arXiv subjects

Thomas Kerdreux

Publications and source records attributed to Thomas Kerdreux.

At least 19 recordsLinked to original sources

arXiv2026

OceanSAR-2: A Universal Feature Extractor for SAR Ocean Observation

We present OceanSAR-2, the second generation of our foundation model for SAR-based ocean observation. Building on our earlier release, which pioneered self-supervised learning on Sentinel-1 Wave Mode data, OceanSAR-2 relies on improved SSL training and dynamic data curation strategies, which enhances performance while reducing training cost. OceanSAR-2 demonstrates strong transfer performance across downstream tasks, including geophysical pattern classification, ocean surface wind vector and significant wave height estimation, and iceberg detection. We release standardized benchmark datasets, providing a foundation for systematic evaluation and advancement of SAR models for ocean applications.

cs.LG↗

arXiv2025

Efficient Self-Supervised Learning for Earth Observation via Dynamic Dataset Curation

Self-supervised learning (SSL) has enabled the development of vision foundation models for Earth Observation (EO), demonstrating strong transferability across diverse remote sensing tasks. While prior work has focused on network architectures and training strategies, the role of dataset curation, especially in balancing and diversifying pre-training datasets, remains underexplored. In EO, this challenge is amplified by the redundancy and heavy-tailed distributions common in satellite imagery, which can lead to biased representations and inefficient training. In this work, we propose a dynamic dataset pruning strategy designed to improve SSL pre-training by maximizing dataset diversity and balance. Our method iteratively refines the training set without requiring a pre-existing feature extractor, making it well-suited for domains where curated datasets are limited or unavailable. We demonstrate our approach on the Sentinel-1 Wave Mode (WV) Synthetic Aperture Radar (SAR) archive, a challenging dataset dominated by ocean observations. We train models from scratch on the entire Sentinel-1 WV archive spanning 10 years. Across three downstream tasks, our results show that dynamic pruning improves both computational efficiency and representation quality, leading to stronger transferability. We also release the weights of OceanSAR-1, the first model in the OceanSAR family, a series of foundation models for ocean observation and analysis using SAR imagery, at github.com/galeio-research/OceanSAR-models/.

cs.CV↗

arXiv2024

Strong Convexity of Sets in Riemannian Manifolds

Curvature properties of convex objects, such as strong convexity, are important in designing and analyzing convex optimization algorithms in the Hilbertian or Riemannian settings. In the case of the Hilbertian setting, strongly convex sets are well studied. Herein, we propose various definitions of strong convexity for uniquely geodesic sets in a Riemannian manifold. We study their relationship, propose tools to determine the geodesic strongly convex nature of sets, and analyze the convergence of optimization algorithms over those sets. In particular, we demonstrate that the Riemannian Frank-Wolfe algorithm enjoys a global linear convergence rate when the Riemannian scaling inequalities hold.

math.OC↗

arXiv2023

Diffusion Models for Interferometric Satellite Aperture Radar

Probabilistic Diffusion Models (PDMs) have recently emerged as a very promising class of generative models, achieving high performance in natural image generation. However, their performance relative to non-natural images, like radar-based satellite data, remains largely unknown. Generating large amounts of synthetic (and especially labelled) satellite data is crucial to implement deep-learning approaches for the processing and analysis of (interferometric) satellite aperture radar data. Here, we leverage PDMs to generate several radar-based satellite image datasets. We show that PDMs succeed in generating images with complex and realistic structures, but that sampling time remains an issue. Indeed, accelerated sampling strategies, which work well on simple image datasets like MNIST, fail on our radar datasets. We provide a simple and versatile open-source https://github.com/thomaskerdreux/PDM_SAR_InSAR_generation to train, sample and evaluate PDMs using any dataset on a single GPU.

