arXiv subjects

Guillaume Charpiat

Publications and source records attributed to Guillaume Charpiat.

At least 19 recordsLinked to original sources

arXiv2026

PRIVET: PRoximIty leakage detection Via Extreme value Theory

Deep generative models are often trained on sensitive data, such as genetic sequences, health data, or more broadly, any copyrighted, licensed or protected content. This raises critical concerns around privacy-preserving synthetic data, and more specifically around privacy leakage, an issue closely tied to overfitting. Existing proximity-based methods mostly assess privacy risk through global criteria, which quantify a model's overall behaviour but cannot attribute risk to an individual record. Sample-level outputs do exist but they are either uncalibrated, discontinuous, or blind to leakage occurring while the model is globally underfit, which limits their practical use. Using extreme value statistics on nearest-neighbor distances, we propose PRIVET, a generic sample-based, modality-agnostic algorithm that assigns an individual proximity leak score to each synthetic sample. These are evaluated under a chosen representation and distance, each synthetic sample being assigned a continuous score measuring how improbable its proximity to the training set is under a no-leakage model. We empirically demonstrate that PRIVET detects memorization and more subtle forms of proximity-based data leakage across diverse data modalities, including settings with very high dimensionality and limited sample sizes such as genetic data, and in underfitting regimes that overfitting-based diagnostics cannot reach by construction. Our analysis further shows that the representation bounds what any distance-based evaluation can detect, existing computer vision embeddings failing to yield perceptually meaningful distances for near-duplicate samples. Accordingly, a low score is evidence of leakage in the chosen metric, while its absence is not a certificate of privacy.

cs.LG↗

arXiv2026

Turbulent pair dispersion with Stochastic Generative Diffusion Models

Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of Lagrangian velocity trajectories, enabling a fully data-driven representation of turbulent pair dispersion, a long-standing fundamental problem with broad relevance in fluid dynamics. We demonstrate that diffusion models accurately reproduce the evolution of particle-pair separation, including deviations from Richardson's classical scaling law, while simultaneously preserving all key single-particle statistical properties reported in previous studies. These findings underscore the potential of diffusion-based generative models to emulate high-dimensional, multi-scale turbulent dynamics, further establishing them as a powerful tool for scientific modeling and for future geophysical and astrophysical applications.

physics.flu-dyn↗

arXiv2026

Neural delay differential equations: learning non-Markovian closures for partially known dynamical systems

Recent advances in learning dynamical systems from data have shown significant promise. However, many existing methods assume access to the full state of the system -- an assumption that is rarely satisfied in practice, where systems are typically monitored through a limited number of sensors, leading to partial observability. To address this challenge, we draw inspiration from the Mori-Zwanzig formalism, which provides a theoretical connection between hidden variables and memory terms. Motivated by this perspective, we introduce a constant-lag Neural Delay Differential Equations (NDDEs) framework, providing a continuous-time approach for learning non-Markovian dynamics directly from data. These memory effects are captured using a finite set of time delays, which are identified via the adjoint method. We validate the proposed approach on a range of datasets, including synthetic systems, chaotic dynamics, and experimental measurements, such as the Kuramoto-Sivashinsky equation and cavity-flow experiments. Results demonstrate that NDDEs compare favourably with existing approaches for partially observed systems, including long short-term memory (LSTM) networks and augmented neural ordinary differential equations (ANODEs). Overall, NDDEs offer a principled and data-efficient framework for modelling non-Markovian dynamics under partial observability. An open-source implementation accompanies this article.

cs.LG↗

arXiv2025

Growth strategies for arbitrary DAG neural architectures

Deep learning has shown impressive results obtained at the cost of training huge neural networks. However, the larger the architecture, the higher the computational, financial, and environmental costs during training and inference. We aim at reducing both training and inference durations. We focus on Neural Architecture Growth, which can increase the size of a small model when needed, directly during training using information from the backpropagation. We expand existing work and freely grow neural networks in the form of any Directed Acyclic Graph by reducing expressivity bottlenecks in the architecture. We explore strategies to reduce excessive computations and steer network growth toward more parameter-efficient architectures.

