arXiv subjects

Federico Ricci-Tersenghi

Publications and source records attributed to Federico Ricci-Tersenghi.

At least 19 recordsLinked to original sources

arXiv2026

Transition path sampling in Ising models on heterogeneous graphs

Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here, we use transition path sampling to evaluate transition probabilities between ferromagnetic states in the Ising model on finite sparse random graphs, which are perhaps the simplest example of a disordered system with metastable states. To interpret the transient onset of the transition probability curve, we introduce a minimal three-state kinetic description that highlights the role of intermediate configurations. We validate the method on the heterogeneous Zachary Karate Club network, where distinct dynamical regimes emerge as temperature varies. We then apply the method to random regular graphs and Erdős-Rényi graphs, showing that sample-to-sample fluctuations are weak in the former but that quenched topological disorder induces sizable instance variability in the latter. For Erdős-Rényi graphs, we introduce an instance-dependent temperature rescaling that restores a consistent finite-size scaling of dynamical rates and enables a direct comparison with the corresponding static free-energy barrier.

cond-mat.dis-nn↗

arXiv2026

Aging Phase Diagram and Exact Asymptotic Energies of Mixed Spherical Spin Glasses

We determine the aging phase diagram of mixed spherical $(p+s)$-spin glasses quenched from random configurations to zero temperature. Solving the asymptotic dynamical equations of Cugliandolo and Kurchan, we find transitions between aging states with one, two, and continuously many effective temperatures, including phases in which discrete and continuous hierarchies coexist. We obtain analytic expressions for the energies reached asymptotically by the dynamics. In models combining pairwise and higher-order interactions, and sufficiently separated interaction orders ($s>3$), a fully continuous phase exists, where the gradient descent relaxation converges to the algorithmic energy lower bound. Instead, in mixed models with only high-order interactions ($p\ge3$) the energy relaxation remains strictly above it. Numerical integration of the dynamical equations is consistent with the predicted two-step and mixed discrete--continuous aging states.

cond-mat.dis-nn↗

arXiv2026

Low energy excitations in a long prism geometry: testing the lower critical dimension of the Ising spin glass

We propose a general method for studying systems that display low-energy excitations in their low-temperature phase. We argue that in a rectangular right-prism geometry (the 3-dimensional generalization of a strip), with one longitudinal size much larger than the transverse size, correlations decay exponentially (at all temperatures) along the longitudinal direction. Still, the scaling of the correlation length with the transverse size carries crucial information from which the lower critical dimension can be inferred. The method is applied in the particularly demanding context of Ising spin glasses at zero magnetic field. The lower critical dimension and the multifractal spectrum for the correlation functions are computed from large-scale numerical simulations. Several technical novelties (such as the unexpectedly crucial performance of Houdayer's cluster method or the convenience of using open---rather than periodic---boundary conditions) allow us to study three-dimensional prisms with transverse dimensions up to $L=24$ and effectively infinite longitudinal dimensions, down to low temperatures. The value that we find for the exponent controlling the behavior of the correlation length agrees with predictions from the Replica Symmetry Breaking (RSB) theory. We argue that our novel setting holds promise in clarifying which of the two competing theories, RSB or the Droplet Model, more accurately describes three-dimensional spin glasses.

cond-mat.dis-nn↗

arXiv2026

Cluster-based Message-Passing (CluMP) Optimization for Complex QUBO Problems

Quadratic Unconstrained Boolean Optimization (QUBO) problems are widespread in both industrial applications and scientific studies. A QUBO problem corresponds to the optimization of a system of Ising spins defined on a generally sparse and heterogeneous graph. When the QUBO problem contains conflicting requests, the corresponding Ising system is frustrated, generating a complex energy landscape, which is hard to explore and optimize. Despite extensive algorithmic and hardware developments, finding low-energy configurations in these systems remains challenging (e.g., local-update heuristics typically become trapped in metastable states), especially when the (possibly frustrated) interactions generate extended correlated domains. We introduce CluMP (Cluster-based Message-Passing), an algorithm that performs collective updates on connected clusters of spins using information from Belief Propagation (BP). By controlling the amount of frustration within clusters, CluMP enables BP convergence on large subgraphs and proposes nonlocal rearrangements involving up to hundreds of spins in a single move. We benchmark CluMP against state-of-the-art local-update heuristics on spin-glass models defined on several graph topologies, including random regular graphs and lattice regular graphs in two and three dimensions. Cluster moves consistently bypass local trapping and reach lower energies with fewer effective operations than single-spin dynamics. These results demonstrate that frustration-tolerant cluster updates can be implemented efficiently on sparse graphs. The CluMP framework provides a scalable strategy for large-scale combinatorial optimization and inference problems, where exploiting medium- and long-range correlations is key to navigating complex energy landscapes.

