arXiv subjects

Francesco Zamponi

Publications and source records attributed to Francesco Zamponi.

At least 37 records · Page 2Linked to original sources

arXiv2025

Nearest-Neighbours Neural Network architecture for efficient sampling of statistical physics models

The task of sampling efficiently the Gibbs-Boltzmann distribution of disordered systems is important both for the theoretical understanding of these models and for the solution of practical optimization problems. Unfortunately, this task is known to be hard, especially for spin glasses at low temperatures. Recently, many attempts have been made to tackle the problem by mixing classical Monte Carlo schemes with newly devised Neural Networks that learn to propose smart moves. In this article we introduce the Nearest-Neighbours Neural Network (4N) architecture, a physically-interpretable deep architecture whose number of parameters scales linearly with the size of the system and that can be applied to a large variety of topologies. We show that the 4N architecture can accurately learn the Gibbs-Boltzmann distribution for the two-dimensional Edwards-Anderson model, and specifically for some of its most difficult instances. In particular, it captures properties such as the energy, the correlation function and the overlap probability distribution. Finally, we show that the 4N performance increases with the number of layers, in a way that clearly connects to the correlation length of the system, thus providing a simple and interpretable criterion to choose the optimal depth.

cond-mat.dis-nn↗

arXiv2025

Exact full-RSB SAT/UNSAT transition in infinitely wide two-layer neural networks

We analyze the problem of storing random pattern-label associations using two classes of continuous non-convex weights models, namely the perceptron with negative margin and an infinite-width two-layer neural network with non-overlapping receptive fields and generic activation function. Using a full-RSB ansatz we compute the exact value of the SAT/UNSAT transition. Furthermore, in the case of the negative perceptron we show that the overlap distribution of typical states displays an overlap gap (a disconnected support) in certain regions of the phase diagram defined by the value of the margin and the density of patterns to be stored. This implies that some recent theorems that ensure convergence of Approximate Message Passing (AMP) based algorithms to capacity are not applicable. Finally, we show that Gradient Descent is not able to reach the maximal capacity, irrespectively of the presence of an overlap gap for typical states. This finding, similarly to what occurs in binary weight models, suggests that gradient-based algorithms are biased towards highly atypical states, whose inaccessibility determines the algorithmic threshold.

cond-mat.dis-nn↗

arXiv2025

adabmDCA 2.0 -- a flexible but easy-to-use package for Direct Coupling Analysis

In this methods article, we provide a flexible but easy-to-use implementation of Direct Coupling Analysis (DCA) based on Boltzmann machine learning, together with a tutorial on how to use it. The package \texttt{adabmDCA 2.0} is available in different programming languages (C++, Julia, Python) usable on different architectures (single-core and multi-core CPU, GPU) using a common front-end interface. In addition to several learning protocols for dense and sparse generative DCA models, it allows to directly address common downstream tasks like residue-residue contact prediction, mutational-effect prediction, scoring of sequence libraries and generation of artificial sequences for sequence design. It is readily applicable to protein and RNA sequence data.

q-bio.QM↗

arXiv2024

Emergent time scales of epistasis in protein evolution

We introduce a data-driven epistatic model of protein evolution, capable of generating evolutionary trajectories spanning very different time scales reaching from individual mutations to diverged homologs. Our in silico evolution encompasses random nucleotide mutations, insertions and deletions, and models selection using a fitness landscape, which is inferred via a generative probabilistic model for protein families. We show that the proposed framework accurately reproduces the sequence statistics of both short-time (experimental) and long-time (natural) protein evolution, suggesting applicability also to relatively data-poor intermediate evolutionary time scales, which are currently inaccessible to evolution experiments. Our model uncovers a highly collective nature of epistasis, gradually changing the fitness effect of mutations in a diverging sequence context, rather than acting via strong interactions between individual mutations. This collective nature triggers the emergence of a long evolutionary time scale, separating fast mutational processes inside a given sequence context, from the slow evolution of the context itself. The model quantitatively reproduces epistatic phenomena such as contingency and entrenchment, as well as the loss of predictability in protein evolution observed in deep mutational scanning experiments of distant homologs. It thereby deepens our understanding of the interplay between mutation and selection in shaping protein diversity and novel functions, allows one to statistically forecast evolution, and challenges the prevailing independent-site models of protein evolution, which are unable to capture the fundamental importance of epistasis.