cs.CV↗

arXiv2023

Acceleration of Frank-Wolfe Algorithms with Open-Loop Step-Sizes

Frank-Wolfe algorithms (FW) are popular first-order methods for solving constrained convex optimization problems that rely on a linear minimization oracle instead of potentially expensive projection-like oracles. Many works have identified accelerated convergence rates under various structural assumptions on the optimization problem and for specific FW variants when using line-search or short-step, requiring feedback from the objective function. Little is known about accelerated convergence regimes when utilizing open-loop step-size rules, a.k.a. FW with pre-determined step-sizes, which are algorithmically extremely simple and stable. Not only is FW with open-loop step-size rules not always subject to the same convergence rate lower bounds as FW with line-search or short-step, but in some specific cases, such as kernel herding in infinite dimensions, it has been empirically observed that FW with open-loop step-size rules enjoys to faster convergence rates than FW with line-search or short-step. We propose a partial answer to this unexplained phenomenon in kernel herding, characterize a general setting for which FW with open-loop step-size rules converges non-asymptotically faster than with line-search or short-step, and derive several accelerated convergence results for FW with open-loop step-size rules. Finally, we demonstrate that FW with open-loop step-sizes can compete with momentum-based open-loop FW variants.

math.OC↗

arXiv2023

Autonomous Detection of Methane Emissions in Multispectral Satellite Data Using Deep Learning

Methane is one of the most potent greenhouse gases, and its short atmospheric half-life makes it a prime target to rapidly curb global warming. However, current methane emission monitoring techniques primarily rely on approximate emission factors or self-reporting, which have been shown to often dramatically underestimate emissions. Although initially designed to monitor surface properties, satellite multispectral data has recently emerged as a powerful method to analyze atmospheric content. However, the spectral resolution of multispectral instruments is poor, and methane measurements are typically very noisy. Methane data products are also sensitive to absorption by the surface and other atmospheric gases (water vapor in particular) and therefore provide noisy maps of potential methane plumes, that typically require extensive human analysis. Here, we show that the image recognition capabilities of deep learning methods can be leveraged to automatize the detection of methane leaks in Sentinel-2 satellite multispectral data, with dramatically reduced false positive rates compared with state-of-the-art multispectral methane data products, and without the need for a priori knowledge of potential leak sites. Our proposed approach paves the way for the automated, high-definition and high-frequency monitoring of point-source methane emissions across the world.

physics.geo-ph↗

arXiv2021

Restarting Frank-Wolfe: Faster Rates Under Hölderian Error Bounds

Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While the vanilla Frank-Wolfe algorithm only ensures a worst-case rate of $\mathcal{O}(1/ε)$, various recent results have shown that for strongly convex functions on polytopes, the method can be slightly modified to achieve linear convergence. However, this still leaves a huge gap between sublinear $\mathcal{O}(1/ε)$ convergence and linear $\mathcal{O}(\log 1/ε)$ convergence to reach an $ε$-approximate solution. Here, we present a new variant of Conditional Gradient algorithms, that can dynamically adapt to the function's geometric properties using restarts and smoothly interpolates between the sublinear and linear regimes. These interpolated convergence rates are obtained when the optimization problem satisfies a new type of error bounds, which we call \textit{strong Wolfe primal bounds}. They combine geometric information on the constraint set with Hölderian Error Bounds on the objective function.

math.OC↗

arXiv2021

Efficient Online-Bandit Strategies for Minimax Learning Problems

Several learning problems involve solving min-max problems, e.g., empirical distributional robust learning or learning with non-standard aggregated losses. More specifically, these problems are convex-linear problems where the minimization is carried out over the model parameters $w\in\mathcal{W}$ and the maximization over the empirical distribution $p\in\mathcal{K}$ of the training set indexes, where $\mathcal{K}$ is the simplex or a subset of it. To design efficient methods, we let an online learning algorithm play against a (combinatorial) bandit algorithm. We argue that the efficiency of such approaches critically depends on the structure of $\mathcal{K}$ and propose two properties of $\mathcal{K}$ that facilitate designing efficient algorithms. We focus on a specific family of sets $\mathcal{S}_{n,k}$ encompassing various learning applications and provide high-probability convergence guarantees to the minimax values.

