arXiv subjects

Davide Carbone

Publications and source records attributed to Davide Carbone.

16 recordsLinked to original sources

arXiv2026

Characterizing the Dynamics of Muscle Regeneration in the mdx Mouse Model

In this work, we explore a model of immune response in the skeletal muscle of the mdx mouse, the preferred animal model for studying Duchenne Muscular Dystrophy. The system studied is based on existing literature and describes the reaction of the tissue, and of the immune cells within it, to external damage, focusing specifically on the regeneration process. This work extends the analysis conducted by the authors of the original paper, highlighting interesting dynamical properties of the system, particularly in terms of longterm behavior and dependence on initial conditions. A modification is then introduced to the original equations, incorporating a diffusion term for immune cells. The dynamics of the system is numerically investigated in both the one-dimensional and two-dimensional cases. Specifically, we investigate the effect of diffusion under various boundary conditions, and the system's response to localized damage.

math.DS↗

arXiv2026

Escaping the Variance Trap: Jacobian-Free Dynamics for Root-Finding Bilevel Optimization

Many central machine learning tasks, from entropy tuning in reinforcement learning to equilibrating generative adversarial networks, are fundamentally stochastic root-finding problems rather than loss minimization. Yet, they are frequently forced into a minimization framework via squared residuals, introducing a critical flaw we identify as the Variance Trap. Standard bilevel minimization algorithms require estimating hypergradients involving implicit Jacobians; in stochastic settings, these terms act as noise amplifiers, destabilizing convergence. We formalize Root-Finding Bilevel Optimization (RF-BO) as a distinct problem class that bypasses this pathology. We propose a Jacobian-free solution using Two-Time-Scale Stochastic Approximation (TTSA) that updates directly along the root error, structurally avoiding variance amplification. We provide the first non-asymptotic convergence guarantees for TTSA in this setting under Markovian noise. Extensive experiments demonstrate the decisive advantage of this paradigm: compared to squared-residual and implicit-gradient baselines, our framework achieves a 2.6\% top-1 accuracy gain in SimCLR, 17$\times$ faster convergence in non-linear ODE control where baselines fail, significantly improved entropy stability in reinforcement learning, and an 11.1\% quality improvement in generative modeling.

cs.LG↗

arXiv2026

Distribution-Aware Robust Bilevel Optimization: Quantile-Guided Huber Updates in Two-Timescale Stochastic Approximation

Bilevel optimization (BLO) is fundamental to hierarchical decision-making but suffers from critical instability under heavy-tailed stochastic noise. Existing variance-reduction techniques typically rely on myopic magnitude checks, which fail to distinguish informative geometric signals from impulsive outliers. To resolve this, we propose \textbf{RQ-TTSA} (Robust Quantile-guided TTSA), a distribution-aware framework that leverages historical gradient buffers to estimate rolling quantiles for adaptive Huber-style clipping, effectively preserving local optimization geometry while strictly bounding effective variance. Theoretically, we provide a convergence analysis for quantile-guided TTSA under nonconvex-strongly convex assumptions with infinite-variance noise ($p \in (1,2]$), deriving a rate of $\mathcal{O}(T^{-\frac{p-1}{3p-2}})$ that recovers optimal dependence on the heavy-tailed parameter. Empirically, across six diverse tasks, spanning heterogeneous vision benchmarks, dynamic games under momentum poisoning, and offline reinforcement learning, RQ-TTSA consistently outperforms state-of-the-art baselines by eliminating divergence spikes and ensuring stable convergence. Our method demonstrates significant robustness to hyperparameter variations and incurs negligible computational overhead ($\approx 2.7\%$ increase), validating distribution-aware gradient control as a practical and necessary component for reliable bilevel learning.

cs.LG↗

arXiv2026

Computing Nonequilibrium Transport from Short-Time Transients: From Lorentz Gas to Heat Conduction in One Dimensional Chains

We test the Transient Time Correlation Function (TTCF) method to compute nonequilibrium transport coefficients, highlighting its conceptual and practical difference from the standard time-average approach. While time averages extract transport properties from long stationary trajectories and discard transient dynamics, TTCF adopts the complementary strategy: it exploits the information contained in short-time transients following the onset of an external perturbation, while discarding the long-time evolution once stationarity is reached. We revisit the theoretical framework of TTCF and assess its numerical performance through representative case studies, the Lorentz gas and a many-body system, namely a chain of oscillators with anharmonic pinning potential. By direct comparison with time averages, we show that for the Lorentz gas TTCF yields consistent transport coefficients in both linear and nonlinear regimes at a reduced computational cost. Moreover, the TTCF displays superior precision in the linear-response regime, and remains reliable in non-ergodic situations, revealing the presence of regions of phase space corresponding to different behaviors, as well as the possibility of phase transitions. For the anharmonic chain, we show that TTCF is a scalable and efficient alternative for the numerical study of nonequilibrium transport.

