arXiv subjects

Yann Chevaleyre

Publications and source records attributed to Yann Chevaleyre.

33 records · Page 2Linked to original sources

arXiv2022

Towards Evading the Limits of Randomized Smoothing: A Theoretical Analysis

Randomized smoothing is the dominant standard for provable defenses against adversarial examples. Nevertheless, this method has recently been proven to suffer from important information theoretic limitations. In this paper, we argue that these limitations are not intrinsic, but merely a byproduct of current certification methods. We first show that these certificates use too little information about the classifier, and are in particular blind to the local curvature of the decision boundary. This leads to severely sub-optimal robustness guarantees as the dimension of the problem increases. We then show that it is theoretically possible to bypass this issue by collecting more information about the classifier. More precisely, we show that it is possible to approximate the optimal certificate with arbitrary precision, by probing the decision boundary with several noise distributions. Since this process is executed at certification time rather than at test time, it entails no loss in natural accuracy while enhancing the quality of the certificates. This result fosters further research on classifier-specific certification and demonstrates that randomized smoothing is still worth investigating. Although classifier-specific certification may induce more computational cost, we also provide some theoretical insight on how to mitigate it.

cs.LG↗

arXiv2022

Towards Consistency in Adversarial Classification

In this paper, we study the problem of consistency in the context of adversarial examples. Specifically, we tackle the following question: can surrogate losses still be used as a proxy for minimizing the $0/1$ loss in the presence of an adversary that alters the inputs at test-time? Different from the standard classification task, this question cannot be reduced to a point-wise minimization problem, and calibration needs not to be sufficient to ensure consistency. In this paper, we expose some pathological behaviors specific to the adversarial problem, and show that no convex surrogate loss can be consistent or calibrated in this context. It is therefore necessary to design another class of surrogate functions that can be used to solve the adversarial consistency issue. As a first step towards designing such a class, we identify sufficient and necessary conditions for a surrogate loss to be calibrated in both the adversarial and standard settings. Finally, we give some directions for building a class of losses that could be consistent in the adversarial framework.

cs.LG↗

arXiv2021

Asymptotic convergence rates for averaging strategies

Parallel black box optimization consists in estimating the optimum of a function using $λ$ parallel evaluations of $f$. Averaging the $μ$ best individuals among the $λ$ evaluations is known to provide better estimates of the optimum of a function than just picking up the best. In continuous domains, this averaging is typically just based on (possibly weighted) arithmetic means. Previous theoretical results were based on quadratic objective functions. In this paper, we extend the results to a wide class of functions, containing three times continuously differentiable functions with unique optimum. We prove formal rate of convergences and show they are indeed better than pure random search asymptotically in $λ$. We validate our theoretical findings with experiments on some standard black box functions.

math.OC↗

arXiv2021

Best Arm Identification in Graphical Bilinear Bandits

We introduce a new graphical bilinear bandit problem where a learner (or a \emph{central entity}) allocates arms to the nodes of a graph and observes for each edge a noisy bilinear reward representing the interaction between the two end nodes. We study the best arm identification problem in which the learner wants to find the graph allocation maximizing the sum of the bilinear rewards. By efficiently exploiting the geometry of this bandit problem, we propose a \emph{decentralized} allocation strategy based on random sampling with theoretical guarantees. In particular, we characterize the influence of the graph structure (e.g. star, complete or circle) on the convergence rate and propose empirical experiments that confirm this dependency.

