arXiv subjects

Quentin Bertrand

Publications and source records attributed to Quentin Bertrand.

At least 19 recordsLinked to original sources

arXiv2026

On the Stability and Convergence of Flow Map Training

Flow maps are a recent method of probabilistic generation that amortize diffusion trajectories into one-step samplers, unlocking efficient generation. While progress has been made in improving their empirical performance, there is still a lack of understanding behind the mechanisms underlying their success. Specifically, many flow map learning methods employ stop gradient operators as a crucial part of their training target. Adaptive weighting also drastically improves the generation capabilities of flow maps. Although many interpretations have been proposed to support the inclusion of these heuristics, none have analyzed the impact of these assumptions on the training dynamics of flow maps themselves. In this work, we address this issue by providing grounded theory explaining why such tricks are required. Analyzing the functional gradient flow induced by the MeanFlow and Lagrangian losses, we show their convergence to the true flow map, settling the validity of these objectives. For finite updates, we highlight a severe roadblock to the usage of these losses in practice: the possible unboundedness of the update. Adaptive normalization not only provides bounded updates, but, combined with a specific weighting, additionally provides convergence guarantees towards a neighborhood of the solution. On synthetic data, we show that our functional gradient flow analysis exactly describes the true training dynamics for flow maps. Experiments on standard image datasets demonstrate that a proper reweighting scheme is essential for strong empirical performance, which is only achieved for a specific range of reweighting strengths.

stat.ML↗

arXiv2026

Beyond the Manifold Hypothesis: Hybrid Spectral Parameterizations for Flow Matching

Flow matching and diffusion can be trained to predict different quantities, most commonly the data $x_1$, the source noise $x_0$, or the velocity~$v$. Although theoretically equivalent, these can lead to substantially different performances. We identify two main drivers for these differences: the source--data signal-to-noise ratio, and the information bottleneck induced by the neural architecture. We show that, beyond intrinsic data dimension, the factor affecting the optimal parametrization the most is a certain signal-to-noise ratio in each data covariance direction. From this analysis, we introduce new \emph{spectral hybrid} parameterizations that adapt across time and data covariance directions; we show that these are optimal for Gaussian data. We also show that architecture-induced compression changes which parameterization is easier to learn, with $v$-prediction being more sensitive to discarded directions than $x_1$-prediction. Experiments across architectures and source scales show that our spectral parameterizations are robust across regimes, can substantially accelerate optimization, while incurring essentially no additional training cost compared with standard parameterizations.

cs.LG↗

arXiv2025

Self-Play Q-learners Can Provably Collude in the Iterated Prisoner's Dilemma

A growing body of computational studies shows that simple machine learning agents converge to cooperative behaviors in social dilemmas, such as collusive price-setting in oligopoly markets, raising questions about what drives this outcome. In this work, we provide theoretical foundations for this phenomenon in the context of self-play multi-agent Q-learners in the iterated prisoner's dilemma. We characterize broad conditions under which such agents provably learn the cooperative Pavlov (win-stay, lose-shift) policy rather than the Pareto-dominated "always defect" policy. We validate our theoretical results through additional experiments, demonstrating their robustness across a broader class of deep learning algorithms.

cs.GT↗

arXiv2025

On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity

Modern deep generative models can now produce high-quality synthetic samples that are often indistinguishable from real training data. A growing body of research aims to understand why recent methods, such as diffusion and flow matching techniques, generalize so effectively. Among the proposed explanations are the inductive biases of deep learning architectures and the stochastic nature of the conditional flow matching loss. In this work, we rule out the noisy nature of the loss as a key factor driving generalization in flow matching. First, we empirically show that in high-dimensional settings, the stochastic and closed-form versions of the flow matching loss yield nearly equivalent losses. Then, using state-of-the-art flow matching models on standard image datasets, we demonstrate that both variants achieve comparable statistical performance, with the surprising observation that using the closed-form can even improve performance.

cs.LG↗

arXiv2024

Self-Consuming Generative Models with Curated Data Provably Optimize Human Preferences

The rapid progress in generative models has resulted in impressive leaps in generation quality, blurring the lines between synthetic and real data. Web-scale datasets are now prone to the inevitable contamination by synthetic data, directly impacting the training of future generated models. Already, some theoretical results on self-consuming generative models (a.k.a., iterative retraining) have emerged in the literature, showcasing that either model collapse or stability could be possible depending on the fraction of generated data used at each retraining step. However, in practice, synthetic data is often subject to human feedback and curated by users before being used and uploaded online. For instance, many interfaces of popular text-to-image generative models, such as Stable Diffusion or Midjourney, produce several variations of an image for a given query which can eventually be curated by the users. In this paper, we theoretically study the impact of data curation on iterated retraining of generative models and show that it can be seen as an \emph{implicit preference optimization mechanism}. However, unlike standard preference optimization, the generative model does not have access to the reward function or negative samples needed for pairwise comparisons. Moreover, our study doesn't require access to the density function, only to samples. We prove that, if the data is curated according to a reward model, then the expected reward of the iterative retraining procedure is maximized. We further provide theoretical results on the stability of the retraining loop when using a positive fraction of real data at each step. Finally, we conduct illustrative experiments on both synthetic datasets and on CIFAR10 showing that such a procedure amplifies biases of the reward model.