cs.LG↗

arXiv2024

Growing Tiny Networks: Spotting Expressivity Bottlenecks and Fixing Them Optimally

Machine learning tasks are generally formulated as optimization problems, where one searches for an optimal function within a certain functional space. In practice, parameterized functional spaces are considered, in order to be able to perform gradient descent. Typically, a neural network architecture is chosen and fixed, and its parameters (connection weights) are optimized, yielding an architecture-dependent result. This way of proceeding however forces the evolution of the function during training to lie within the realm of what is expressible with the chosen architecture, and prevents any optimization across architectures. Costly architectural hyper-parameter optimization is often performed to compensate for this. Instead, we propose to adapt the architecture on the fly during training. We show that the information about desirable architectural changes, due to expressivity bottlenecks when attempting to follow the functional gradient, can be extracted from backpropagation. To do this, we propose a mathematical definition of expressivity bottlenecks, which enables us to detect, quantify and solve them while training, by adding suitable neurons. Thus, while the standard approach requires large networks, in terms of number of neurons per layer, for expressivity and optimization reasons, we provide tools and properties to develop an architecture starting with a very small number of neurons. As a proof of concept, we show results~on the CIFAR dataset, matching large neural network accuracy, with competitive training time, while removing the need for standard architectural hyper-parameter search.

cs.AI↗

arXiv2024

Time and State Dependent Neural Delay Differential Equations

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard Ordinary Differential Equations (ODE), or data-driven approximations such as Neural Ordinary Differential Equations (NODE). To circumvent this issue, latent variables are typically introduced to solve the dynamics of the system in a higher dimensional space and obtain the solution as a projection to the original space. However, this solution lacks physical interpretability. In contrast, Delay Differential Equations (DDEs), and their data-driven approximated counterparts, naturally appear as good candidates to characterize such systems. In this work we revisit the recently proposed Neural DDE by introducing Neural State-Dependent DDE (SDDDE), a general and flexible framework that can model multiple and state- and time-dependent delays. We show that our method is competitive and outperforms other continuous-class models on a wide variety of delayed dynamical systems. Code is available at the repository \href{https://github.com/thibmonsel/Time-and-State-Dependent-Neural-Delay-Differential-Equations}{here}.

cs.AI↗

arXiv2024

Rotation-equivariant Graph Neural Networks for Learning Glassy Liquids Representations

The difficult problem of relating the static structure of glassy liquids and their dynamics is a good target for Machine Learning, an approach which excels at finding complex patterns hidden in data. Indeed, this approach is currently a hot topic in the glassy liquids community, where the state of the art consists in Graph Neural Networks (GNNs), which have great expressive power but are heavy models and lack interpretability. Inspired by recent advances in the field of Machine Learning group-equivariant representations, we build a GNN that learns a robust representation of the glass' static structure by constraining it to preserve the roto-translation (SE(3)) equivariance. We show that this constraint significantly improves the predictive power at comparable or reduced number of parameters but most importantly, improves the ability to generalize to unseen temperatures. While remaining a Deep network, our model has improved interpretability compared to other GNNs, as the action of our basic convolution layer relates directly to well-known rotation-invariant expert features. Through transfer-learning experiments displaying unprecedented performance, we demonstrate that our network learns a robust representation, which allows us to push forward the idea of a learned structural order parameter for glasses.

cond-mat.soft↗

arXiv2024

An Implicit GNN Solver for Poisson-like problems

This paper presents $Ψ$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $Ψ$-GNN models an "infinitely" deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical prerequisite for physical applications, and is able to adapt to any initially provided solution. $Ψ$-GNN is trained using a "physics-informed" loss, and the training process is stable by design, and insensitive to its initialization. Furthermore, the consistency of the approach is theoretically proven, and its flexibility and generalization efficiency are experimentally demonstrated: the same learned model can accurately handle unstructured meshes of various sizes, as well as different boundary conditions. To the best of our knowledge, $Ψ$-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.