cond-mat.stat-mech↗

arXiv2026

WST-X Series: Wavelet Scattering Transform for Interpretable Speech Deepfake Detection

In this work, we focus on front-end design for speech deepfake detectors, the component that determines the discriminative acoustic cues provided to the classifier. Existing approaches are primarily categorized into two types. Hand-crafted filterbank features are transparent but limited in capturing higher-level information. SSL features, in turn, lack interpretability and may overlook fine-grained spectral anomalies. We propose the WST-X series, a novel family of feature extractors that combines the best of both worlds via the wavelet scattering transform (WST), which cascades wavelet convolutions with modulus nonlinearities to produce deformation-stable, multi-scale features. Experiments on the recent Deepfake-Eval-2024 benchmark, together with cross-dataset evaluations on the SpoofCeleb and In-the-Wild, show that WST-X outperforms existing front-ends by a wide margin. Our analysis reveals that a small averaging scale ($J$), combined with high-frequency and directional resolutions ($Q$, $L$), is critical for capturing subtle artifacts. This underscores the value of stable and translation-invariant features for speech deepfake detection. The code is available at https://github.com/xxuan-acoustics/WST-X-Series.

eess.AS↗

arXiv2026

Efficient Stochastic Optimisation via Sequential Monte Carlo

The problem of optimising functions with intractable gradients frequently arises in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation methods for this class of problems typically require inner sampling loops to obtain (biased) stochastic gradient estimates, which rapidly becomes computationally expensive. In this work, we develop sequential Monte Carlo (SMC) samplers for optimisation of functions with intractable gradients. Our approach replaces expensive inner sampling methods with efficient SMC approximations, which can result in significant computational gains. We establish convergence results for the basic recursions defined by our methodology which SMC samplers approximate. We demonstrate the effectiveness of our approach on the reward-tuning of energy-based models within various settings.

stat.ML↗

arXiv2025

Efficient Monte Carlo sampling of metastable systems using non-local collective variable updates

Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several works. Here, we generalize these approaches and explicitly spell out an algorithm for non-linear CVs and underdamped Langevin dynamics. We prove reversibility of the resulting scheme and demonstrate its performance on several numerical examples, observing a substantial performance increase compared to methods based on overdamped Langevin dynamics as considered previously. Advances in generative machine-learning-based proposal samplers now enable efficient sampling in CV spaces of intermediate dimensionality (tens to hundreds of variables), and our results extend their applicability toward more realistic molecular systems.

cond-mat.stat-mech↗

arXiv2025

Wavelet Scattering Transform and Fourier Representation for Offline Detection of Malicious Clients in Federated Learning

Federated Learning (FL) enables the training of machine learning models across decentralized clients while preserving data privacy. However, the presence of anomalous or corrupted clients - such as those with faulty sensors or non representative data distributions - can significantly degrade model performance. Detecting such clients without accessing raw data remains a key challenge. We propose WAFFLE (Wavelet and Fourier representations for Federated Learning) a detection algorithm that labels malicious clients {\it before training}, using locally computed compressed representations derived from either the Wavelet Scattering Transform (WST) or the Fourier Transform. Both approaches provide low-dimensional, task-agnostic embeddings suitable for unsupervised client separation. A lightweight detector, trained on a distillated public dataset, performs the labeling with minimal communication and computational overhead. While both transforms enable effective detection, WST offers theoretical advantages, such as non-invertibility and stability to local deformations, that make it particularly well-suited to federated scenarios. Experiments on benchmark datasets show that our method improves detection accuracy and downstream classification performance compared to existing FL anomaly detection algorithms, validating its effectiveness as a pre-training alternative to online detection strategies.

cs.LG↗

arXiv2025

Jarzynski Reweighting and Sampling Dynamics for Training Energy-Based Models: Theoretical Analysis of Different Transition Kernels

Energy-Based Models (EBMs) provide a flexible framework for generative modeling, but their training remains theoretically challenging due to the need to approximate normalization constants and efficiently sample from complex, multi-modal distributions. Traditional methods, such as contrastive divergence and score matching, introduce biases that can hinder accurate learning. In this work, we present a theoretical analysis of Jarzynski reweighting, a technique from non-equilibrium statistical mechanics, and its implications for training EBMs. We focus on the role of the choice of the kernel and we illustrate these theoretical considerations in two key generative frameworks: (i) flow-based diffusion models, where we reinterpret Jarzynski reweighting in the context of stochastic interpolants to mitigate discretization errors and improve sample quality, and (ii) Restricted Boltzmann Machines, where we analyze its role in correcting the biases of contrastive divergence. Our results provide insights into the interplay between kernel choice and model performance, highlighting the potential of Jarzynski reweighting as a principled tool for generative learning.