cs.CV↗

arXiv2024

Multipacting mitigation by atomic layer deposition: the case study of Titanium Nitride

This study investigates the use of Atomic Layer deposition (ALD) to mitigate multipacting phenomena inside superconducting radio frequency (SRF) cavities used in particle accelerators. The unique ALD capability to control the film thickness down to the atomic level on arbitrary complex shape objects enable the fine tuning of TiN film resistivity and total electron emission yield (TEEY) from coupons to devices. This level of control allows us to adequately choose a TiN film thickness that provide both a high resistivity to prevent Ohmic losses and low TEEY to mitigate multipacting for the application of interest. The methodology presented in this work can be scaled to other domain and devices subject to RF fields in vacuum and sensitive to multipacting or electron discharge processes with their own requirements in resistivities and TEEY values

physics.app-ph↗

arXiv2024

On the Stability of Iterative Retraining of Generative Models on their own Data

Deep generative models have made tremendous progress in modeling complex data, often exhibiting generation quality that surpasses a typical human's ability to discern the authenticity of samples. Undeniably, a key driver of this success is enabled by the massive amounts of web-scale data consumed by these models. Due to these models' striking performance and ease of availability, the web will inevitably be increasingly populated with synthetic content. Such a fact directly implies that future iterations of generative models will be trained on both clean and artificially generated data from past models. In this paper, we develop a framework to rigorously study the impact of training generative models on mixed datasets -- from classical training on real data to self-consuming generative models trained on purely synthetic data. We first prove the stability of iterative training under the condition that the initial generative models approximate the data distribution well enough and the proportion of clean training data (w.r.t. synthetic data) is large enough. We empirically validate our theory on both synthetic and natural images by iteratively training normalizing flows and state-of-the-art diffusion models on CIFAR10 and FFHQ.

cs.LG↗

arXiv2024

Omega: Optimistic EMA Gradients

Stochastic min-max optimization has gained interest in the machine learning community with the advancements in GANs and adversarial training. Although game optimization is fairly well understood in the deterministic setting, some issues persist in the stochastic regime. Recent work has shown that stochastic gradient descent-ascent methods such as the optimistic gradient are highly sensitive to noise or can fail to converge. Although alternative strategies exist, they can be prohibitively expensive. We introduce Omega, a method with optimistic-like updates that mitigates the impact of noise by incorporating an EMA of historic gradients in its update rule. We also explore a variation of this algorithm that incorporates momentum. Although we do not provide convergence guarantees, our experiments on stochastic games show that Omega outperforms the optimistic gradient method when applied to linear players.

cs.LG↗

arXiv2023

The Control System of the Elliptical Cavity and Cryomodule Test Stand Demonstrator for ESS

CEA IRFU Saclay is taking part of ESS (European Spallation Source) construction through several packages and, especially in the last three years on the Elliptical Cavity and Cryomodule Test stand Demonstrator (ECCTD). The project consists of RF test, conditioning, cryogenic cool-down and regulations of eight cryomodules with theirs four cavities each. For now, two medium beta cavities cryomodules have been successfully tested. This paper describes the context and the realization of the control system for cryogenic and RF processes, added to cavities tuning motorization relying on COTS solutions: Siemens PLC, EtherCAT Beckhoff modules, IOxOS fast acquisition cards and MRF timing cards.

physics.acc-ph↗

arXiv2023

The Curse of Unrolling: Rate of Differentiating Through Optimization

Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few. Unrolled differentiation is a popular heuristic that approximates the solution using an iterative solver and differentiates it through the computational path. This work provides a non-asymptotic convergence-rate analysis of this approach on quadratic objectives for gradient descent and the Chebyshev method. We show that to ensure convergence of the Jacobian, we can either 1) choose a large learning rate leading to a fast asymptotic convergence but accept that the algorithm may have an arbitrarily long burn-in phase or 2) choose a smaller learning rate leading to an immediate but slower convergence. We refer to this phenomenon as the curse of unrolling. Finally, we discuss open problems relative to this approach, such as deriving a practical update rule for the optimal unrolling strategy and making novel connections with the field of Sobolev orthogonal polynomials.

