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Amaury Habrard

Publications and source records attributed to Amaury Habrard.

At least 19 recordsLinked to original sources
arXiv2026

On the disintegration of the stochastic majority vote: From PAC-Bayesian bounds to a self-bounding algorithm

Weighted majority votes are central to many successful ensemble methods. PAC-Bayesian theory provides tight generalization guarantees for such models by analyzing the expected risk of stochastic classifiers, while analyzing the risk of deterministic majority votes relies on surrogate bounds. To avoid these surrogates, Zantedeschi et al. ( 2021) introduced guarantees for stochastic majority votes, but the resulting models remain randomized. In this paper, we propose a derandomization framework for stochastic majority votes. To do so, we apply recent advances in disintegrated PAC-Bayesian theory directly to the space of majority vote weight vectors, transforming stochastic guarantees into certificates for a single deterministic majority vote. We derive two families of high-probability generalization bounds, covering both data-independent and data-dependent constructions of the ensemble, which naturally lead to a self-bounding learning algorithm optimizing deterministic majority vote guarantees.

stat.ML↗
arXiv2026

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system. Constituting a cornerstone of scientific advancement, it has become during the past decade a major line of research in the rapidly evolving field of Physics-informed Machine Learning (PiML). Among the remaining open problems to address in this domain, the post-hoc evaluation of discovered PDEs raises the particular difficulty of being multifaceted. Indeed, it requires jointly considering predictive accuracy, physical consistency, interpretability, and out-of-distribution generalization capacity. Given that some of these properties are conflicting, it is worth noting that the wide range of existing evaluation metrics only partially address the overall problem, potentially leading to overly interpreted conclusions about the validity of a presumed new physical theory. From an abundant literature spanning machine learning, numerical analysis, information theory or symbolic regression, we propose, to our knowledge, the first taxonomy of PDE evaluation metrics, and discuss their advantages and limitations in depth. Based on the observation that evaluation is often achieved on a case-by-case basis and that a universally accepted methodology remains elusive, we further provide recommendations with the aim of promoting standardized and reliable practices, before sketching promising future lines of research in this field. We argue that this paper is intended both for ML experts who design new PDE discovery algorithms and for users of these methods aiming, in real applications, to discover and validate well-founded scientific laws.

cs.LG↗
arXiv2026

A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation properties remain poorly understood, particularly in the regression setting with unbounded losses. Existing analyses rely on approximation or stability arguments and do not fully capture how physical structure influences generalisation from finite data. In this work, we develop a PAC-Bayesian framework for PIML that provides high-probability generalisation guarantees in the presence of unbounded losses. We adopt a multi-task perspective that jointly treats data fidelity, PDE residuals, initial and boundary conditions, avoiding the looseness induced by standard union-bound approaches. Our analysis leverages the structure of physics-informed objectives to derive novel bounds where the complexity scales with input-gradient norms of the losses, revealing a direct link between physical regularity and generalisation. We instantiate this framework under Sobolev and Poincaré-type assumptions, yielding two classes of bounds that trade off statistical complexity and smoothness in different regimes. Building on these results, we propose a self-bounding-aware learning algorithm that directly optimises tractable surrogates of the derived bounds, along with a practical procedure to estimate the associated constants in realistic settings. Empirical evaluations on standard PDE benchmarks demonstrate that our bounds are non-vacuous, significantly tighter than union-bound baselines, and can be effectively minimised during training. Overall, our results provide a principled statistical foundation for the generalisation of physics-informed models.

cs.LG↗
arXiv2026

From GNNs to Symbolic Surrogates via Kolmogorov-Arnold Networks for Delay Prediction

