arXiv subjects

Alain Rakotomamonjy

Publications and source records attributed to Alain Rakotomamonjy.

At least 19 recordsLinked to original sources

arXiv2025

On the MIA Vulnerability Gap Between Private GANs and Diffusion Models

Generative Adversarial Networks (GANs) and diffusion models have emerged as leading approaches for high-quality image synthesis. While both can be trained under differential privacy (DP) to protect sensitive data, their sensitivity to membership inference attacks (MIAs), a key threat to data confidentiality, remains poorly understood. In this work, we present the first unified theoretical and empirical analysis of the privacy risks faced by differentially private generative models. We begin by showing, through a stability-based analysis, that GANs exhibit fundamentally lower sensitivity to data perturbations than diffusion models, suggesting a structural advantage in resisting MIAs. We then validate this insight with a comprehensive empirical study using a standardized MIA pipeline to evaluate privacy leakage across datasets and privacy budgets. Our results consistently reveal a marked privacy robustness gap in favor of GANs, even in strong DP regimes, highlighting that model type alone can critically shape privacy leakage.

cs.LG↗

arXiv2025

Improving Consistency Models with Generator-Augmented Flows

Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true velocity field of the corresponding differential equation, approximated by a pre-trained neural network. In contrast, the latter uses a single-sample Monte Carlo estimate of this velocity field. The related estimation error induces a discrepancy between consistency distillation and training that, we show, still holds in the continuous-time limit. To alleviate this issue, we propose a novel flow that transports noisy data towards their corresponding outputs derived from a consistency model. We prove that this flow reduces the previously identified discrepancy and the noise-data transport cost. Consequently, our method not only accelerates consistency training convergence but also enhances its overall performance. The code is available at: https://github.com/thibautissenhuth/consistency_GC.

cs.LG↗

arXiv2025

Differentially Private Gradient Flow based on the Sliced Wasserstein Distance

Safeguarding privacy in sensitive training data is paramount, particularly in the context of generative modeling. This can be achieved through either differentially private stochastic gradient descent or a differentially private metric for training models or generators. In this paper, we introduce a novel differentially private generative modeling approach based on a gradient flow in the space of probability measures. To this end, we define the gradient flow of the Gaussian-smoothed Sliced Wasserstein Distance, including the associated stochastic differential equation (SDE). By discretizing and defining a numerical scheme for solving this SDE, we demonstrate the link between smoothing and differential privacy based on a Gaussian mechanism, due to a specific form of the SDE's drift term. We then analyze the differential privacy guarantee of our gradient flow, which accounts for both the smoothing and the Wiener process introduced by the SDE itself. Experiments show that our proposed model can generate higher-fidelity data at a low privacy budget compared to a generator-based model, offering a promising alternative.

stat.ML↗

arXiv2024

Gaussian-Smoothed Sliced Probability Divergences

Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown that it provides performances similar to its non-smoothed (non-private) counterpart. However, the computationaland statistical properties of such a metric have not yet been well-established. This work investigates the theoretical properties of this distance as well as those of generalized versions denoted as Gaussian-smoothed sliced divergences. We first show that smoothing and slicing preserve the metric property and the weak topology. To study the sample complexity of such divergences, we then introduce $\hat{\hatμ}_{n}$ the double empirical distribution for the smoothed-projected $μ$. The distribution $\hat{\hatμ}_{n}$ is a result of a double sampling process: one from sampling according to the origin distribution $μ$ and the second according to the convolution of the projection of $μ$ on the unit sphere and the Gaussian smoothing. We particularly focus on the Gaussian smoothed sliced Wasserstein distance and prove that it converges with a rate $O(n^{-1/2})$. We also derive other properties, including continuity, of different divergences with respect to the smoothing parameter. We support our theoretical findings with empirical studies in the context of privacy-preserving domain adaptation.

cs.LG↗

arXiv2023

Unifying GANs and Score-Based Diffusion as Generative Particle Models

Particle-based deep generative models, such as gradient flows and score-based diffusion models, have recently gained traction thanks to their striking performance. Their principle of displacing particle distributions using differential equations is conventionally seen as opposed to the previously widespread generative adversarial networks (GANs), which involve training a pushforward generator network. In this paper we challenge this interpretation, and propose a novel framework that unifies particle and adversarial generative models by framing generator training as a generalization of particle models. This suggests that a generator is an optional addition to any such generative model. Consequently, integrating a generator into a score-based diffusion model and training a GAN without a generator naturally emerge from our framework. We empirically test the viability of these original models as proofs of concepts of potential applications of our framework.