cond-mat.dis-nn↗

arXiv2026

Daydreaming algorithm for Biased Patterns

The \emph{Daydreaming} algorithm has been recently proposed in Ref.~\cite{Serricchio2025} as a learning rule that simultaneously reinforces stored patterns and suppresses spurious attractors to improve the storage capacity of the Hopfield model. Its effectiveness has been reported for both uncorrelated and correlated data. However, the existing formulation has mainly assumed unbiased patterns, and the formulation for biased patterns has not yet been sufficiently established. Biased patterns are known to be much more problematic for models of associative memories. In this study, we reformulate Daydreaming for biased patterns motivated by the underlying rationale of the pseudo-inverse rule. Specifically, we introduce the retrieval dynamics and an energy function based on the centered representation, and we derive a corresponding update rule for centered Daydreaming. We compare the centered pseudo-inverse rule with centered Daydreaming for biased patterns and examine the retrieval maps and eigenvalue distributions of the coupling matrices. As a result, the centered Daydreaming yields larger basins of attraction than the centered pseudo-inverse rule, and such a beneficial property seems to be due to the broadness of the eigenvalue spectrum of the coupling matrix. To better understand this connection, we construct modified coupling matrices whose spectra interpolate between a pseudo-inverse-like spectrum and the Daydreaming one. The results clearly indicate that the broader spectrum generated by Daydreaming contributes to the enlarged basin of attraction.

cond-mat.dis-nn↗

arXiv2026

Partial annealing and pattern decorrelation in associative neural networks

Using the Hopfield model as a benchmark case, the present work focuses on the investigation of partially annealed associative neural networks, wherein neural dynamics is coupled to slowly evolving patterns within the two-temperature-two-timescale framework. This setting inherently introduces a real parameter n, reminiscent of the number of replicas in the celebrated replica trick, that tunes the separation of timescales and the effective interaction between fast (i.e. the neurons) and slow (i.e. the synapses) degrees of freedom. By adapting Guerra's interpolation to the case, we derive the free energy without relying on analytical continuation. The obtained results demonstrate that negative values of n induce a progressive decorrelation of the stored patterns, thereby effectively reducing interference, promoting orthogonal configurations and ultimately conferring to the network the maximal storage alphac=1. Numerical simulations based on a mean field Monte Carlo dynamics have been employed to confirm this scenario and prove that partial annealing restores retrieval in challenging regimes, such as in the presence of biased patterns, outperforming standard decorrelation methods. These findings underscore the notion of partial annealing as an adaptive mechanism for enhancing memory organisation and retrieval in complex systems.

cond-mat.dis-nn↗

arXiv2026

Overlap locking and non-perturbative effects in spin glasses

We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when $1 \ll ΔH \ll N$, being $ΔH$ the coupling Hamiltonian and $N$ the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model.

cond-mat.dis-nn↗

arXiv2026

Discontinuous BBP transitions

The Baik-Ben Arous-Peche (BBP) transition sets fundamental limits for detecting low-rank structure in noisy high-dimensional data and underlies a wide range of spectral methods in many fields from physics to statistics and data sciences. In standard settings, this transition is continuous, implying that signal recovery emerges gradually above a sharp threshold. We show that BBP transitions can instead be discontinuous in very general settings and provide a full theory of this phenomenon. When the eigenvalue density vanishes faster than linearly at the spectral edge, the overlap between the leading eigenvector and the signal jumps discontinuously at the critical point. We study this mechanism in deformed Gaussian and reweighted Wishart ensembles. We analyze in detail the finite-size effects, which play a central and qualitatively new role in the discontinuous BBP transition. Unlike the continuous BBP transition, we establish the existence of an extended pre-critical region where informative eigenvectors emerge well before the asymptotic threshold. The main consequence-and difference from the continuous BBP transition-is that signal recovery can occur at significantly lower signal-to-noise ratio and it is accompanied by strong sample-to-sample variability. Our results show the relevance and the novelty of the discontinuous BBP transition, and highlight the practical implications for signal detection.

cond-mat.dis-nn↗

arXiv2026

Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimization

Combinatorial optimization problems are central to both practical applications and the development of optimization methods. While classical and quantum algorithms have been refined over decades, machine learning--assisted approaches are comparatively recent and have not yet consistently outperformed simple, state-of-the-art classical methods. Here, we focus on a class of Quadratic Unconstrained Binary Optimization (QUBO) problems, specifically the challenge of finding minimum energy configurations in three-dimensional Ising spin glasses. We use a Global Annealing Monte Carlo algorithm that integrates standard local moves with global moves proposed via machine learning. We show that local moves play a crucial role in achieving optimal performance. Benchmarking against Simulated Annealing and Population Annealing, we demonstrate that Global Annealing not only surpasses the performance of Simulated Annealing but also exhibits greater robustness than Population Annealing, maintaining effectiveness across problem hardness and system size without hyperparameter tuning. These results provide clear and robust evidence that a machine learning--assisted optimization method can exceed the capabilities of classical state-of-the-art techniques in a combinatorial optimization setting.