cs.LG↗

arXiv2024

Multi-Level GNN Preconditioner for Solving Large Scale Problems

Large-scale numerical simulations often come at the expense of daunting computations. High-Performance Computing has enhanced the process, but adapting legacy codes to leverage parallel GPU computations remains challenging. Meanwhile, Machine Learning models can harness GPU computations effectively but often struggle with generalization and accuracy. Graph Neural Networks (GNNs), in particular, are great for learning from unstructured data like meshes but are often limited to small-scale problems. Moreover, the capabilities of the trained model usually restrict the accuracy of the data-driven solution. To benefit from both worlds, this paper introduces a novel preconditioner integrating a GNN model within a multi-level Domain Decomposition framework. The proposed GNN-based preconditioner is used to enhance the efficiency of a Krylov method, resulting in a hybrid solver that can converge with any desired level of accuracy. The efficiency of the Krylov method greatly benefits from the GNN preconditioner, which is adaptable to meshes of any size and shape, is executed on GPUs, and features a multi-level approach to enforce the scalability of the entire process. Several experiments are conducted to validate the numerical behavior of the hybrid solver, and an in-depth analysis of its performance is proposed to assess its competitiveness against a C++ legacy solver.

cs.LG↗

arXiv2024

An Equivalence between Bayesian Priors and Penalties in Variational Inference

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contains a Kullback--Leibler divergence term between the approximate posterior and a Bayesian prior. We fully characterize the regularizers that can arise according to this procedure, and provide a systematic way to compute the prior corresponding to a given penalty. Such a characterization can be used to discover constraints over the penalty function, so that the overall procedure remains Bayesian.

cs.LG↗

arXiv2023

Designing losses for data-free training of normalizing flows on Boltzmann distributions

Generating a Boltzmann distribution in high dimension has recently been achieved with Normalizing Flows, which enable fast and exact computation of the generated density, and thus unbiased estimation of expectations. However, current implementations rely on accurate training data, which typically comes from computationally expensive simulations. There is therefore a clear incentive to train models with incomplete or no data by relying solely on the target density, which can be obtained from a physical energy model (up to a constant factor). For that purpose, we analyze the properties of standard losses based on Kullback-Leibler divergences. We showcase their limitations, in particular a strong propensity for mode collapse during optimization on high-dimensional distributions. We then propose strategies to alleviate these issues, most importantly a new loss function well-grounded in theory and with suitable optimization properties. Using as a benchmark the generation of 3D molecular configurations, we show on several tasks that, for the first time, imperfect pre-trained models can be further optimized in the absence of training data.

cs.LG↗

arXiv2022

DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)

This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing boundary conditions by design. By directly minimizing the residual of the Poisson equation, the model attempts to learn the physics of the problem without the need for exact solutions, in contrast to most previous data-driven processes where the distance with the available solutions is minimized.

cs.LG↗

arXiv2022

Docent: A content-based recommendation system to discover contemporary art

Recommendation systems have been widely used in various domains such as music, films, e-shopping etc. After mostly avoiding digitization, the art world has recently reached a technological turning point due to the pandemic, making online sales grow significantly as well as providing quantitative online data about artists and artworks. In this work, we present a content-based recommendation system on contemporary art relying on images of artworks and contextual metadata of artists. We gathered and annotated artworks with advanced and art-specific information to create a completely unique database that was used to train our models. With this information, we built a proximity graph between artworks. Similarly, we used NLP techniques to characterize the practices of the artists and we extracted information from exhibitions and other event history to create a proximity graph between artists. The power of graph analysis enables us to provide an artwork recommendation system based on a combination of visual and contextual information from artworks and artists. After an assessment by a team of art specialists, we get an average final rating of 75% of meaningful artworks when compared to their professional evaluations.

cs.LG↗

arXiv2022

Machine Learning model for gas-liquid interface reconstruction in CFD numerical simulations

The volume of fluid (VoF) method is widely used in multi-phase flow simulations to track and locate the interface between two immiscible fluids. A major bottleneck of the VoF method is the interface reconstruction step due to its high computational cost and low accuracy on unstructured grids. We propose a machine learning enhanced VoF method based on Graph Neural Networks (GNN) to accelerate the interface reconstruction on general unstructured meshes. We first develop a methodology to generate a synthetic dataset based on paraboloid surfaces discretized on unstructured meshes. We then train a GNN based model and perform generalization tests. Our results demonstrate the efficiency of a GNN based approach for interface reconstruction in multi-phase flow simulations in the industrial context.