cs.LG↗

arXiv2023

Federated Wasserstein Distance

We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients whilst a central entity/server orchestrates the computations (again, without having access to the samples). To achieve this feat, we take advantage of the geometric properties of the Wasserstein distance -- in particular, the triangle inequality -- and that of the associated {\em geodesics}: our algorithm, FedWad (for Federated Wasserstein Distance), iteratively approximates the Wasserstein distance by manipulating and exchanging distributions from the space of geodesics in lieu of the input samples. In addition to establishing the convergence properties of FedWad, we provide empirical results on federated coresets and federate optimal transport dataset distance, that we respectively exploit for building a novel federated model and for boosting performance of popular federated learning algorithms.

cs.LG↗

arXiv2023

Adversarial Sample Detection Through Neural Network Transport Dynamics

We propose a detector of adversarial samples that is based on the view of neural networks as discrete dynamic systems. The detector tells clean inputs from abnormal ones by comparing the discrete vector fields they follow through the layers. We also show that regularizing this vector field during training makes the network more regular on the data distribution's support, thus making the activations of clean inputs more distinguishable from those of abnormal ones. Experimentally, we compare our detector favorably to other detectors on seen and unseen attacks, and show that the regularization of the network's dynamics improves the performance of adversarial detectors that use the internal embeddings as inputs, while also improving test accuracy.

cs.LG↗

arXiv2023

Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties -- with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.

stat.ML↗

arXiv2023

Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires using Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this distance to brain-age prediction from MEG data and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.

cs.LG↗

arXiv2023

Continuous PDE Dynamics Forecasting with Implicit Neural Representations

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

cs.LG↗

arXiv2023

Approximating DTW with a convolutional neural network on EEG data

Dynamic Time Wrapping (DTW) is a widely used algorithm for measuring similarities between two time series. It is especially valuable in a wide variety of applications, such as clustering, anomaly detection, classification, or video segmentation, where the time-series have different timescales, are irregularly sampled, or are shifted. However, it is not prone to be considered as a loss function in an end-to-end learning framework because of its non-differentiability and its quadratic temporal complexity. While differentiable variants of DTW have been introduced by the community, they still present some drawbacks: computing the distance is still expensive and this similarity tends to blur some differences in the time-series. In this paper, we propose a fast and differentiable approximation of DTW by comparing two architectures: the first one for learning an embedding in which the Euclidean distance mimics the DTW, and the second one for directly predicting the DTW output using regression. We build the former by training a siamese neural network to regress the DTW value between two time-series. Depending on the nature of the activation function, this approximation naturally supports differentiation, and it is efficient to compute. We show, in a time-series retrieval context on EEG datasets, that our methods achieve at least the same level of accuracy as other DTW main approximations with higher computational efficiency. We also show that it can be used to learn in an end-to-end setting on long time series by proposing generative models of EEGs.

cs.LG↗

arXiv2023

Diverse Weight Averaging for Out-of-Distribution Generalization

Standard neural networks struggle to generalize under distribution shifts in computer vision. Fortunately, combining multiple networks can consistently improve out-of-distribution generalization. In particular, weight averaging (WA) strategies were shown to perform best on the competitive DomainBed benchmark; they directly average the weights of multiple networks despite their nonlinearities. In this paper, we propose Diverse Weight Averaging (DiWA), a new WA strategy whose main motivation is to increase the functional diversity across averaged models. To this end, DiWA averages weights obtained from several independent training runs: indeed, models obtained from different runs are more diverse than those collected along a single run thanks to differences in hyperparameters and training procedures. We motivate the need for diversity by a new bias-variance-covariance-locality decomposition of the expected error, exploiting similarities between WA and standard functional ensembling. Moreover, this decomposition highlights that WA succeeds when the variance term dominates, which we show occurs when the marginal distribution changes at test time. Experimentally, DiWA consistently improves the state of the art on DomainBed without inference overhead.