cond-mat.dis-nn↗

arXiv2026

Phase transition in compressed sensing using log-sum penalty and adaptive smoothing

In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching the Bayes-optimal reconstruction limit. Nonconvex alternatives, such as the log-sum penalty, have been proposed to promote stronger sparsity. However, maintaining their algorithmic stability is challenging. To address this challenge, we introduce an adaptive smoothing strategy within an approximate message passing framework to mitigate algorithmic instability. Furthermore, we evaluate the typical exact-recovery threshold for Gaussian measurement matrices using the replica method and state evolution. The results indicate that the adaptive method achieves exact recovery over a broader region than $\ell_1$ norm minimization, although metastable states hinder reaching the information-theoretic limit.

cs.IT↗

arXiv2026

DYNAMITE: A high-performance framework for solving Dynamical Mean-Field Equations

Understanding the dynamics of systems evolving in complex and rugged energy landscapes is central across physics, economics, biology, and computer science. Disordered mean-field models provide a powerful framework, as exact Dynamical Mean-Field Equations (DMFE) can be derived. However, solving the DMFE -- a set of coupled integral-differential equations for two-time functions -- remains a major numerical challenge. So far, large-time solutions of DMFE rely either on analytical approaches, such as the Cugliandolo--Kurchan ansatz based on assumptions like weak ergodicity breaking (which is known to fail in some cases), or on numerical integrations that reliably reach times $O(10^3)$ and extend further only via poorly controlled approximations. Consequently, no general method currently exists to solve DMFE at very long times, limiting the study of slow dynamics in complex landscapes. We present \textsc{Dynamite} (DYNAmical Mean-fIeld Time Evolution solver), a high-performance framework for solving DMFE up to unprecedented times $t=O(10^7)$. It combines non-uniform interpolation, adaptive time stepping, and numerical `renormalization' of memory, enabling accurate evaluation of history integrals. Its asymptotic runtime is linear, with sublinear memory scaling. Stability and precision are ensured via an adaptive Runge--Kutta scheme and periodic sparsification of the past. \textsc{Dynamite} achieves orders-of-magnitude speedups over uniform-grid methods while maintaining accuracy and reproducibility on CPU and GPU architectures. Benchmarks on glassy mean-field models, including the mixed spherical $p$-spin system, demonstrate access to aging and relaxation regimes previously out of reach. The framework provides a reproducible and extensible foundation for studying long-memory dynamical systems.

cond-mat.dis-nn↗

arXiv2026

Benchmarking Graph Neural Networks in Solving Hard Constraint Satisfaction Problems

Graph neural networks (GNNs) are increasingly applied to hard optimization problems, often claiming superiority over classical heuristics. However, such claims risk being unsolid due to a lack of standard benchmarks on truly hard instances. From a statistical physics perspective, we propose new hard benchmarks based on random problems. We provide these benchmarks, along with performance results from both classical heuristics and GNNs. Our fair comparison shows that classical algorithms still outperform GNNs. We discuss the challenges for neural networks in this domain. Future claims of superiority can be made more robust using our benchmarks, available at https://github.com/ArtLabBocconi/RandCSPBench.

cond-mat.dis-nn↗

arXiv2026

Efficient Graph Coloring with Neural Networks: A Physics-Inspired Approach for Large Graphs

Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint satisfaction problem exhibiting sharp dynamical and satisfiability thresholds. Here we introduce a physics-inspired neural framework that learns to solve large-scale graph coloring instances by combining graph neural networks with statistical-mechanics principles. Our approach integrates a planting-based supervised signal, symmetry-breaking regularization, and iterative noise-annealed neural dynamics to navigate clustered solution landscapes. When the number of iterations scales quadratically with graph size, the learned solver reaches algorithmic thresholds close to the theoretical dynamical transition in random graphs and achieves near-optimal detection performance in the planted inference regime. The model generalizes from small training graphs to instances orders of magnitude larger, demonstrating that neural architectures can learn scalable algorithmic strategies that remain effective in hard connectivity regions. These results establish a general paradigm for learning neural solvers that operate near fundamental phase boundaries in combinatorial optimization and inference.

cs.LG↗

arXiv2025

Strong ergodicity breaking in dynamical mean-field equations for mixed p-spin glasses