cs.LG↗

arXiv2021

Linear Bandits on Uniformly Convex Sets

Linear bandit algorithms yield $\tilde{\mathcal{O}}(n\sqrt{T})$ pseudo-regret bounds on compact convex action sets $\mathcal{K}\subset\mathbb{R}^n$ and two types of structural assumptions lead to better pseudo-regret bounds. When $\mathcal{K}$ is the simplex or an $\ell_p$ ball with $p\in]1,2]$, there exist bandits algorithms with $\tilde{\mathcal{O}}(\sqrt{nT})$ pseudo-regret bounds. Here, we derive bandit algorithms for some strongly convex sets beyond $\ell_p$ balls that enjoy pseudo-regret bounds of $\tilde{\mathcal{O}}(\sqrt{nT})$, which answers an open question from [BCB12, §5.5.]. Interestingly, when the action set is uniformly convex but not necessarily strongly convex, we obtain pseudo-regret bounds with a dimension dependency smaller than $\mathcal{O}(\sqrt{n})$. However, this comes at the expense of asymptotic rates in $T$ varying between $\tilde{\mathcal{O}}(\sqrt{T})$ and $\tilde{\mathcal{O}}(T)$.

cs.LG↗

arXiv2021

Local and Global Uniform Convexity Conditions

We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the convergence of optimization methods. In particular, we establish local versions of these conditions to provide sharper insights on a recent body of complexity results in learning theory, online learning, or offline optimization, which rely on the strong convexity of the feasible set. While they have a significant impact on complexity, these strong convexity or uniform convexity properties of feasible sets are not exploited as thoroughly as their functional counterparts, and this work is an effort to correct this imbalance. We conclude with some practical examples in optimization and machine learning where leveraging these conditions and localized assumptions lead to new complexity results.

math.OC↗

arXiv2021

Generating Structured Adversarial Attacks Using Frank-Wolfe Method

White box adversarial perturbations are generated via iterative optimization algorithms most often by minimizing an adversarial loss on a $\ell_p$ neighborhood of the original image, the so-called distortion set. Constraining the adversarial search with different norms results in disparately structured adversarial examples. Here we explore several distortion sets with structure-enhancing algorithms. These new structures for adversarial examples might provide challenges for provable and empirical robust mechanisms. Because adversarial robustness is still an empirical field, defense mechanisms should also reasonably be evaluated against differently structured attacks. Besides, these structured adversarial perturbations may allow for larger distortions size than their $\ell_p$ counter-part while remaining imperceptible or perceptible as natural distortions of the image. We will demonstrate in this work that the proposed structured adversarial examples can significantly bring down the classification accuracy of adversarialy trained classifiers while showing low $\ell_2$ distortion rate. For instance, on ImagNet dataset the structured attacks drop the accuracy of adversarial model to near zero with only 50\% of $\ell_2$ distortion generated using white-box attacks like PGD. As a byproduct, our finding on structured adversarial examples can be used for adversarial regularization of models to make models more robust or improve their generalization performance on datasets which are structurally different.

cs.LG↗

arXiv2020

Affine Invariant Analysis of Frank-Wolfe on Strongly Convex Sets

It is known that the Frank-Wolfe (FW) algorithm, which is affine-covariant, enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring non-affine invariant bounds, in contradiction with FW's affine-covariant property. In this work, we introduce new structural assumptions on the problem (such as the directional smoothness) and derive an affine invariant, norm-independent analysis of Frank-Wolfe. Based on our analysis, we propose an affine invariant backtracking line-search. Interestingly, we show that typical backtracking line-searches using smoothness of the objective function surprisingly converge to an affine invariant step size, despite using affine-dependent norms in the step size's computation. This indicates that we do not necessarily need to know the set's structure in advance to enjoy the affine-invariant accelerated rate.