cs.LG↗

arXiv2021

On the robustness of randomized classifiers to adversarial examples

This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of statistical learning theory and information theory. To this aim, we introduce a new notion of robustness for randomized classifiers, enforcing local Lipschitzness using probability metrics. Equipped with this definition, we make two new contributions. The first one consists in devising a new upper bound on the adversarial generalization gap of randomized classifiers. More precisely, we devise bounds on the generalization gap and the adversarial gap (\emph{i.e.} the gap between the risk and the worst-case risk under attack) of randomized classifiers. The second contribution presents a yet simple but efficient noise injection method to design robust randomized classifiers. We show that our results are applicable to a wide range of machine learning models under mild hypotheses. We further corroborate our findings with experimental results using deep neural networks on standard image datasets, namely CIFAR-10 and CIFAR-100. All robust models we trained models can simultaneously achieve state-of-the-art accuracy (over $0.82$ clean accuracy on CIFAR-10) and enjoy \emph{guaranteed} robust accuracy bounds ($0.45$ against $\ell_2$ adversaries with magnitude $0.5$ on CIFAR-10).

cs.LG↗

arXiv2021

Mixed Nash Equilibria in the Adversarial Examples Game

This paper tackles the problem of adversarial examples from a game theoretic point of view. We study the open question of the existence of mixed Nash equilibria in the zero-sum game formed by the attacker and the classifier. While previous works usually allow only one player to use randomized strategies, we show the necessity of considering randomization for both the classifier and the attacker. We demonstrate that this game has no duality gap, meaning that it always admits approximate Nash equilibria. We also provide the first optimization algorithms to learn a mixture of classifiers that approximately realizes the value of this game, \emph{i.e.} procedures to build an optimally robust randomized classifier.

cs.GT↗

arXiv2021

Randomization matters. How to defend against strong adversarial attacks

Is there a classifier that ensures optimal robustness against all adversarial attacks? This paper answers this question by adopting a game-theoretic point of view. We show that adversarial attacks and defenses form an infinite zero-sum game where classical results (e.g. Sion theorem) do not apply. We demonstrate the non-existence of a Nash equilibrium in our game when the classifier and the Adversary are both deterministic, hence giving a negative answer to the above question in the deterministic regime. Nonetheless, the question remains open in the randomized regime. We tackle this problem by showing that, undermild conditions on the dataset distribution, any deterministic classifier can be outperformed by a randomized one. This gives arguments for using randomization, and leads us to a new algorithm for building randomized classifiers that are robust to strong adversarial attacks. Empirical results validate our theoretical analysis, and show that our defense method considerably outperforms Adversarial Training against state-of-the-art attacks.

cs.LG↗

arXiv2020

On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization, robustness against adversarial examples, etc. However, computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. Recent attempts from the literature introduce upper bounds to approximate this constant that are either efficient but loose or accurate but computationally expensive. In this work, by leveraging the theory of Toeplitz matrices, we introduce a new upper bound for convolutional layers that is both tight and easy to compute. Based on this result we devise an algorithm to train Lipschitz regularized Convolutional Neural Networks.

cs.LG↗

arXiv2020

On averaging the best samples in evolutionary computation

Choosing the right selection rate is a long standing issue in evolutionary computation. In the continuous unconstrained case, we prove mathematically that a single parent $μ=1$ leads to a sub-optimal simple regret in the case of the sphere function. We provide a theoretically-based selection rate $μ/λ$ that leads to better progress rates. With our choice of selection rate, we get a provable regret of order $O(λ^{-1})$ which has to be compared with $O(λ^{-2/d})$ in the case where $μ=1$. We complete our study with experiments to confirm our theoretical claims.

cs.NE↗

arXiv2020

Online Trajectory Planning Through Combined Trajectory Optimization and Function Approximation: Application to the Exoskeleton Atalante

Autonomous robots require online trajectory planning capability to operate in the real world. Efficient offline trajectory planning methods already exist, but are computationally demanding, preventing their use online. In this paper, we present a novel algorithm called Guided Trajectory Learning that learns a function approximation of solutions computed through trajectory optimization while ensuring accurate and reliable predictions. This function approximation is then used online to generate trajectories. This algorithm is designed to be easy to implement, and practical since it does not require massive computing power. It is readily applicable to any robotics systems and effortless to set up on real hardware since robust control strategies are usually already available. We demonstrate the computational performance of our algorithm on flat-foot walking with the self-balanced exoskeleton Atalante.

