arXiv subjects

Marylou Gabrié

Publications and source records attributed to Marylou Gabrié.

At least 19 recordsLinked to original sources

arXiv2026

Boltzmann generators for amorphous particle systems

Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators address this problem by employing generative models to propose independent configurations, which are then reweighted via importance sampling using exact likelihood evaluations. Recent Boltzmann Generators based on continuous normalizing flows and flow matching have achieved significant success for particle systems and biomolecules. However, these approaches have not been extended to amorphous materials (glasses), for which equilibrium sampling is notoriously slow. Because of their disordered structure, the invariances and geometrical constraints of amorphous materials differ from those of crystals and biomolecules, preventing the direct use of existing generative models. Here, we develop Boltzmann Generators tailored to amorphous materials by building the required equivariances directly into Riemannian stochastic interpolants. Our framework incorporates periodic boundary conditions and particle symmetries using equivariant graph neural networks. Numerical experiments demonstrate that enforcing physical symmetries significantly improves the accuracy of Boltzmann Generators, but also reveal an intrinsic limitation of the continuous-flow formulation: accumulated numerical errors during likelihood integration break time-reversibility, compromising exact thermodynamic reweighting. These results reveal a fundamental challenge for continuous-flow generative models in statistical mechanics and call for alternative approaches that preserve exact thermodynamic consistency.

stat.ML↗

arXiv2026

Weighting Schedules Govern What and When Score-Based Generative Models Learn from Multimodal Data

Score-based generative models generate new samples by integrating a time-dependent drift that carries Gaussian noise onto the target distribution. In practice this drift is modeled by a neural network, trained on a loss integrated over time $t$ with a weighting schedule $w(t)$. Along the backward dynamics, and for multi-modal distributions, trajectories commit to modes of the target within a narrow time window, the \textit{speciation time}. In this work, focusing on high-dimensional data, we decompose the integrated loss into its single-time contributions and analyze each at fixed signal-to-noise ratio $Λ(t)$: we show that $Λ(t)$ sets the rate at which each feature of a multimodal target - the mode directions and their relative weights - is acquired during training. Crucially, at high $Λ(t)$ all mode directions are acquired together, on a single timescale insensitive to their amplitudes, while the relative weights are not learned at all. Only near the speciation time, where $Λ(t)$ becomes of order one, do all features become learnable, each on its own timescale: the weights are acquired jointly with the directions, and the directions at rates set by their relative amplitudes. For models trained on time-integrated objectives, the learning dynamics is then governed by how much of the weighting effectively sits near the speciation time, which provides insights on $w(t)$ design choices. These results follow from an exact high-dimensional analysis of the training dynamics of unbalanced and hierarchical Gaussian mixtures. Numerical experiments on image and human genome haplotype generation recover the predicted hierarchy of learning timescales in more complex settings.

cs.LG↗

arXiv2026

The critical slowing down in training diffusion models

Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior remains poorly understood, with limited theoretical control over when and why they succeed. Here we provide such insight for diffusion models---a class of generative schemes highly effective in practice---by analyzing their application to the $O(n)$ model of statistical field theory in the Gaussian limit $n \to \infty$. In this analytically tractable setting, we show that training a score model with a one-layer network architecture matching the exact solution exhibits a form of critical slowing down in parameter learning. This slowing down also impacts the generation process, indicating that the well-known difficulties of sampling near criticality persist even for learned generative models. To overcome this bottleneck, we consider the power of architectural depth. We find that using a two-layer architecture drastically reduces the critical slowing down, with the training time scaling logarithmically rather than quadratically with system size. Using a Fourier implementation of the architecture, we further show that this acceleration in training time can be achieved without drastically increasing operational complexity. Taken together, these results demonstrate that diffusion models can overcome the critical slowing down through appropriate architectural design, and establish a controlled framework for understanding and improving learned sampling methods in statistical physics and beyond.