math.OC↗

arXiv2020

Diptychs of human and machine perceptions

We propose visual creations that put differences in algorithms and humans \emph{perceptions} into perspective. We exploit saliency maps of neural networks and visual focus of humans to create diptychs that are reinterpretations of an original image according to both machine and human attentions. Using those diptychs as a qualitative evaluation of perception, we discuss some crucial issues of current \textit{task-oriented} artificial intelligence.

cs.GR↗

arXiv2020

Trace-Norm Adversarial Examples

White box adversarial perturbations are sought via iterative optimization algorithms most often minimizing an adversarial loss on a $l_p$ neighborhood of the original image, the so-called distortion set. Constraining the adversarial search with different norms results in disparately structured adversarial examples. Here we explore several distortion sets with structure-enhancing algorithms. These new structures for adversarial examples, yet pervasive in optimization, are for instance a challenge for adversarial theoretical certification which again provides only $l_p$ certificates. Because adversarial robustness is still an empirical field, defense mechanisms should also reasonably be evaluated against differently structured attacks. Besides, these structured adversarial perturbations may allow for larger distortions size than their $l_p$ counter-part while remaining imperceptible or perceptible as natural slight distortions of the image. Finally, they allow some control on the generation of the adversarial perturbation, like (localized) bluriness.

cs.LG↗

arXiv2020

Projection-Free Optimization on Uniformly Convex Sets

The Frank-Wolfe method solves smooth constrained convex optimization problems at a generic sublinear rate of $\mathcal{O}(1/T)$, and it (or its variants) enjoys accelerated convergence rates for two fundamental classes of constraints: polytopes and strongly-convex sets. Uniformly convex sets non-trivially subsume strongly convex sets and form a large variety of \textit{curved} convex sets commonly encountered in machine learning and signal processing. For instance, the $\ell_p$-balls are uniformly convex for all $p > 1$, but strongly convex for $p\in]1,2]$ only. We show that these sets systematically induce accelerated convergence rates for the original Frank-Wolfe algorithm, which continuously interpolate between known rates. Our accelerated convergence rates emphasize that it is the curvature of the constraint sets -- not just their strong convexity -- that leads to accelerated convergence rates. These results also importantly highlight that the Frank-Wolfe algorithm is adaptive to much more generic constraint set structures, thus explaining faster empirical convergence. Finally, we also show accelerated convergence rates when the set is only locally uniformly convex and provide similar results in online linear optimization.

math.OC↗

arXiv2020

Interactive Neural Style Transfer with Artists

We present interactive painting processes in which a painter and various neural style transfer algorithms interact on a real canvas. Understanding what these algorithms' outputs achieve is then paramount to describe the creative agency in our interactive experiments. We gather a set of paired painting-pictures images and present a new evaluation methodology based on the predictivity of neural style transfer algorithms. We point some algorithms' instabilities and show that they can be used to enlarge the diversity and pleasing oddity of the images synthesized by the numerous existing neural style transfer algorithms. This diversity of images was perceived as a source of inspiration for human painters, portraying the machine as a computational catalyst.

cs.HC↗

arXiv2019

Dialog on a canvas with a machine

We propose a new form of human-machine interaction. It is a pictorial game consisting of interactive rounds of creation between artists and a machine. They repetitively paint one after the other. At its rounds, the computer partially completes the drawing using machine learning algorithms, and projects its additions directly on the canvas, which the artists are free to insert or modify. Alongside fostering creativity, the process is designed to question the growing interaction between humans and machines.

cs.GR↗

arXiv2019

An Approximate Shapley-Folkman Theorem

The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that this produces an a priori bound on the duality gap of separable nonconvex optimization problems involving finite sums. This bound is highly conservative and depends on unstable quantities, and we relax it in several directions to show that non convexity can have a much milder impact on finite sum minimization problems such as empirical risk minimization and multi-task classification. As a byproduct, we show a new version of Maurey's classical approximate Carathéodory lemma where we sample a significant fraction of the coefficients, without replacement, as well as a result on sampling constraints using an approximate Helly theorem, both of independent interest.

math.OC↗