cs.RO↗

arXiv2019

Understanding and Training Deep Diagonal Circulant Neural Networks

In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we introduced principled techniques for training these models: we devise an initialization scheme and proposed a smart use of non-linearity functions in order to train deep diagonal circulant networks. Furthermore, we show that these networks outperform recently introduced deep networks with other types of structured layers. We conduct a thorough experimental study to compare the performance of deep diagonal circulant networks with state of the art models based on structured matrices and with dense models. We show that our models achieve better accuracy than other structured approaches while required 2x fewer weights as the next best approach. Finally we train deep diagonal circulant networks to build a compact and accurate models on a real world video classification dataset with over 3.8 million training examples.

cs.LG↗

arXiv2018

Training compact deep learning models for video classification using circulant matrices

In real world scenarios, model accuracy is hardly the only factor to consider. Large models consume more memory and are computationally more intensive, which makes them difficult to train and to deploy, especially on mobile devices. In this paper, we build on recent results at the crossroads of Linear Algebra and Deep Learning which demonstrate how imposing a structure on large weight matrices can be used to reduce the size of the model. We propose very compact models for video classification based on state-of-the-art network architectures such as Deep Bag-of-Frames, NetVLAD and NetFisherVectors. We then conduct thorough experiments using the large YouTube-8M video classification dataset. As we will show, the circulant DBoF embedding achieves an excellent trade-off between size and accuracy.

cs.CV↗

arXiv2018

Disease Classification in Metagenomics with 2D Embeddings and Deep Learning

Deep learning (DL) techniques have shown unprecedented success when applied to images, waveforms, and text. Generally, when the sample size ($N$) is much bigger than the number of features ($d$), DL often outperforms other machine learning (ML) techniques, often through the use of Convolutional Neural Networks (CNNs). However, in many bioinformatics fields (including metagenomics), we encounter the opposite situation where $d$ is significantly greater than $N$. In these situations, applying DL techniques would lead to severe overfitting. Here we aim to improve classification of various diseases with metagenomic data through the use of CNNs. For this we proposed to represent metagenomic data as images. The proposed Met2Img approach relies on taxonomic and t-SNE embeddings to transform abundance data into "synthetic images". We applied our approach to twelve benchmark data sets including more than 1400 metagenomic samples. Our results show significant improvements over the state-of-the-art algorithms (Random Forest (RF), Support Vector Machine (SVM)). We observe that the integration of phylogenetic information alongside abundance data improves classification. The proposed approach is not only important in classification setting but also allows to visualize complex metagenomic data. The Met2Img is implemented in Python.

cs.CV↗

arXiv2017

Deep Learning for Metagenomic Data: using 2D Embeddings and Convolutional Neural Networks

Deep learning (DL) techniques have had unprecedented success when applied to images, waveforms, and texts to cite a few. In general, when the sample size (N) is much greater than the number of features (d), DL outperforms previous machine learning (ML) techniques, often through the use of convolution neural networks (CNNs). However, in many bioinformatics ML tasks, we encounter the opposite situation where d is greater than N. In these situations, applying DL techniques (such as feed-forward networks) would lead to severe overfitting. Thus, sparse ML techniques (such as LASSO e.g.) usually yield the best results on these tasks. In this paper, we show how to apply CNNs on data which do not have originally an image structure (in particular on metagenomic data). Our first contribution is to show how to map metagenomic data in a meaningful way to 1D or 2D images. Based on this representation, we then apply a CNN, with the aim of predicting various diseases. The proposed approach is applied on six different datasets including in total over 1000 samples from various diseases. This approach could be a promising one for prediction tasks in the bioinformatics field.

cs.CV↗

arXiv2011

New Candidates Welcome! Possible Winners with respect to the Addition of New Candidates

In voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number $k$ of new candidates will be added. We give a computational study of this problem, focusing on scoring rules, and we provide a formal comparison with related problems such as control via adding candidates or cloning.

cs.AI↗