cs.CV↗

arXiv2023

Personalised Federated Learning On Heterogeneous Feature Spaces

Most personalised federated learning (FL) approaches assume that raw data of all clients are defined in a common subspace i.e. all clients store their data according to the same schema. For real-world applications, this assumption is restrictive as clients, having their own systems to collect and then store data, may use heterogeneous data representations. We aim at filling this gap. To this end, we propose a general framework coined FLIC that maps client's data onto a common feature space via local embedding functions. The common feature space is learnt in a federated manner using Wasserstein barycenters while the local embedding functions are trained on each client via distribution alignment. We integrate this distribution alignement mechanism into a federated learning approach and provide the algorithmics of FLIC. We compare its performances against FL benchmarks involving heterogeneous input features spaces. In addition, we provide theoretical insights supporting the relevance of our methodology.

cs.LG↗

arXiv2022

Benchopt: Reproducible, efficient and collaborative optimization benchmarks

Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automate, reproduce and publish optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard learning tasks: $\ell_2$-regularized logistic regression, Lasso, and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of the state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details. We hope that Benchopt will foster collaborative work in the community hence improving the reproducibility of research findings.

cs.LG↗

arXiv2022

Generalizing to New Physical Systems via Context-Informed Dynamics Model

Data-driven approaches to modeling physical systems fail to generalize to unseen systems that share the same general dynamics with the learning domain, but correspond to different physical contexts. We propose a new framework for this key problem, context-informed dynamics adaptation (CoDA), which takes into account the distributional shift across systems for fast and efficient adaptation to new dynamics. CoDA leverages multiple environments, each associated to a different dynamic, and learns to condition the dynamics model on contextual parameters, specific to each environment. The conditioning is performed via a hypernetwork, learned jointly with a context vector from observed data. The proposed formulation constrains the search hypothesis space to foster fast adaptation and better generalization across environments. We theoretically motivate our approach and show state-of-the-art generalization results on a set of nonlinear dynamics, representative of a variety of application domains. We also show, on these systems, that new system parameters can be inferred from context vectors with minimal supervision. Code is available at https://github.com/yuan-yin/CoDA .

cs.LG↗

arXiv2022

Multi-source Domain Adaptation via Weighted Joint Distributions Optimal Transport

The problem of domain adaptation on an unlabeled target dataset using knowledge from multiple labelled source datasets is becoming increasingly important. A key challenge is to design an approach that overcomes the covariate and target shift both among the sources, and between the source and target domains. In this paper, we address this problem from a new perspective: instead of looking for a latent representation invariant between source and target domains, we exploit the diversity of source distributions by tuning their weights to the target task at hand. Our method, named Weighted Joint Distribution Optimal Transport (WJDOT), aims at finding simultaneously an Optimal Transport-based alignment between the source and target distributions and a re-weighting of the sources distributions. We discuss the theoretical aspects of the method and propose a conceptually simple algorithm. Numerical experiments indicate that the proposed method achieves state-of-the-art performance on simulated and real-life datasets.

cs.LG↗

arXiv2022

Photonic Differential Privacy with Direct Feedback Alignment

Optical Processing Units (OPUs) -- low-power photonic chips dedicated to large scale random projections -- have been used in previous work to train deep neural networks using Direct Feedback Alignment (DFA), an effective alternative to backpropagation. Here, we demonstrate how to leverage the intrinsic noise of optical random projections to build a differentially private DFA mechanism, making OPUs a solution of choice to provide a private-by-design training. We provide a theoretical analysis of our adaptive privacy mechanism, carefully measuring how the noise of optical random projections propagates in the process and gives rise to provable Differential Privacy. Finally, we conduct experiments demonstrating the ability of our learning procedure to achieve solid end-task performance.

cs.LG↗

arXiv2022

Mapping conditional distributions for domain adaptation under generalized target shift

We consider the problem of unsupervised domain adaptation (UDA) between a source and a target domain under conditional and label shift a.k.a Generalized Target Shift (GeTarS). Unlike simpler UDA settings, few works have addressed this challenging problem. Recent approaches learn domain-invariant representations, yet they have practical limitations and rely on strong assumptions that may not hold in practice. In this paper, we explore a novel and general approach to align pretrained representations, which circumvents existing drawbacks. Instead of constraining representation invariance, it learns an optimal transport map, implemented as a NN, which maps source representations onto target ones. Our approach is flexible and scalable, it preserves the problem's structure and it has strong theoretical guarantees under mild assumptions. In particular, our solution is unique, matches conditional distributions across domains, recovers target proportions and explicitly controls the target generalization risk. Through an exhaustive comparison on several datasets, we challenge the state-of-the-art in GeTarS.

cs.LG↗