cond-mat.dis-nn↗

arXiv2026

Leveraging generative models to assist Monte Carlo sampling

Sampling high-dimensional probability distributions is a central task in scientific computing, with applications ranging from Bayesian inference to statistical physics and molecular simulation. Despite decades of methodological developments, two major challenges remain: scaling to high dimensions and efficiently exploring multimodal distributions characterized by metastable states. Classical approaches such as Markov chain Monte Carlo, tempering methods, or enhanced sampling based on collective variables have achieved major successes, but they also face intrinsic limitations. This tutorial review explores a new paradigm that has recently emerged at the interface of machine learning and computational statistical physics: the use of generative models as tools for sampling. In this context, models such as normalizing flows and diffusion models are not used in their traditional data-driven setting, but rather as flexible probabilistic models that can assist the sampling of distributions known only up to a normalization constant. This manuscript reviews the early development of this rapidly evolving field and discusses several methodological directions, including exact samplers based on generative models and strategies to train such models in the absence of data. While an exhaustive survey of the literature is not attempted, we present a selection of key ideas and methods, along with a discussion of their strengths and limitations. The review is intended to be an accessible tutorial for both physics and machine learning audiences, and it aims to provide a starting point for researchers interested in exploring this exciting area of research.

stat.ML↗

arXiv2026

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↗

arXiv2026

Stochastic Localization via Iterative Posterior Sampling

Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process, and progressively learns a denoiser associated to this dynamics. Apart from specific applications, the use of stochastic localization for the problem of sampling from an unnormalized target density has not been explored extensively. This work contributes to fill this gap. We consider a general stochastic localization framework and introduce an explicit class of observation processes, associated with flexible denoising schedules. We provide a complete methodology, $\textit{Stochastic Localization via Iterative Posterior Sampling}$ (SLIPS), to obtain approximate samples of this dynamics, and as a by-product, samples from the target distribution. Our scheme is based on a Markov chain Monte Carlo estimation of the denoiser and comes with detailed practical guidelines. We illustrate the benefits and applicability of SLIPS on several benchmarks of multi-modal distributions, including Gaussian mixtures in increasing dimensions, Bayesian logistic regression and a high-dimensional field system from statistical-mechanics.

stat.ML↗

arXiv2026

Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixtures

Mode collapse, the failure to capture one or more modes when targetting a multimodal distribution, is a central challenge in modern variational inference. In this work, we provide a mathematical analysis of annealing based strategies for mitigating mode collapse in a tractable setting: learning a Gaussian mixture, where mode collapse is known to arise. Leveraging a low dimensional summary statistics description, we precisely characterize the interplay between the initial temperature and the annealing rate, and derive a sharp formula for the probability of mode collapse. Our analysis shows that an appropriately chosen annealing scheme can robustly prevent mode collapse. Finally, we present numerical evidence that these theoretical tradeoffs qualitatively extend to neural network based models, RealNVP normalizing flows, providing guidance for designing annealing strategies mitigating mode collapse in practical variational inference pipelines.

stat.ML↗

arXiv2025

Modern applications of machine learning in quantum sciences

In this book, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.

quant-ph↗

arXiv2025

Learned Reference-based Diffusion Sampling for multi-modal distributions

Over the past few years, several approaches utilizing score-based diffusion have been proposed to sample from probability distributions, that is without having access to exact samples and relying solely on evaluations of unnormalized densities. The resulting samplers approximate the time-reversal of a noising diffusion process, bridging the target distribution to an easy-to-sample base distribution. In practice, the performance of these methods heavily depends on key hyperparameters that require ground truth samples to be accurately tuned. Our work aims to highlight and address this fundamental issue, focusing in particular on multi-modal distributions, which pose significant challenges for existing sampling methods. Building on existing approaches, we introduce Learned Reference-based Diffusion Sampler (LRDS), a methodology specifically designed to leverage prior knowledge on the location of the target modes in order to bypass the obstacle of hyperparameter tuning. LRDS proceeds in two steps by (i) learning a reference diffusion model on samples located in high-density space regions and tailored for multimodality, and (ii) using this reference model to foster the training of a diffusion-based sampler. We experimentally demonstrate that LRDS best exploits prior knowledge on the target distribution compared to competing algorithms on a variety of challenging distributions.