The analytical solution to the out-of-equilibrium dynamics of mean-field spin glasses has profoundly shaped our understanding of glassy dynamics, which take place in many diverse physical systems. In particular, the idea that during the aging dynamics, the evolution becomes slower and slower, but keeps wandering in an unbounded space (a manifold of marginal states), thus forgetting any previously found configuration, has been one of the key hypotheses to achieve an analytical solution. This hypothesis, called weak ergodicity breaking, has recently been questioned by numerical simulations and attempts to solve the dynamical mean-field equations (DMFE). In this work, we introduce a new integration scheme for solving DMFE that allows us to reach very large integration times, $t=O(10^6)$, in the solution of the spherical 3+4-spin model, quenched from close to the mode coupling temperature down to zero temperature. Thanks to this new solution, we can provide solid evidence for \emph{strong ergodicity breaking} in the out-of-equilibrium dynamics on mixed $p$-spin glass models. Our solution to the DMFE shows that the out-of-equilibrium dynamics undergo aging, but in a restricted space: the initial condition is never forgotten, and the dynamics take place closer and closer to configurations reached at later times. During this new restricted aging dynamics, the fluctuation-dissipation relation is richer than expected.

cond-mat.dis-nn↗

arXiv2025

The geometry of jamming algorithms in the random Lorentz gas

Deterministic optimization algorithms unequivocally partition a complex energy landscape in inherent structures (ISs) and their respective basins of attraction. Can these basins be defined solely through geometric principles? This question is paramount to understanding hard sphere jamming, a key model of disordered matter. We here address the issue by proposing a geometric class of gradient descent-like algorithms, which we use to study a system in the hard-sphere universality class, the random Lorentz gas. The statistics of the resulting ISs is found to be strictly inherited from those of Poisson-Voronoi tessellations. The landscape roughness is further found to give rise to a hierarchical organization of ISs, which various algorithms explore differently. In particular, greedy and reluctant schemes tend to favor ISs of markedly different densities. The resulting ISs nevertheless robustly exhibit a universal force distribution, thus confirming the geometric nature of the jamming universality class. Along the way, the physical origin of a dynamical Gardner transition is identified.

cond-mat.dis-nn↗

arXiv2025

Networks of neural networks: more is different

The common thread behind the recent Nobel Prize in Physics to John Hopfield and those conferred to Giorgio Parisi in 2021 and Philip Anderson in 1977 is disorder. Quoting Philip Anderson: "more is different". This principle has been extensively demonstrated in magnetic systems and spin glasses, and, in this work, we test its validity on Hopfield neural networks to show how an assembly of these models displays emergent capabilities that are not present at a single network level. Such an assembly is designed as a layered associative Hebbian network that, beyond accomplishing standard pattern recognition, spontaneously performs also pattern disentanglement. Namely, when inputted with a composite signal -- e.g., a musical chord -- it can return the single constituting elements -- e.g., the notes making up the chord. Here, restricting to notes coded as Rademacher vectors and chords that are their mixtures (i.e., spurious states), we use tools borrowed from statistical mechanics of disordered systems to investigate this task, obtaining the conditions over the model control-parameters such that pattern disentanglement is successfully executed.

cond-mat.dis-nn↗

arXiv2025

Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models

Recent years have seen a rise in the application of machine learning techniques to aid the simulation of hard-to-sample systems that cannot be studied using traditional methods. Despite the introduction of many different architectures and procedures, a wide theoretical understanding is still lacking, with the risk of suboptimal implementations. As a first step to address this gap, we provide here a complete analytic study of the widely-used Sequential Tempering procedure applied to a shallow MADE architecture for the Curie-Weiss model. The contribution of this work is twofold: firstly, we give a description of the optimal weights and of the training under Gradient Descent optimization. Secondly, we compare what happens in Sequential Tempering with and without the addition of local Metropolis Monte Carlo steps. We are thus able to give theoretical predictions on the best procedure to apply in this case. This work establishes a clear theoretical basis for the integration of machine learning techniques into Monte Carlo sampling and optimization.

cond-mat.dis-nn↗

arXiv2025

Pushing the Boundary of Quantum Advantage in Hard Combinatorial Optimization with Probabilistic Computers

Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic computers (p-computers), when co-designed with hardware to implement powerful Monte Carlo algorithms, provide a compelling and scalable classical pathway for solving hard optimization problems. We focus on two key algorithms applied to 3D spin glasses: discrete-time simulated quantum annealing (DT-SQA) and adaptive parallel tempering (APT). We benchmark these methods against the performance of a leading quantum annealer on the same problem instances. For DT-SQA, we find that increasing the number of replicas improves residual energy scaling, in line with expectations from extreme value theory. We then show that APT, when supported by non-local isoenergetic cluster moves, exhibits a more favorable scaling and ultimately outperforms DT-SQA. We demonstrate these algorithms are readily implementable in modern hardware, projecting that custom Field Programmable Gate Arrays (FPGA) or specialized chips can leverage massive parallelism to accelerate these algorithms by orders of magnitude while drastically improving energy efficiency. Our results establish a new, rigorous classical baseline, clarifying the landscape for assessing a practical quantum advantage and presenting p-computers as a scalable platform for real-world optimization challenges.

quant-ph↗