cs.LG↗

arXiv2025

Learning Latent Variable Models via Jarzynski-adjusted Langevin Algorithm

We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging Jarzynski's equality and developing algorithms based on a weighted version of the unadjusted Langevin algorithm (ULA) with recursively updated weights. Adapting this for latent variable models, we develop a sequential Monte Carlo (SMC) method that provides the maximum marginal likelihood estimate of the parameters, termed JALA-EM. Under suitable regularity assumptions on the marginal likelihood, we provide a nonasymptotic analysis of the JALA-EM scheme implemented with stochastic gradient descent and show that it provably converges to the maximum marginal likelihood estimate. We demonstrate the performance of JALA-EM on a variety of latent variable models and show that it performs comparably to existing methods in terms of accuracy and computational efficiency. Importantly, the ability to recursively estimate marginal likelihoods - an uncommon feature among scalable methods - makes our approach particularly suited for model selection, which we validate through dedicated experiments.

stat.CO↗

arXiv2024

Wavelet Scattering Transform for Gravitational Waves Analysis. An Application to Glitch Characterization

Gravitational waves, first predicted by Albert Einstein within the framework of general relativity, were confirmed in 2015 by the LIGO/Virgo collaboration, marking a pivotal breakthrough in astrophysics. Despite this achievement, a key challenge remains in distinguishing true gravitational wave signals from noise artifacts, or "glitches," which can distort data and affect the quality of observations. Current state-of-the-art methods, such as the Q-transform, are widely used for signal processing, but face limitations when addressing certain types of signals. In this study, we investigate the Wavelet Scattering Transform (WST), a recent signal analysis method, as a complementary approach. Theoretical motivation for WST arises from its stability under signal deformations and its equivariance properties, which make it particularly suited for the complex nature of gravitational wave data. Our experiments on the LIGO O1a dataset show that WST simplifies classification tasks and enables the use of more efficient architectures compared to traditional methods. Furthermore, we explore the potential benefits of integrating WST with the Q-transform, demonstrating that ensemble methods exploiting both techniques can capture complementary features of the signal and improve overall performance. This work contributes to advancing machine learning applications in gravitational wave analysis, introducing refined preprocessing techniques that improve signal detection and classification.

gr-qc↗

arXiv2024

Hitchhiker's guide on the relation of Energy-Based Models with other generative models, sampling and statistical physics: a comprehensive review

Energy-Based Models have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a comprehensive understanding of EBMs, delineating their connection to other generative models such as Generative Adversarial Networks, Variational Autoencoders, and Normalizing Flows. We explore the sampling techniques crucial for EBMs, including Markov Chain Monte Carlo (MCMC) methods, and draw parallels between EBM concepts and statistical mechanics, highlighting the significance of energy functions and partition functions. Furthermore, we delve into recent training methodologies for EBMs, covering recent advancements and their implications for enhanced model performance and efficiency. This review is designed to clarify the often complex interconnections between these models, which can be challenging due to the diverse communities working on the topic.

cs.LG↗

arXiv2024

WhaleNet: a Novel Deep Learning Architecture for Marine Mammals Vocalizations on Watkins Marine Mammal Sound Database

Marine mammal communication is a complex field, hindered by the diversity of vocalizations and environmental factors. The Watkins Marine Mammal Sound Database (WMMD) constitutes a comprehensive labeled dataset employed in machine learning applications. Nevertheless, the methodologies for data preparation, preprocessing, and classification documented in the literature exhibit considerable variability and are typically not applied to the dataset in its entirety. This study initially undertakes a concise review of the state-of-the-art benchmarks pertaining to the dataset, with a particular focus on clarifying data preparation and preprocessing techniques. Subsequently, we explore the utilization of the Wavelet Scattering Transform (WST) and Mel spectrogram as preprocessing mechanisms for feature extraction. In this paper, we introduce \textbf{WhaleNet} (Wavelet Highly Adaptive Learning Ensemble Network), a sophisticated deep ensemble architecture for the classification of marine mammal vocalizations, leveraging both WST and Mel spectrogram for enhanced feature discrimination. By integrating the insights derived from WST and Mel representations, we achieved an improvement in classification accuracy by $8-10\%$ over existing architectures, corresponding to a classification accuracy of $97.61\%$.

eess.SP↗

arXiv2023

Efficient Training of Energy-Based Models Using Jarzynski Equality

Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is however challenging because the computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality together with tools from sequential Monte-Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA) in which each walker acquires a weight that enables the estimation of the gradient of the cross-entropy at any step during GD, thereby bypassing sampling biases induced by slow mixing of ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST dataset. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.

cs.LG↗

arXiv2021

Time Reversal Symmetry for Classical, Nonrelativistic Quantum and Spin Systems in Presence of Magnetic Fields

We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are nonrelativistic, and are described by the Schr{\"o}dinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases.

quant-ph↗

arXiv2020

Necessary and sufficient conditions for time reversal symmetry in presence of magnetic fields

Time reversal invariance (TRI) of particles systems has many consequences, among~which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the~strict traditional notion of reversibility that led to Casimir's work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We~first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.

cond-mat.stat-mech↗