arXiv subjects

Mathieu Serrurier

Publications and source records attributed to Mathieu Serrurier.

At least 19 recordsLinked to original sources

arXiv2026

LiST: Lipschitz Scaling Training for Robust and Calibrated Neural Networks

While accuracy, robustness, and calibration are all essential for reliable neural networks, they are often studied separately; developing models that satisfy all three simultaneously remains a central challenge. Lipschitz-constrained models guarantee robustness by design, yet the manual selection of the Lipschitz constraint L governs the resulting accuracy-robustness trade-off, and their calibration properties remain largely underexplored. In this work, we highlight a theoretical and empirical link between the enforced Lipschitz constraint and Temperature Scaling, a state-of-the-art calibration method. Specifically, we find that for a given training scheme, there exists a non-trivial value L* that yields an out-of-the-box calibrated network, and that calibration acts as a principled criterion to select a well-defined operating point on the accuracy-robustness Pareto front. Leveraging these insights, we introduce Lipschitz Scaling Training (LiST), a novel training paradigm that iteratively adjusts the global Lipschitz constant to reach this operating point. Through a margin parameter in the training loss, LiST further enables the construction of a fully calibrated Pareto front, allowing users to navigate the accuracy-robustness trade-off while remaining calibrated throughout. At convergence, LiST also enables the reintegration of calibration data into training, improving sample efficiency without sacrificing calibration. We validate LiST on CIFAR-10/100 and Tiny-ImageNet, demonstrating competitive accuracy and robustness against constrained and unconstrained baselines, while remaining calibrated out of the box. Code is available at GitHub.

cs.LG↗

arXiv2026

From SGD to Muon: Adaptive Optimization via Schatten-p Norms

Modern optimizers, like Muon, impose matrix-wise geometry constraints on their updates. These matrix-wise constraints can be unified under Linear Minimization Oracle (LMO) theory. However, all current methods impose fixed LMO geometries for the update rules, chosen by-design or empirically, which are not necessarily optimal according to the problem's geometry. We introduce a novel efficient datadriven criterion for dynamically choosing proxy-optimal update LMO geometries on individual Deep Neural Network layers. Derived in closed form from gradient and activation statistics using a single-step random feature regression surrogate model, our criterion navigates a design space interpolating from SGD to Muon updates. Moreover, integrating parameter-wise preconditioning allows our framework to recover SGD, Muon, Adam, and MuAdam as specific extrema. To make this adaptive approach scalable, we pair it with efficient computational strategies, achieving only a $\sim$ 3% runtime overhead on highly optimized baselines. As a proof of concept, we show that this data-driven optimizer beats or remains competitive with the performance of the best performing optimizer between Muon and AdamW across three different training scenarios. Ultimately, this work provides evidence that LMO geometry can be successfully and efficiently adapted from runtime data, opening a new pathway for optimizer design beyond static geometries.

cs.AI↗

arXiv2026

Orthogonium : A Unified, Efficient Library of Orthogonal and 1-Lipschitz Building Blocks

Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite significant advancements, existing implementations remain fragmented, limited, and computationally demanding. To address these issues, we introduce Orthogonium , a unified, efficient, and comprehensive PyTorch library providing orthogonal and 1-Lipschitz layers. Orthogonium provides access to standard convolution features-including support for strides, dilation, grouping, and transposed-while maintaining strict mathematical guarantees. Its optimized implementations reduce overhead on large scale benchmarks such as ImageNet. Moreover, rigorous testing within the library has uncovered critical errors in existing implementations, emphasizing the importance of standardized and reliable tools. Orthogonium thus significantly lowers adoption barriers, enabling scalable experimentation and integration across diverse applications requiring orthogonality and robust Lipschitz constraints. Orthogonium is available at https://github.com/deel-ai/orthogonium.