Accurate prediction of flow delay is essential for optimizing and managing modern communication networks. We investigate three levels of modeling for this task. First, we implement a heterogeneous GNN with attention-based message passing, establishing a strong neural baseline. Second, we propose FlowKANet in which Kolmogorov-Arnold Networks replace standard MLP layers, reducing trainable parameters while maintaining competitive predictive performance. FlowKANet integrates KAMP-Attn (Kolmogorov-Arnold Message Passing with Attention), embedding KAN operators directly into message-passing and attention computation. Finally, we distill the model into symbolic surrogate models using block-wise regression, producing closed-form equations that eliminate trainable weights while preserving graph-structured dependencies. The results show that KAN layers provide a favorable trade-off between efficiency and accuracy and that symbolic surrogates emphasize the potential for lightweight deployment and enhanced transparency.

cs.LG↗
arXiv2026

PAC-Bayesian Generalization Guarantees for Fairness on Stochastic and Deterministic Classifiers

Classical PAC generalization bounds on the prediction risk of a classifier are insufficient to provide theoretical guarantees on fairness when the goal is to learn models balancing predictive risk and fairness constraints. We propose a PAC-Bayesian framework for deriving generalization bounds for fairness, covering both stochastic and deterministic classifiers. For stochastic classifiers, we derive a fairness bound using standard PAC-Bayes techniques. Whereas for deterministic classifiers, as usual PAC-Bayes arguments do not apply directly, we leverage a recent advance in PAC-Bayes to extend the fairness bound beyond the stochastic setting. Our framework has two advantages: (i) It applies to a broad class of fairness measures that can be expressed as a risk discrepancy, and (ii) it leads to a self-bounding algorithm in which the learning procedure directly optimizes a trade-off between generalization bounds on the prediction risk and on the fairness. We empirically evaluate our framework with three classical fairness measures, demonstrating not only its usefulness but also the tightness of our bounds.

stat.ML↗
arXiv2025

Méthode de quadrature pour les PINNs fondée théoriquement sur la hessienne des résiduels

Physics-informed Neural Networks (PINNs) have emerged as an efficient way to learn surrogate neural solvers of PDEs by embedding the physical model in the loss function and minimizing its residuals using automatic differentiation at so-called collocation points. Originally uniformly sampled, the choice of the latter has been the subject of recent advances leading to adaptive sampling refinements. In this paper, we propose a new quadrature method for approximating definite integrals based on the hessian of the considered function, and that we leverage to guide the selection of the collocation points during the training process of PINNs.

cs.LG↗
arXiv2025

Provably Accurate Adaptive Sampling for Collocation Points in Physics-informed Neural Networks

Despite considerable scientific advances in numerical simulation, efficiently solving PDEs remains a complex and often expensive problem. Physics-informed Neural Networks (PINN) have emerged as an efficient way to learn surrogate solvers by embedding the PDE in the loss function and minimizing its residuals using automatic differentiation at so-called collocation points. Originally uniformly sampled, the choice of the latter has been the subject of recent advances leading to adaptive sampling refinements for PINNs. In this paper, leveraging a new quadrature method for approximating definite integrals, we introduce a provably accurate sampling method for collocation points based on the Hessian of the PDE residuals. Comparative experiments conducted on a set of 1D and 2D PDEs demonstrate the benefits of our method.

cs.LG↗
arXiv2025

Interpretable Reinforcement Learning for Load Balancing using Kolmogorov-Arnold Networks

Reinforcement learning (RL) has been increasingly applied to network control problems, such as load balancing. However, existing RL approaches often suffer from lack of interpretability and difficulty in extracting controller equations. In this paper, we propose the use of Kolmogorov-Arnold Networks (KAN) for interpretable RL in network control. We employ a PPO agent with a 1-layer actor KAN model and an MLP Critic network to learn load balancing policies that maximise throughput utility, minimize loss as well as delay. Our approach allows us to extract controller equations from the learned neural networks, providing insights into the decision-making process. We evaluate our approach using different reward functions demonstrating its effectiveness in improving network performance while providing interpretable policies.

cs.LG↗
arXiv2024

Leveraging PAC-Bayes Theory and Gibbs Distributions for Generalization Bounds with Complexity Measures

In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measures or regularizations are used in algorithms. In this paper, we leverage the framework of disintegrated PAC-Bayes bounds to derive a general generalization bound instantiable with arbitrary complexity measures. One trick to prove such a result involves considering a commonly used family of distributions: the Gibbs distributions. Our bound stands in probability jointly over the hypothesis and the learning sample, which allows the complexity to be adapted to the generalization gap as it can be customized to fit both the hypothesis class and the task.

stat.ML↗
arXiv2023

Towards Few-Annotation Learning for Object Detection: Are Transformer-based Models More Efficient ?