q-bio.BM↗

arXiv2024

Roadmap on machine learning glassy dynamics

Unraveling the connections between microscopic structure, emergent physical properties, and slow dynamics has long been a challenge when studying the glass transition. The absence of clear visible structural order in amorphous configurations complicates the identification of the key physical mechanisms underpinning slow dynamics. The difficulty in sampling equilibrated configurations at low temperatures hampers thorough numerical and theoretical investigations. This perspective article explores the potential of machine learning (ML) techniques to face these challenges, building on the algorithms that have revolutionized computer vision and image recognition. We present recent successful ML applications, as well as many open problems for the future, such as transferability and interpretability of ML approaches. We highlight new ideas and directions in which ML could provide breakthroughs to better understand the fundamental mechanisms at play in glass-forming liquids. To foster a collaborative community effort, this article also introduces the ``GlassBench" dataset, providing simulation data and benchmarks for both two-dimensional and three-dimensional glass-formers. We propose critical metrics to compare the performance of emerging ML methodologies, in line with benchmarking practices in image and text recognition. The goal of this roadmap is to provide guidelines for the development of ML techniques in systems displaying slow dynamics, while inspiring new directions to improve our theoretical understanding of glassy liquids.

cond-mat.soft↗

arXiv2024

Unlearning regularization for Boltzmann Machines

Boltzmann Machines (BMs) are graphical models with interconnected binary units, employed for the unsupervised modeling of data distributions. When trained on real data, BMs show the tendency to behave like critical systems, displaying a high susceptibility of the model under a small rescaling of the inferred parameters. This behaviour is not convenient for the purpose of generating data, because it slows down the sampling process, and induces the model to overfit the training-data. In this study, we introduce a regularization method for BMs to improve the robustness of the model under rescaling of the parameters. The new technique shares formal similarities with the unlearning algorithm, an iterative procedure used to improve memory associativity in Hopfield-like neural networks. We test our unlearning regularization on synthetic data generated by two simple models, the Curie-Weiss ferromagnetic model and the Sherrington-Kirkpatrick spin glass model. We show that it outperforms $L_p$-norm schemes and discuss the role of parameter initialization. Eventually, the method is applied to learn the activity of real neuronal cells, confirming its efficacy at shifting the inferred model away from criticality and coming out as a powerful candidate for actual scientific implementations.

cond-mat.dis-nn↗

arXiv2024

Yielding and plasticity in amorphous solids

The physics of disordered media, from metallic glasses to colloidal suspensions, granular matter and biological tissues, offers difficult challenges because it often occurs far from equilibrium, in materials lacking symmetries and evolving through complex energy landscapes. Here, we review recent theoretical efforts to provide microscopic insights into the mechanical properties of amorphous media using approaches from statistical mechanics as unifying frameworks. We cover both the initial regime corresponding to small deformations, and the yielding transition marking a change between elastic response and plastic flow. We discuss the specific features arising for systems evolving near a jamming transition, and extend our discussion to recent studies of the rheology of dense biological and active materials.

cond-mat.stat-mech↗

arXiv2023

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

cond-mat.soft↗

arXiv2023

Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition

Under decompression, disordered solids undergo an unjamming transition where they become under-coordinated and lose their structural rigidity. The mechanical and vibrational properties of these materials have been an object of theoretical, numerical, and experimental research for decades. In the study of low-coordination solids, understanding the behavior and physical interpretation of observables that diverge near the transition is of particular importance. Several such quantities are length scales ($ξ$ or $l$) that characterize the size of excitations, the decay of spatial correlations, the response to perturbations, or the effect of physical constraints in the boundary or bulk of the material. Additionally, the spatial and sample-to-sample fluctuations of macroscopic observables such as contact statistics or elastic moduli diverge approaching unjamming. Here, we discuss important connections between all of these quantities, and present numerical results that characterize the scaling properties of sample-to-sample contact and shear modulus fluctuations in ensembles of low-coordination disordered sphere packings and spring networks. Overall, we highlight three distinct scaling regimes and two crossovers in the disorder quantifiers $χ_z$ and $χ_μ$ as functions of system size $N$ and proximity to unjamming $δz$. As we discuss, $χ_X$ relates to the standard deviation $σ_X$ of the sample-to-sample distribution of the quantity $X$ (e.g. excess coordination $δz$ or shear modulus $μ$) for an ensemble of systems. Importantly, $χ_μ$ has been linked to experimentally accessible quantities that pertain to sound attenuation and the density of vibrational states in glasses.