cs.LG↗

arXiv2025

Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates

Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges. However, these methods rely on a costly gradient orthogonalization step. Even efficient iterative approximations such as Newton-Schulz remain expensive, typically requiring dozens of matrix multiplications to converge. We introduce a pre-conditioning procedure that improves the initialization of the Newton--Schulz iterations while incurring negligible overhead. Furthermore, our pre-conditioning reduces the initial polar error and enables the removal of one Newton-Schulz iteration (out of the five iterations usually used in practice). The resulting implementation significantly reduces Muon's overhead. At the end-to-end training level, we observe consistent runtime improvements across speed-run and standard benchmarks, including $\sim$3% reductions in training time on multiple fast training benchmarks, while matching reference performance on both language and vision tasks. Crucially, these improvements require no hyperparameter tuning and can be adopted as a simple drop-in replacement. Beyond empirical gains, we provide theoretical insight into the geometry of the update and its potential robustness against feature collapse. Our code is publicly available on github, in optax and huggingface kernels.

cs.AI↗

arXiv2025

Fast and Flexible Robustness Certificates for Semantic Segmentation

Deep Neural Networks are vulnerable to small perturbations that can drastically alter their predictions for perceptually unchanged inputs. The literature on adversarially robust Deep Learning attempts to either enhance the robustness of neural networks (e.g, via adversarial training) or to certify their decisions up to a given robustness level (e.g, by using randomized smoothing, formal methods or Lipschitz bounds). These studies mostly focus on classification tasks and few efficient certification procedures currently exist for semantic segmentation. In this work, we introduce a new class of certifiably robust Semantic Segmentation networks with built-in Lipschitz constraints that are efficiently trainable and achieve competitive pixel accuracy on challenging datasets such as Cityscapes. Additionally, we provide a novel framework that generalizes robustness certificates for semantic segmentation tasks, where we showcase the flexibility and computational efficiency of using Lipschitz networks. Our approach unlocks real-time compatible certifiably robust semantic segmentation for the first time. Moreover, it allows the computation of worst-case performance under $\ell_2$ attacks of radius $\epsilon$ across a wide range of performance measures. Crucially, we benchmark the runtime of our certification process and find our approach to be around 600 times faster than randomized smoothing methods at inference with comparable certificates on an NVIDIA A100 GPU. Finally, we evaluate the tightness of our worstcase certificates against state-of-the-art adversarial attacks to further validate the performance of our method.

cs.CV↗

arXiv2025

Generating Heterogeneous Multi-dimensional Data : A Comparative Study

Allocation of personnel and material resources is highly sensible in the case of firefighter interventions. This allocation relies on simulations to experiment with various scenarios. The main objective of this allocation is the global optimization of the firefighters response. Data generation is then mandatory to study various scenarios In this study, we propose to compare different data generation methods. Methods such as Random Sampling, Tabular Variational Autoencoders, standard Generative Adversarial Networks, Conditional Tabular Generative Adversarial Networks and Diffusion Probabilistic Models are examined to ascertain their efficacy in capturing the intricacies of firefighter interventions. Traditional evaluation metrics often fall short in capturing the nuanced requirements of synthetic datasets for real-world scenarios. To address this gap, an evaluation of synthetic data quality is conducted using a combination of domain-specific metrics tailored to the firefighting domain and standard measures such as the Wasserstein distance. Domain-specific metrics include response time distribution, spatial-temporal distribution of interventions, and accidents representation. These metrics are designed to assess data variability, the preservation of fine and complex correlations and anomalies such as event with a very low occurrence, the conformity with the initial statistical distribution and the operational relevance of the synthetic data. The distribution has the particularity of being highly unbalanced, none of the variables following a Gaussian distribution, adding complexity to the data generation process.