For specialized and dense downstream tasks such as object detection, labeling data requires expertise and can be very expensive, making few-shot and semi-supervised models much more attractive alternatives. While in the few-shot setup we observe that transformer-based object detectors perform better than convolution-based two-stage models for a similar amount of parameters, they are not as effective when used with recent approaches in the semi-supervised setting. In this paper, we propose a semi-supervised method tailored for the current state-of-the-art object detector Deformable DETR in the few-annotation learning setup using a student-teacher architecture, which avoids relying on a sensitive post-processing of the pseudo-labels generated by the teacher model. We evaluate our method on the semi-supervised object detection benchmarks COCO and Pascal VOC, and it outperforms previous methods, especially when annotations are scarce. We believe that our contributions open new possibilities to adapt similar object detection methods in this setup as well.

cs.CV↗
arXiv2023

Proposal-Contrastive Pretraining for Object Detection from Fewer Data

The use of pretrained deep neural networks represents an attractive way to achieve strong results with few data available. When specialized in dense problems such as object detection, learning local rather than global information in images has proven to be more efficient. However, for unsupervised pretraining, the popular contrastive learning requires a large batch size and, therefore, a lot of resources. To address this problem, we are interested in transformer-based object detectors that have recently gained traction in the community with good performance and with the particularity of generating many diverse object proposals. In this work, we present Proposal Selection Contrast (ProSeCo), a novel unsupervised overall pretraining approach that leverages this property. ProSeCo uses the large number of object proposals generated by the detector for contrastive learning, which allows the use of a smaller batch size, combined with object-level features to learn local information in the images. To improve the effectiveness of the contrastive loss, we introduce the object location information in the selection of positive examples to take into account multiple overlapping object proposals. When reusing pretrained backbone, we advocate for consistency in learning local information between the backbone and the detection head. We show that our method outperforms state of the art in unsupervised pretraining for object detection on standard and novel benchmarks in learning with fewer data.

cs.CV↗
arXiv2023

Learning complexity to guide light-induced self-organized nanopatterns

Ultrafast laser irradiation can induce spontaneous self-organization of surfaces into dissipative structures with nanoscale reliefs. These surface patterns emerge from symmetry-breaking dynamical processes that occur in Rayleigh-Bénard-like instabilities. In this study, we demonstrate that the coexistence and competition between surface patterns of different symmetries in two dimensions can be numerically unraveled using the stochastic generalized Swift-Hohenberg model. We originally propose a deep convolutional network to identify and learn the dominant modes that stabilize for a given bifurcation and quadratic model coefficients. The model is scale-invariant and has been calibrated on microscopy measurements using a physics-guided machine learning strategy. Our approach enables the identification of experimental irradiation conditions for a desired self-organization pattern. It can be applied generally to predict structure formation in situations where the underlying physics can be approximately described by a self-organization process and data is sparse and non-time series. Our work paves the way for supervised local manipulation of matter using timely-controlled optical fields in laser manufacturing.

cond-mat.mtrl-sci↗
arXiv2023

A General Framework for the Practical Disintegration of PAC-Bayesian Bounds

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic models such as neural networks. As an alternative to this step, we introduce new PAC-Bayesian generalization bounds that have the originality to provide disintegrated bounds, i.e., they give guarantees over one single hypothesis instead of the usual averaged analysis. Our bounds are easily optimizable and can be used to design learning algorithms. We illustrate this behavior on neural networks, and we show a significant practical improvement over the state-of-the-art framework.