stat.ML↗

arXiv2025

Improving the evaluation of samplers on multi-modal targets

Addressing multi-modality constitutes one of the major challenges of sampling. In this reflection paper, we advocate for a more systematic evaluation of samplers towards two sources of difficulty that are mode separation and dimension. For this, we propose a synthetic experimental setting that we illustrate on a selection of samplers, focusing on the challenging criterion of recovery of the mode relative importance. These evaluations are crucial to diagnose the potential of samplers to handle multi-modality and therefore to drive progress in the field.

stat.ML↗

arXiv2024

Sampling metastable systems using collective variables and Jarzynski-Crooks paths

We consider the problem of sampling a high dimensional multimodal target probability measure. We assume that a good proposal kernel to move only a subset of the degrees of freedoms (also known as collective variables) is known a priori. This proposal kernel can for example be built using normalizing flows. We show how to extend the move from the collective variable space to the full space and how to implement an accept-reject step in order to get a reversible chain with respect to a target probability measure. The accept-reject step does not require to know the marginal of the original measure in the collective variable (namely to know the free energy). The obtained algorithm admits several variants, some of them being very close to methods which have been proposed previously in the literature. We show how the obtained acceptance ratio can be expressed in terms of the work which appears in the Jarzynski-Crooks equality, at least for some variants. Numerical illustrations demonstrate the efficiency of the approach on various simple test cases, and allow us to compare the variants of the algorithm.

cond-mat.stat-mech↗

arXiv2024

A theoretical perspective on mode collapse in variational inference

While deep learning has expanded the possibilities for highly expressive variational families, the practical benefits of these tools for variational inference (VI) are often limited by the minimization of the traditional Kullback-Leibler objective, which can yield suboptimal solutions. A major challenge in this context is \emph{mode collapse}: the phenomenon where a model concentrates on a few modes of the target distribution during training, despite being statistically capable of expressing them all. In this work, we carry a theoretical investigation of mode collapse for the gradient flow on Gaussian mixture models. We identify the key low-dimensional statistics characterizing the flow, and derive a closed set of low-dimensional equations governing their evolution. Leveraging this compact description, we show that mode collapse is present even in statistically favorable scenarios, and identify two key mechanisms driving it: mean alignment and vanishing weight. Our theoretical findings are consistent with the implementation of VI using normalizing flows, a class of popular generative models, thereby offering practical insights.

stat.ML↗

arXiv2024

Coarse Grained Molecular Dynamics with Normalizing Flows

We propose a sampling algorithm relying on a collective variable (CV) of mid-size dimension modelled by a normalizing flow and using non-equilibrium dynamics to propose full configurational moves from the proposition of a refreshed value of the CV made by the flow. The algorithm takes the form of a Markov chain with non-local updates, allowing jumps through energy barriers across metastable states. The flow is trained throughout the algorithm to reproduce the free energy landscape of the CV. The output of the algorithm are a sample of thermalized configurations and the trained network that can be used to efficiently produce more configurations. We show the functioning of the algorithm first on a test case with a mixture of Gaussians. Then we successfully test it on a higher dimensional system consisting in a polymer in solution with a compact and an extended stable state separated by a high free energy barrier.

cond-mat.stat-mech↗

arXiv2024

Active learning of Boltzmann samplers and potential energies with quantum mechanical accuracy

Extracting consistent statistics between relevant free-energy minima of a molecular system is essential for physics, chemistry and biology. Molecular dynamics (MD) simulations can aid in this task but are computationally expensive, especially for systems that require quantum accuracy. To overcome this challenge, we develop an approach combining enhanced sampling with deep generative models and active learning of a machine learning potential (MLP). We introduce an adaptive Markov chain Monte Carlo framework that enables the training of one Normalizing Flow (NF) and one MLP per state, achieving rapid convergence towards the Boltzmann distribution. Leveraging the trained NF and MLP models, we compute thermodynamic observables such as free-energy differences or optical spectra. We apply this method to study the isomerization of an ultrasmall silver nanocluster, belonging to a set of systems with diverse applications in the fields of medicine and catalysis.