cs.LG↗

arXiv2025

Efficient Robust Conformal Prediction via Lipschitz-Bounded Networks

Conformal Prediction (CP) has proven to be an effective post-hoc method for improving the trustworthiness of neural networks by providing prediction sets with finite-sample guarantees. However, under adversarial attacks, classical conformal guarantees do not hold anymore: this problem is addressed in the field of Robust Conformal Prediction. Several methods have been proposed to provide robust CP sets with guarantees under adversarial perturbations, but, for large scale problems, these sets are either too large or the methods are too computationally demanding to be deployed in real life scenarios. In this work, we propose a new method that leverages Lipschitz-bounded networks to precisely and efficiently estimate robust CP sets. When combined with a 1-Lipschitz robust network, we demonstrate that our lip-rcp method outperforms state-of-the-art results in both the size of the robust CP sets and computational efficiency in medium and large-scale scenarios such as ImageNet. Taking a different angle, we also study vanilla CP under attack, and derive new worst-case coverage bounds of vanilla CP sets, which are valid simultaneously for all adversarial attack levels. Our lip-rcp method makes this second approach as efficient as vanilla CP while also allowing robustness guarantees.

cs.LG↗

arXiv2025

An Adaptive Orthogonal Convolution Scheme for Efficient and Flexible CNN Architectures

Orthogonal convolutional layers are valuable components in multiple areas of machine learning, such as adversarial robustness, normalizing flows, GANs, and Lipschitz-constrained models. Their ability to preserve norms and ensure stable gradient propagation makes them valuable for a large range of problems. Despite their promise, the deployment of orthogonal convolution in large-scale applications is a significant challenge due to computational overhead and limited support for modern features like strides, dilations, group convolutions, and transposed convolutions. In this paper, we introduce AOC (Adaptative Orthogonal Convolution), a scalable method that extends a previous method (BCOP), effectively overcoming existing limitations in the construction of orthogonal convolutions. This advancement unlocks the construction of architectures that were previously considered impractical. We demonstrate through our experiments that our method produces expressive models that become increasingly efficient as they scale. To foster further advancement, we provide an open-source python package implementing this method, called Orthogonium ( https://github.com/deel-ai/orthogonium ) .

cs.AI↗

arXiv2023

DP-SGD Without Clipping: The Lipschitz Neural Network Way

State-of-the-art approaches for training Differentially Private (DP) Deep Neural Networks (DNN) face difficulties to estimate tight bounds on the sensitivity of the network's layers, and instead rely on a process of per-sample gradient clipping. This clipping process not only biases the direction of gradients but also proves costly both in memory consumption and in computation. To provide sensitivity bounds and bypass the drawbacks of the clipping process, we propose to rely on Lipschitz constrained networks. Our theoretical analysis reveals an unexplored link between the Lipschitz constant with respect to their input and the one with respect to their parameters. By bounding the Lipschitz constant of each layer with respect to its parameters, we prove that we can train these networks with privacy guarantees. Our analysis not only allows the computation of the aforementioned sensitivities at scale, but also provides guidance on how to maximize the gradient-to-noise ratio for fixed privacy guarantees. The code has been released as a Python package available at https://github.com/Algue-Rythme/lip-dp

cs.LG↗

arXiv2023

Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks

We propose a new method, dubbed One Class Signed Distance Function (OCSDF), to perform One Class Classification (OCC) by provably learning the Signed Distance Function (SDF) to the boundary of the support of any distribution. The distance to the support can be interpreted as a normality score, and its approximation using 1-Lipschitz neural networks provides robustness bounds against $l2$ adversarial attacks, an under-explored weakness of deep learning-based OCC algorithms. As a result, OCSDF comes with a new metric, certified AUROC, that can be computed at the same cost as any classical AUROC. We show that OCSDF is competitive against concurrent methods on tabular and image data while being way more robust to adversarial attacks, illustrating its theoretical properties. Finally, as exploratory research perspectives, we theoretically and empirically show how OCSDF connects OCC with image generation and implicit neural surface parametrization. Our code is available at https://github.com/Algue-Rythme/OneClassMetricLearning

cs.LG↗

arXiv2022

On the explainable properties of 1-Lipschitz Neural Networks: An Optimal Transport Perspective