stat.ML↗
arXiv2022

A Simple Way to Learn Metrics Between Attributed Graphs

The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to improve performance of classification or clustering methods. However, due to difficulties in establishing computable, efficient and differentiable distances between attributed graphs, few metric learning algorithms adapted to graphs have been developed despite the strong interest of the community. In this paper, we address this issue by proposing a new Simple Graph Metric Learning - SGML - model with few trainable parameters based on Simple Graph Convolutional Neural Networks - SGCN - and elements of Optimal Transport theory. This model allows us to build an appropriate distance from a database of labeled (attributed) graphs to improve the performance of simple classification algorithms such as $k$-NN. This distance can be quickly trained while maintaining good performances as illustrated by the experimental study presented in this paper.

cs.LG↗
arXiv2022

Improving Few-Shot Learning through Multi-task Representation Learning Theory

In this paper, we consider the framework of multi-task representation (MTR) learning where the goal is to use source tasks to learn a representation that reduces the sample complexity of solving a target task. We start by reviewing recent advances in MTR theory and show that they can provide novel insights for popular meta-learning algorithms when analyzed within this framework. In particular, we highlight a fundamental difference between gradient-based and metric-based algorithms in practice and put forward a theoretical analysis to explain it. Finally, we use the derived insights to improve the performance of meta-learning methods via a new spectral-based regularization term and confirm its efficiency through experimental studies on few-shot classification benchmarks. To the best of our knowledge, this is the first contribution that puts the most recent learning bounds of MTR theory into practice for the task of few-shot classification.

cs.LG↗
arXiv2022

A survey on domain adaptation theory: learning bounds and theoretical guarantees

All famous machine learning algorithms that comprise both supervised and semi-supervised learning work well only under a common assumption: the training and test data follow the same distribution. When the distribution changes, most statistical models must be reconstructed from newly collected data, which for some applications can be costly or impossible to obtain. Therefore, it has become necessary to develop approaches that reduce the need and the effort to obtain new labeled samples by exploiting data that are available in related areas, and using these further across similar fields. This has given rise to a new machine learning framework known as transfer learning: a learning setting inspired by the capability of a human being to extrapolate knowledge across tasks to learn more efficiently. Despite a large amount of different transfer learning scenarios, the main objective of this survey is to provide an overview of the state-of-the-art theoretical results in a specific, and arguably the most popular, sub-field of transfer learning, called domain adaptation. In this sub-field, the data distribution is assumed to change across the training and the test data, while the learning task remains the same. We provide a first up-to-date description of existing results related to domain adaptation problem that cover learning bounds based on different statistical learning frameworks.

cs.LG↗
arXiv2021

A PAC-Bayes Analysis of Adversarial Robustness

We propose the first general PAC-Bayesian generalization bounds for adversarial robustness, that estimate, at test time, how much a model will be invariant to imperceptible perturbations in the input. Instead of deriving a worst-case analysis of the risk of a hypothesis over all the possible perturbations, we leverage the PAC-Bayesian framework to bound the averaged risk on the perturbations for majority votes (over the whole class of hypotheses). Our theoretically founded analysis has the advantage to provide general bounds (i) that are valid for any kind of attacks (i.e., the adversarial attacks), (ii) that are tight thanks to the PAC-Bayesian framework, (iii) that can be directly minimized during the learning phase to obtain a robust model on different attacks at test time.

cs.LG↗
arXiv2021

Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound

We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows for a closed-form and differentiable expression for the expected risk, which then turns the generalization bound into a tractable training objective. The resulting stochastic majority vote learning algorithm achieves state-of-the-art accuracy and benefits from (non-vacuous) tight generalization bounds, in a series of numerical experiments when compared to competing algorithms which also minimize PAC-Bayes objectives -- both with uninformed (data-independent) and informed (data-dependent) priors.

cs.LG↗