math.OC↗

arXiv2023

Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding is limited. In this work, we provide evidence that disentangled representations coupled with sparse base-predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM base-predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.

cs.LG↗

arXiv2023

Beyond L1: Faster and Better Sparse Models with skglm

We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on coordinate descent, working sets and Anderson acceleration. It handles previously unaddressed models, and is extensively shown to improve state-of-art algorithms. We provide a flexible, scikit-learn compatible package, which easily handles customized datafits and penalties.

stat.ML↗

arXiv2023

On the Limitations of Elo: Real-World Games, are Transitive, not Additive

Real-world competitive games, such as chess, go, or StarCraft II, rely on Elo models to measure the strength of their players. Since these games are not fully transitive, using Elo implicitly assumes they have a strong transitive component that can correctly be identified and extracted. In this study, we investigate the challenge of identifying the strength of the transitive component in games. First, we show that Elo models can fail to extract this transitive component, even in elementary transitive games. Then, based on this observation, we propose an extension of the Elo score: we end up with a disc ranking system that assigns each player two scores, which we refer to as skill and consistency. Finally, we propose an empirical validation on payoff matrices coming from real-world games played by bots and humans.

cs.GT↗

arXiv2022

Implicit differentiation for fast hyperparameter selection in non-smooth convex learning

Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but non-smooth. We show that the forward-mode differentiation of proximal gradient descent and proximal coordinate descent yield sequences of Jacobians converging toward the exact Jacobian. Using implicit differentiation, we show it is possible to leverage the non-smoothness of the inner problem to speed up the computation. Finally, we provide a bound on the error made on the hypergradient when the inner optimization problem is solved approximately. Results on regression and classification problems reveal computational benefits for hyperparameter optimization, especially when multiple hyperparameters are required.

stat.ML↗

arXiv2021

Anderson acceleration of coordinate descent

Acceleration of first order methods is mainly obtained via inertial techniques à la Nesterov, or via nonlinear extrapolation. The latter has known a recent surge of interest, with successful applications to gradient and proximal gradient techniques. On multiple Machine Learning problems, coordinate descent achieves performance significantly superior to full-gradient methods. Speeding up coordinate descent in practice is not easy: inertially accelerated versions of coordinate descent are theoretically accelerated, but might not always lead to practical speed-ups. We propose an accelerated version of coordinate descent using extrapolation, showing considerable speed up in practice, compared to inertial accelerated coordinate descent and extrapolated (proximal) gradient descent. Experiments on least squares, Lasso, elastic net and logistic regression validate the approach.

stat.ML↗

arXiv2021

Electromagnetic neural source imaging under sparsity constraints with SURE-based hyperparameter tuning

Estimators based on non-convex sparsity-promoting penalties were shown to yield state-of-the-art solutions to the magneto-/electroencephalography (M/EEG) brain source localization problem. In this paper we tackle the model selection problem of these estimators: we propose to use a proxy of the Stein's Unbiased Risk Estimator (SURE) to automatically select their regularization parameters. The effectiveness of the method is demonstrated on realistic simulations and $30$ subjects from the Cam-CAN dataset. To our knowledge, this is the first time that sparsity promoting estimators are automatically calibrated at such a scale. Results show that the proposed SURE approach outperforms cross-validation strategies and state-of-the-art Bayesian statistics methods both computationally and statistically.

eess.IV↗

arXiv2020

Model identification and local linear convergence of coordinate descent

For composite nonsmooth optimization problems, Forward-Backward algorithm achieves model identification (e.g. support identification for the Lasso) after a finite number of iterations, provided the objective function is regular enough. Results concerning coordinate descent are scarcer and model identification has only been shown for specific estimators, the support-vector machine for instance. In this work, we show that cyclic coordinate descent achieves model identification in finite time for a wide class of functions. In addition, we prove explicit local linear convergence rates for coordinate descent. Extensive experiments on various estimators and on real datasets demonstrate that these rates match well empirical results.

stat.ML↗

arXiv2020

Handling correlated and repeated measurements with the smoothed multivariate square-root Lasso

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regression coefficients. Additionally, in many applications, the data is obtained by averaging multiple measurements: this reduces the noise variance, but it dramatically reduces sample sizes and prevents refined noise modeling. In this work, we propose a concomitant estimator that can cope with complex noise structure by using non-averaged measurements. The resulting optimization problem is convex and amenable, thanks to smoothing theory, to state-of-the-art optimization techniques that leverage the sparsity of the solutions. Practical benefits are demonstrated on toy datasets, realistic simulated data and real neuroimaging data.

stat.ML↗