cond-mat.soft↗

arXiv2023

Creating equilibrium glassy states via random particle bonding

Creating amorphous solid states by randomly bonding an ensemble of dense liquid monomers is a common procedure which is applied to create a variety of materials such as epoxy resins, colloidal gels, and vitrimers. The properties of the resulting solid do, however, {\it a priori} strongly depend on the preparation history. This can lead to substantial aging of the material, i.e., properties such as mechanical moduli and transport coefficients depend on the time elapsed since solidification, which can lead to a slow degradation of the material in technological applications. It is therefore important to understand under which conditions random monomer bonding can lead to stable solid states, i.e., long-lived metastable states whose properties do not change over time. In this work, we present a theoretical and computational analysis of this problem, and introduce a random bonding procedure that guarantees the proper equilibration of the resulting amorphous states. Our procedure also provides a new route to investigate the fundamental properties of glassy energy landscapes by producing translationally-invariant ultrastable glassy states of simple particle models.

cond-mat.soft↗

arXiv2023

Towards Parsimonious Generative Modeling of RNA Families

Generative probabilistic models emerge as a new paradigm in data-driven, evolution-informed design of biomolecular sequences. This paper introduces a novel approach, called Edge Activation Direct Coupling Analysis (eaDCA), tailored to the characteristics of RNA sequences, with a strong emphasis on simplicity, efficiency, and interpretability. eaDCA explicitly constructs sparse coevolutionary models for RNA families, achieving performance levels comparable to more complex methods while utilizing a significantly lower number of parameters. Our approach demonstrates efficiency in generating artificial RNA sequences that closely resemble their natural counterparts in both statistical analyses and SHAPE-MaP experiments, and in predicting the effect of mutations. Notably, eaDCA provides a unique feature: estimating the number of potential functional sequences within a given RNA family. For example, in the case of cyclic di-AMP riboswitches (RF00379), our analysis suggests the existence of approximately $\mathbf{10^{39}}$ functional nucleotide sequences. While huge compared to the known $< \mathbf{4,000}$ natural sequences, this number represents only a tiny fraction of the vast pool of nearly $\mathbf{10^{82}}$ possible nucleotide sequences of the same length (136 nucleotides). These results underscore the promise of sparse and interpretable generative models, such as eaDCA, in enhancing our understanding of the expansive RNA sequence space.

q-bio.BM↗

arXiv2023

The nature of non-phononic excitations in disordered systems

Using heterogeneous-elasticity theory (HET) and a generalisation of HET theory (GHET), obtained by applying a newly developed procedure for obtaining the continuum limit of the glass's Hessian, we investigate the nature of vibrational excitations, which are present in small systems, which do not allow for low-frequency phonons. We identify two types of such non-phononic excitations. In marginally stable systems, which can be prepared by quenching from a rather high parental temperature, the low-frequency regime is dominated by random-matrix vibrational wavefunctions (type-I) which in macroscopic samples gives rise to the boson peak. They show a density of states (DOS), which scales as $g(ω)\sim ω^2$. In more stable systems (reached by a somewhat lower parental temperature) a gap appears in the type-I spectrum. This gap is filled with other type-II non-phononic excitations, which are not described by the previous version of HET, and have a DOS, which scales as $g(ω)\simω^s$ with $3<s<5$. Using GHET we demonstrate that the type-II excitations are due to local non-irrotational oscillations associated with the stress field. The frequency scaling exponent $s$ turns out to be non-universal, depending on the details of the interaction potential. Specifically, we demonstrate that $s$ depends on the statistics of the small values of the local frozen-in stresses, which are, in turn, governed by the shape of the pair potential close to values where the potential or its first derivative vanishes. All these findings are verified by extensive numerical simulations of small soft-sphere glasses. Further, using level-distance statistics, we demonstrate that both types of non-phononic excitations obey the Gaussian-Orthogonal-Ensemble random-matrix statistics, which means that they are extended and not localized.