physics.flu-dyn↗

arXiv2021

DISCO Verification: Division of Input Space into COnvex polytopes for neural network verification

The impressive results of modern neural networks partly come from their non linear behaviour. Unfortunately, this property makes it very difficult to apply formal verification tools, even if we restrict ourselves to networks with a piecewise linear structure. However, such networks yields subregions that are linear and thus simpler to analyse independently. In this paper, we propose a method to simplify the verification problem by operating a partitionning into multiple linear subproblems. To evaluate the feasibility of such an approach, we perform an empirical analysis of neural networks to estimate the number of linear regions, and compare them to the bounds currently known. We also present the impact of a technique aiming at reducing the number of linear regions during training.

cs.AI↗

arXiv2021

Input Similarity from the Neural Network Perspective

We first exhibit a multimodal image registration task, for which a neural network trained on a dataset with noisy labels reaches almost perfect accuracy, far beyond noise variance. This surprising auto-denoising phenomenon can be explained as a noise averaging effect over the labels of similar input examples. This effect theoretically grows with the number of similar examples; the question is then to define and estimate the similarity of examples. We express a proper definition of similarity, from the neural network perspective, i.e. we quantify how undissociable two inputs $A$ and $B$ are, taking a machine learning viewpoint: how much a parameter variation designed to change the output for $A$ would impact the output for $B$ as well? We study the mathematical properties of this similarity measure, and show how to use it on a trained network to estimate sample density, in low complexity, enabling new types of statistical analysis for neural networks. We analyze data by retrieving samples perceived as similar by the network, and are able to quantify the denoising effect without requiring true labels. We also propose, during training, to enforce that examples known to be similar should also be seen as similar by the network, and notice speed-up training effects for certain datasets.

cs.LG↗

arXiv2020

Tropical Cyclone Track Forecasting using Fused Deep Learning from Aligned Reanalysis Data

The forecast of tropical cyclone trajectories is crucial for the protection of people and property. Although forecast dynamical models can provide high-precision short-term forecasts, they are computationally demanding, and current statistical forecasting models have much room for improvement given that the database of past hurricanes is constantly growing. Machine learning methods, that can capture non-linearities and complex relations, have only been scarcely tested for this application. We propose a neural network model fusing past trajectory data and reanalysis atmospheric images (wind and pressure 3D fields). We use a moving frame of reference that follows the storm center for the 24h tracking forecast. The network is trained to estimate the longitude and latitude displacement of tropical cyclones and depressions from a large database from both hemispheres (more than 3000 storms since 1979, sampled at a 6 hour frequency). The advantage of the fused network is demonstrated and a comparison with current forecast models shows that deep learning methods could provide a valuable and complementary prediction. Moreover, our method can give a forecast for a new storm in a few seconds, which is an important asset for real-time forecasts compared to traditional forecasts.

physics.ao-ph↗

arXiv2019

CAMUS: A Framework to Build Formal Specifications for Deep Perception Systems Using Simulators

The topic of provable deep neural network robustness has raised considerable interest in recent years. Most research has focused on adversarial robustness, which studies the robustness of perceptive models in the neighbourhood of particular samples. However, other works have proved global properties of smaller neural networks. Yet, formally verifying perception remains uncharted. This is due notably to the lack of relevant properties to verify, as the distribution of possible inputs cannot be formally specified. We propose to take advantage of the simulators often used either to train machine learning models or to check them with statistical tests, a growing trend in industry. Our formulation allows us to formally express and verify safety properties on perception units, covering all cases that could ever be generated by the simulator, to the difference of statistical tests which cover only seen examples. Along with this theoretical formulation , we provide a tool to translate deep learning models into standard logical formulae. As a proof of concept, we train a toy example mimicking an autonomous car perceptive unit, and we formally verify that it will never fail to capture the relevant information in the provided inputs.

cs.LG↗