Jean-Yves Franceschi

Yuan Yin, Matthieu Kirchmeyer, Jean-Yves Franceschi et al.

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.

Antoine Schnepf, Karim Kassab, Jean-Yves Franceschi et al.

While pre-trained image autoencoders are increasingly utilized in computer vision, the application of inverse graphics in 2D latent spaces has been under-explored. Yet, besides reducing the training and rendering complexity, applying inverse graphics in the latent space enables a valuable interoperability with other latent-based 2D methods. The major challenge is that inverse graphics cannot be directly applied to such image latent spaces because they lack an underlying 3D geometry. In this paper, we propose an Inverse Graphics Autoencoder (IG-AE) that specifically addresses this issue. To this end, we regularize an image autoencoder with 3D-geometry by aligning its latent space with jointly trained latent 3D scenes. We utilize the trained IG-AE to bring NeRFs to the latent space with a latent NeRF training pipeline, which we implement in an open-source extension of the Nerfstudio framework, thereby unlocking latent scene learning for its supported methods. We experimentally confirm that Latent NeRFs trained with IG-AE present an improved quality compared to a standard autoencoder, all while exhibiting training and rendering accelerations with respect to NeRFs trained in the image space. Our project page can be found at https://ig-ae.github.io .

Thibaut Issenhuth, Sangchul Lee, Ludovic Dos Santos et al.

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.

Karim Kassab, Antoine Schnepf, Jean-Yves Franceschi et al.

To learn large sets of scenes, Tri-Planes are commonly employed for their planar structure that enables an interoperability with image models, and thus diverse 3D applications. However, this advantage comes at the cost of resource efficiency, as Tri-Planes are not the most computationally efficient option. In this paper, we introduce Fused-Planes, a new planar architecture that improves Tri-Planes resource-efficiency in the framework of learning large sets of scenes, which we call "multi-scene inverse graphics". To learn a large set of scenes, our method divides it into two subsets and operates as follows: (i) we train the first subset of scenes jointly with a compression model, (ii) we use that compression model to learn the remaining scenes. This compression model consists of a 3D-aware latent space in which Fused-Planes are learned, enabling a reduced rendering resolution, and shared structures across scenes that reduce scene representation complexity. Fused-Planes present competitive resource costs in multi-scene inverse graphics, while preserving Tri-Planes rendering quality, and maintaining their widely favored planar structure. Our codebase is publicly available as open-source. Our project page can be found at https://fused-planes.github.io .

Ilana Sebag, Muni Sreenivas Pydi, Jean-Yves Franceschi et al.

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.

Ilana Sebag, Jean-Yves Franceschi, Alain Rakotomamonjy et al.

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.

Antoine Schnepf, Karim Kassab, Jean-Yves Franceschi et al.

We present a method enabling the scaling of NeRFs to learn a large number of semantically-similar scenes. We combine two techniques to improve the required training time and memory cost per scene. First, we learn a 3D-aware latent space in which we train Tri-Plane scene representations, hence reducing the resolution at which scenes are learned. Moreover, we present a way to share common information across scenes, hence allowing for a reduction of model complexity to learn a particular scene. Our method reduces effective per-scene memory costs by 44% and per-scene time costs by 86% when training 1000 scenes. Our project page can be found at https://3da-ae.github.io .

Jean-Yves Franceschi, Mike Gartrell, Ludovic Dos Santos et al.

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.

Jean-Yves Franceschi, Emmanuel de Bézenac, Ibrahim Ayed et al.

We propose a novel theoretical framework of analysis for Generative Adversarial Networks (GANs). We reveal a fundamental flaw of previous analyses which, by incorrectly modeling GANs' training scheme, are subject to ill-defined discriminator gradients. We overcome this issue which impedes a principled study of GAN training, solving it within our framework by taking into account the discriminator's architecture. To this end, we leverage the theory of infinite-width neural networks for the discriminator via its Neural Tangent Kernel. We characterize the trained discriminator for a wide range of losses and establish general differentiability properties of the network. From this, we derive new insights about the convergence of the generated distribution, advancing our understanding of GANs' training dynamics. We empirically corroborate these results via an analysis toolkit based on our framework, unveiling intuitions that are consistent with GAN practice.

Jérémie Donà, Jean-Yves Franceschi, Sylvain Lamprier et al.

A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose in this article a novel and general paradigm for this task based on a resolution method for partial differential equations: the separation of variables. This inspiration allows us to introduce a dynamical interpretation of spatiotemporal disentanglement. It induces a principled model based on learning disentangled spatial and temporal representations of a phenomenon to accurately predict future observations. We experimentally demonstrate the performance and broad applicability of our method against prior state-of-the-art models on physical and synthetic video datasets.

Jean-Yves Franceschi, Edouard Delasalles, Mickaël Chen et al.

Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and applicability issues. An alternative is to use fully latent temporal models which untie frame synthesis and temporal dynamics. However, no such model for stochastic video prediction has been proposed in the literature yet, due to design and training difficulties. In this paper, we overcome these difficulties by introducing a novel stochastic temporal model whose dynamics are governed in a latent space by a residual update rule. This first-order scheme is motivated by discretization schemes of differential equations. It naturally models video dynamics as it allows our simpler, more interpretable, latent model to outperform prior state-of-the-art methods on challenging datasets.

Jean-Yves Franceschi, Aymeric Dieuleveut, Martin Jaggi

Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn universal embeddings of time series. Unlike previous works, it is scalable with respect to their length and we demonstrate the quality, transferability and practicability of the learned representations with thorough experiments and comparisons. To this end, we combine an encoder based on causal dilated convolutions with a novel triplet loss employing time-based negative sampling, obtaining general-purpose representations for variable length and multivariate time series.

Jean-Yves Franceschi, Alhussein Fawzi, Omar Fawzi

We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell\_p$ ball for $p \in [1, \infty]$ and Gaussian noise with an arbitrary covariance matrix. We characterize this robustness to random noise in terms of the distance to the decision boundary of the classifier. This analysis applies to linear classifiers as well as classifiers with locally approximately flat decision boundaries, a condition which is satisfied by state-of-the-art deep neural networks. The predicted robustness is verified experimentally.