch between the true generative model and the inference model, the performance of AMP rapidly degrades both in terms of MSE and of convergence, while ASP converges in a larger regime and can reach lower errors. Among other results, our analysis leads us to a striking hypothesis that whenever s (or other parameters) can be set in such a way that the Nishimori condition $M=Q>0$ is restored, then the corresponding algorithm is able to reach mean-squared error as low as the Bayes-optimal error obtained when the model and its parameters are known and exactly matched in the inference procedure.

cond-mat.dis-nn↗

arXiv2018

Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables

We propose and test improvements to state-of-the-art techniques of Bayeasian statistical inference based on pseudolikelihood maximization with $\ell_1$ regularization and with decimation. In particular, we present a method to determine the best value of the regularizer parameter starting from a hypothesis testing technique. Concerning the decimation, we also analyze the worst case scenario in which there is no sharp peak in the tilded-pseudolikelihood function, firstly defined as a criterion to stop the decimation. Techniques are applied to noisy systems with non-linear dynamics, mapped onto multi-variable interacting Hamiltonian effective models for waves and phasors. Results are analyzed varying the number of available samples and the externally tunable temperature-like parameter mimicing real data noise. Eventually the behavior of inference procedures described are tested against a wrong hypothesis: non-linearly generated data are analyzed with a pairwise interacting hypothesis. Our analysis shows that, looking at the behavior of the inverse graphical problem as data size increases, the methods exposed allow to rule out a wrong hypothesis.

physics.data-an↗

arXiv2017

Inverse problem for multi-body interaction of nonlinear waves

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.

cond-mat.dis-nn↗

arXiv2016

Regularization and decimation pseudolikelihood approaches to statistical inference in $XY$-spin models

We implement a pseudolikelyhood approach with l2-regularization as well as the recently introduced pseudolikelihood with decimation procedure to the inverse problem in continuous spin models on arbitrary networks, with arbitrarily disordered couplings. Performances of the approaches are tested against data produced by Monte Carlo numerical simulations and compared also from previously studied fully-connected mean-field-based inference techniques. The results clearly show that the best network reconstruction is obtained through the decimation scheme, that also allows to dwell the inference down to lower temperature regimes. Possible applications to phasor models for light propagation in random media are proposed and discussed.

cond-mat.dis-nn↗

arXiv2015

The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra

The behavior of a newly introduced overlap parameter is analyzed, measuring the correlation between intensity fluctuations of waves in random media in different physical regimes, with varying amount of disorder and non-linearity. Its relationship is established to the standard Parisi overlap order parameter in replica theory for spin-glasses. In the complex spherical spin-glass model, describing the onset and behavior of random lasers, replica symmetry breaking in the intensity fluctuation overlap is shown to occur at high pumping or low temperature. This order parameter identifies the laser transition in random media and describes its glassy nature in terms of emission spectra data, the only data so far accessible in random laser measurements. The theoretical analysis is, eventually, compared to recent intensity fluctuation overlap measurements demonstrating the validity of the theory and providing a straightforward interpretation of different spectral behaviors in different random lasers.

cond-mat.stat-mech↗

arXiv2015

The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media

A disordered mean field model for multimode laser in open and irregular cavities is proposed and discussed within the replica analysis. The model includes the dynamics of the mode intensity and accounts also for the possible presence of a linear coupling between the modes, due, e.g., to the leakages from an open cavity. The complete phase diagram, in terms of disorder strength, source pumping and non-linearity, consists of four different optical regimes: incoherent fluorescence, standard mode locking, random lasing and the novel spontaneous phase locking. A replica symmetry breaking phase transition is predicted at the random lasing threshold. For a high enough strength of non-linearity, a whole region with nonvanishing complexity anticipates the transition, and the light modes in the disordered medium display typical discontinuous glassy behavior, i.e., the photonic glass has a multitude of metastable states that corresponds to different mode-locking processes in random lasers. The lasing regime is still present for very open cavities, though the transition becomes continuous at the lasing threshold.

cond-mat.stat-mech↗

arXiv2015

Statistical physical theory of mode-locking laser generation with a frequency comb

A study of the Mode-locking lasing pulse formation in closed cavities is presented within a statistical mechanical framework where the onset of laser coincides with a thermodynamic phase transition driven by the optical power pumped into the system. Electromagnetic modes are represented by classical degrees of freedom of a Hamiltonian model at equilibrium in an effective ensemble corresponding to the stationary laser regime. By means of optimized Monte Carlo numerical simulations, the system properties are analyzed varying mode interaction dilution, gain profile and number of modes. Novel properties of the resulting mode-locking laser phase are presented, not observable by previous mean-field approaches. For strong dilution of the nonlinear interaction network, power condensation occurs as the whole optical intensity is taken by a few electromagnetic modes, whose number does not depend on the size of the system. For all reported cases laser thresholds, intensity spectra, and ultra-fast electromagnetic pulses are computed.

physics.optics↗

arXiv2014

Statistical physics of nonlinear wave interaction

The thermodynamic properties of vector (O(2) and Complex Spherical) models with four-body interactions are analyzed. When defined in dense topologies, these are effective models for the nonlinear interaction of scalar fields in the presence of a stochastic noise, as has been well established for the case of the mode locking laser formation in a closed cavity. With the help of a novel efficient Monte Carlo algorithm we show how beyond the fully connected case novel and rich phenomenology emerges. Below a certain dilution threshold, the spherical model condensates in a non-equipartite way, while in the XY model the transition becomes continuous and the O(2) symmetry remains unbroken, we attribute this fact to the invariance under local gauge transformations. The introduction of topological inhomogeneities in the network of quadruplets induces novel features: again symmetry conservation; the vanishing of two-point correlators; and a dynamical correlation function presenting two timescales, the large one being related to the transition between different degenerated configurations, connected by nonlocal gauge transformations. We discuss possible experimental implications of these results in the context of nonlinear optics.

cond-mat.stat-mech↗

arXiv2014

Small clusters Renormalization Group in 2D and 3D Ising and BEG models with ferro, antiferro and quenched disordered magnetic interactions

The Ising and BEG models critical behavior is analyzed in 2D and 3D by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under decimation allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield the strong disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.

cond-mat.stat-mech↗

arXiv2014

General phase-diagram of multimodal ordered and disordered lasers in closed and open cavities

We present a unified approach to the theory of multimodal laser cavities including a variable amount of structural disorder. A general mean-field theory is studied for waves in media with variable non-linearity and randomness. Phase diagrams are reported in terms of optical power, degree of disorder and degree of non-linearity, tuning between closed and open cavity scenario's. In the thermodynamic limit of infinitely many modes the theory predicts four distinct regimes: a continuous wave behavior for low power, a standard mode-locking laser regime for high power and weak disorder, a random laser for high pumped power and large disorder and an intermediate regime of phase locking occurring in presence of disorder below the lasing threshold.

physics.optics↗