Input gradients have a pivotal role in a variety of applications, including adversarial attack algorithms for evaluating model robustness, explainable AI techniques for generating Saliency Maps, and counterfactual explanations.However, Saliency Maps generated by traditional neural networks are often noisy and provide limited insights. In this paper, we demonstrate that, on the contrary, the Saliency Maps of 1-Lipschitz neural networks, learned with the dual loss of an optimal transportation problem, exhibit desirable XAI properties:They are highly concentrated on the essential parts of the image with low noise, significantly outperforming state-of-the-art explanation approaches across various models and metrics. We also prove that these maps align unprecedentedly well with human explanations on ImageNet.To explain the particularly beneficial properties of the Saliency Map for such models, we prove this gradient encodes both the direction of the transportation plan and the direction towards the nearest adversarial attack. Following the gradient down to the decision boundary is no longer considered an adversarial attack, but rather a counterfactual explanation that explicitly transports the input from one class to another. Thus, Learning with such a loss jointly optimizes the classification objective and the alignment of the gradient, i.e. the Saliency Map, to the transportation plan direction.These networks were previously known to be certifiably robust by design, and we demonstrate that they scale well for large problems and models, and are tailored for explainability using a fast and straightforward method.

cs.AI↗

arXiv2022

Precipitaion Nowcasting using Deep Neural Network

Precipitation nowcasting is of great importance for weather forecast users, for activities ranging from outdoor activities and sports competitions to airport traffic management. In contrast to long-term precipitation forecasts which are traditionally obtained from numerical models, precipitation nowcasting needs to be very fast. It is therefore more challenging to obtain because of this time constraint. Recently, many machine learning based methods had been proposed. We propose the use three popular deep learning models (U-net, ConvLSTM and SVG-LP) trained on two-dimensional precipitation maps for precipitation nowcasting. We proposed an algorithm for patch extraction to obtain high resolution precipitation maps. We proposed a loss function to solve the blurry image issue and to reduce the influence of zero value pixels in precipitation maps.

cs.LG↗

arXiv2021

Achieving robustness in classification using optimal transport with hinge regularization

Adversarial examples have pointed out Deep Neural Networks vulnerability to small local noise. It has been shown that constraining their Lipschitz constant should enhance robustness, but make them harder to learn with classical loss functions. We propose a new framework for binary classification, based on optimal transport, which integrates this Lipschitz constraint as a theoretical requirement. We propose to learn 1-Lipschitz networks using a new loss that is an hinge regularized version of the Kantorovich-Rubinstein dual formulation for the Wasserstein distance estimation. This loss function has a direct interpretation in terms of adversarial robustness together with certifiable robustness bound. We also prove that this hinge regularized version is still the dual formulation of an optimal transportation problem, and has a solution. We also establish several geometrical properties of this optimal solution, and extend the approach to multi-class problems. Experiments show that the proposed approach provides the expected guarantees in terms of robustness without any significant accuracy drop. The adversarial examples, on the proposed models, visibly and meaningfully change the input providing an explanation for the classification.

cs.LG↗

arXiv2021

Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networks

Lipschitz constrained networks have gathered considerable attention in the deep learning community, with usages ranging from Wasserstein distance estimation to the training of certifiably robust classifiers. However they remain commonly considered as less accurate, and their properties in learning are still not fully understood. In this paper we clarify the matter: when it comes to classification 1-Lipschitz neural networks enjoy several advantages over their unconstrained counterpart. First, we show that these networks are as accurate as classical ones, and can fit arbitrarily difficult boundaries. Then, relying on a robustness metric that reflects operational needs we characterize the most robust classifier: the WGAN discriminator. Next, we show that 1-Lipschitz neural networks generalize well under milder assumptions. Finally, we show that hyper-parameters of the loss are crucial for controlling the accuracy-robustness trade-off. We conclude that they exhibit appealing properties to pave the way toward provably accurate, and provably robust neural networks.