cond-mat.dis-nn↗

arXiv2023

On weak ergodicity breaking in mean-field spin glasses

The weak ergodicity breaking hypothesis postulates that out-of-equilibrium glassy systems lose memory of their initial state despite being unable to reach an equilibrium stationary state. It is a milestone of glass physics, and has provided a lot of insight on the physical properties of glass aging. Despite its undoubted usefulness as a guiding principle, its general validity remains a subject of debate. Here, we present evidence that this hypothesis does not hold for a class of mean-field spin glass models. While most of the qualitative physical picture of aging remains unaffected, our results suggest that some important technical aspects should be revisited.

cond-mat.dis-nn↗

arXiv2023

Finding defects in glasses through machine learning

Structural defects control the kinetic, thermodynamic and mechanical properties of glasses. For instance, rare quantum tunneling two-level systems (TLS) govern the physics of glasses at very low temperature. Because of their extremely low density, it is very hard to directly identify them in computer simulations. We introduce a machine learning approach to efficiently explore the potential energy landscape of glass models and identify desired classes of defects. We focus in particular on TLS and we design an algorithm that is able to rapidly predict the quantum splitting between any two amorphous configurations produced by classical simulations. This in turn allows us to shift the computational effort towards the collection and identification of a larger number of TLS, rather than the useless characterization of non-tunneling defects which are much more abundant. Finally, we interpret our machine learning model to understand how TLS are identified and characterized, thus giving direct physical insight into their microscopic nature.

cond-mat.dis-nn↗

arXiv2023

Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems

Several strategies have been recently proposed in order to improve Monte Carlo sampling efficiency using machine learning tools. Here, we challenge these methods by considering a class of problems that are known to be exponentially hard to sample using conventional local Monte Carlo at low enough temperatures. In particular, we study the antiferromagnetic Potts model on a random graph, which reduces to the coloring of random graphs at zero temperature. We test several machine-learning-assisted Monte Carlo approaches, and we find that they all fail. Our work thus provides good benchmarks for future proposals for smart sampling algorithms.

cond-mat.dis-nn↗

arXiv2023

Microscopic observation of two-level systems in a metallic glass model

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.

cond-mat.dis-nn↗

arXiv2022

Creating bulk ultrastable glasses by random particle bonding

A recent breakthrough in glass science has been the synthesis of ultrastable glasses via physical vapor deposition techniques. These samples display enhanced thermodynamic, kinetic and mechanical stability, with important implications for fundamental science and technological applications. However, the vapor deposition technique is limited to atomic, polymer and organic glass-formers and is only able to produce thin film samples. Here, we propose a novel approach to generate ultrastable glassy configurations in the bulk, via random particle bonding, and using computer simulations we show that this method does indeed allow for the production of ultrastable glasses. Our technique is in principle applicable to any molecular or soft matter system, such as colloidal particles with tunable bonding interactions, thus opening the way to the design of a large class of ultrastable glasses.

cond-mat.soft↗

arXiv2022

Finite-disorder critical point in the yielding transition of elasto-plastic models

Upon loading, amorphous solids can exhibit brittle yielding, with the abrupt formation of macroscopic shear bands leading to fracture, or ductile yielding, with a multitude of plastic events leading to homogeneous flow. It has been recently proposed, and subsequently questioned, that the two regimes are separated by a sharp critical point, as a function of some control parameter characterizing the intrinsic disorder strength and the degree of stability of the solid. In order to resolve this issue, we have performed extensive numerical simulations of athermally driven elasto-plastic models with long-range and anisotropic realistic interaction kernels in two and three dimensions. Our results provide clear evidence for a finite-disorder critical point separating brittle and ductile yielding, and we provide an estimate of the critical exponents in 2D and 3D.

cond-mat.soft↗