physics.chem-ph↗

arXiv2024

On Sampling with Approximate Transport Maps

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF) which are maps parameterized with deep neural networks trained to push a reference distribution towards a target. NF-enhanced samplers recently proposed blend (Markov chain) Monte Carlo methods with either (i) proposal draws from the flow or (ii) a flow-based reparametrization. In both cases, the quality of the learned transport conditions performance. The present work clarifies for the first time the relative strengths and weaknesses of these two approaches. Our study concludes that multimodal targets can be reliably handled with flow-based proposals up to moderately high dimensions. In contrast, methods relying on reparametrization struggle with multimodality but are more robust otherwise in high-dimensional settings and under poor training. To further illustrate the influence of target-proposal adequacy, we also derive a new quantitative bound for the mixing time of the Independent Metropolis-Hastings sampler.

stat.ML↗

arXiv2024

Balanced Training of Energy-Based Models with Adaptive Flow Sampling

Energy-based models (EBMs) are versatile density estimation models that directly parameterize an unnormalized log density. Although very flexible, EBMs lack a specified normalization constant of the model, making the likelihood of the model computationally intractable. Several approximate samplers and variational inference techniques have been proposed to estimate the likelihood gradients for training. These techniques have shown promising results in generating samples, but little attention has been paid to the statistical accuracy of the estimated density, such as determining the relative importance of different classes in a dataset. In this work, we propose a new maximum likelihood training algorithm for EBMs that uses a different type of generative model, normalizing flows (NF), which have recently been proposed to facilitate sampling. Our method fits an NF to an EBM during training so that an NF-assisted sampling scheme provides an accurate gradient for the EBMs at all times, ultimately leading to a fast sampler for generating new data.

cs.LG↗

arXiv2023

Neural networks: from the perceptron to deep nets

Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming data is generated by a teacher model, asymptotic generalisation predictions were originally derived using the replica method and the online learning dynamics has been described in the large system limit. In this chapter, we review the key original ideas of this literature along with their heritage in the ongoing quest to understand the efficiency of modern deep learning algorithms. One goal of current and future research is to characterize the bias of the learning algorithms toward well-generalising minima in a complex overparametrized loss landscapes with many solutions perfectly interpolating the training data. Works on perceptrons, two-layer committee machines and kernel-like learning machines shed light on these benefits of overparametrization. Another goal is to understand the advantage of depth while models now commonly feature tens or hundreds of layers. If replica computations apparently fall short in describing general deep neural networks learning, studies of simplified linear or untrained models, as well as the derivation of scaling laws provide the first elements of answers.

cond-mat.dis-nn↗

arXiv2022

flowMC: Normalizing-flow enhanced sampling package for probabilistic inference in Jax

flowMC is a Python library for accelerated Markov Chain Monte Carlo (MCMC) leveraging deep generative modeling. It is built on top of the machine learning libraries JAX and Flax. At its core, flowMC uses a local sampler and a learnable global sampler in tandem to efficiently sample posterior distributions. While multiple chains of the local sampler generate samples over the region of interest in the target parameter space, the package uses these samples to train a normalizing flow model, then uses it to propose global jumps across the parameter space. The flowMC sampler can handle non-trivial geometry, such as multimodal distributions and distributions with local correlations. The key features of flowMC are summarized in the following list: * Since flowMC is built on top of JAX, it supports gradient-based samplers through automatic differentiation such as MALA and Hamiltonian Monte Carlo (HMC). * flowMC uses state-of-the-art normalizing flow models such as Rational-Quadratic Splines to power its global sampler. These models are very efficient in capturing important features within a relatively short training time. * Use of accelerators such as GPUs and TPUs are natively supported. The code also supports the use of multiple accelerators with SIMD parallelism. * By default, Just-in-time (JIT) compilations are used to further speed up the sampling process. * We provide a simple black box interface for the users who want to use flowMC by its default parameters, yet provide at the same time an extensive guide explaining trade-offs while tuning the sampler parameters. The tight integration of all the above features makes flowMC a highly performant yet simple- to-use package for statistical inference.

astro-ph.IM↗