cs.LG↗

arXiv2020

A Hölderian backtracking method for min-max and min-min problems

We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method applicable to many optimization problems. Our approach takes advantage of hidden regularity properties and allows us to devise a simple algorithm of ridge type. An original feature of our method is to come with automatic step size adaptation which departs from the usual overly cautious backtracking methods. In a general framework, we provide convergence theoretical guarantees and rates. We apply our findings on simple GAN problems obtaining promising numerical results.

cs.LG↗

arXiv2020

ARPEGE Cloud Cover Forecast Post-Processing with Convolutional Neural Network

Cloud cover is crucial information for many applications such as planning land observation missions from space. It remains however a challenging variable to forecast, and Numerical Weather Prediction (NWP) models suffer from significant biases, hence justifying the use of statistical post-processing techniques. In this study, ARPEGE (Météo-France global NWP) cloud cover is post-processed using a convolutional neural network (CNN). CNN is the most popular machine learning tool to deal with images. In our case, CNN allows the integration of spatial information contained in NWP outputs. We use a gridded cloud cover product derived from satellite observations over Europe as ground truth, and predictors are spatial fields of various variables produced by ARPEGE at the corresponding lead time. We show that a simple U-Net architecture produces significant improvements over Europe. Moreover, the U-Net outclasses more traditional machine learning methods used operationally such as a random forest and a logistic quantile regression. We introduced a weighting predictor layer prior to the traditional U-Net architecture which produces a ranking of predictors by importance, facilitating the interpretation of the results. Using $N$ predictors, only $N$ additional weights are trained which does not impact the computational time, representing a huge advantage compared to traditional methods of ranking (permutation importance, sequential selection, ...).

physics.ao-ph↗

arXiv2020

Surrogate Models for Rainfall Nowcasting

Nowcasting (or short-term weather forecasting) is particularly important in the case of extreme events as it helps prevent human losses. Many of our activities, however, also depend on the weather. Therefore, nowcasting has shown to be useful in many different domains. Currently, immediate rainfall forecasts in France are calculated using the Arome-NWC model developed by Météo-France, which is a complex physical model. Arome-NWC forecasts are stored with a 15 minute time interval. A higher time resolution is, however, desirable for other meteorological applications. Complex model calculations, such as Arome-NWC, can be very expensive and time consuming. A surrogate model aims at producing results which are very close to the ones obtained using a complex model, but with largely reduced calculation times. Building a surrogate model requires only a few calculations with the real model. Once the surrogate model is built, further calculations can be quickly realized. In this study, we propose to build surrogate models for immediate rainfall forecasts with two different approaches: combining Proper Orthogonal Decomposition (POD) and Kriging, or combining POD and Random Forest (RF). We show that results obtained with our surrogate models are not only close to the ones obtained by Arome-NWC, but they also have a higher time resolution (1 minute) with a reduced calculation time.

physics.comp-ph↗

arXiv2020

Dyslexia and Dysgraphia prediction: A new machine learning approach

Learning disabilities like dysgraphia, dyslexia, dyspraxia, etc. interfere with academic achievements but have also long terms consequences beyond the academic time. It is widely admitted that between 5% to 10% of the world population is subject to this kind of disabilities. For assessing such disabilities in early childhood, children have to solve a battery of tests. Human experts score these tests, and decide whether the children require specific education strategy on the basis of their marks. The assessment can be lengthy, costly and emotionally painful. In this paper, we investigate how Artificial Intelligence can help in automating this assessment. Gathering a dataset of handwritten text pictures and audio recordings, both from standard children and from dyslexic and/or dysgraphic children, we apply machine learning techniques for classification in order to analyze the differences between dyslexic/dysgraphic and standard readers/writers and to build a model. The model is trained on simple features obtained by analysing the pictures and the audio files. Our preliminary implementation shows relatively high performances on the dataset we have used. This suggests the possibility to screen dyslexia and dysgraphia via non-invasive methods in an accurate way as soon as enough data are available.

cs.OH↗