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Researcher profile

Julien Mairal

Julien Mairal contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningComputer Visionmath.OCeess.IVNeural and Evolutionary Computing

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Published work

16 published item(s)

preprint2026arXiv

Beyond MMSE: Enhancing PnP Restoration with ProxiMAP

Plug-and-Play (PnP) methods have become standard tools for solving imaging inverse problems by replacing the intractable maximum a posteriori (MAP) denoiser with the MMSE one. While this mismatch has been widely treated as unavoidable, recent works have sought to close this gap by targeting the MAP with diffusion-model scores. We show this is problematic in practice: learned scores do not match the true ones, so MAP-targeting iterations converge to cartoon-like images rather than realistic ones, and better results are obtained by stopping short of convergence. We turn this observation into a design principle and introduce ProxiMAP, an iterative MAP approximation whose noise schedule keeps the iterate's residual noise matched to the denoiser's training noise. This keeps the denoiser in-distribution where its score is reliable, and yields implicit early stopping that avoids the failure mode above. ProxiMAP is a modular drop-in replacement for MMSE denoisers in standard PnP algorithms and consistently sharpens reconstructions across deblurring, inpainting, super-resolution, and phase retrieval. Building on the same principle, we propose a hybrid variant that applies ProxiMAP only in the late iterations of PnP, where the denoiser is most reliable -- matching or exceeding the full-replacement variant at a fraction of the cost.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Amortized Implicit Differentiation for Stochastic Bilevel Optimization

We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit differentiation and we exploit a warm-start strategy to amortize the estimation of the exact gradient. We then introduce a unified theoretical framework inspired by the study of singularly perturbed systems (Habets, 1974) to analyze such amortized algorithms. By using this framework, our analysis shows these algorithms to match the computational complexity of oracle methods that have access to an unbiased estimate of the gradient, thus outperforming many existing results for bilevel optimization. We illustrate these findings on synthetic experiments and demonstrate the efficiency of these algorithms on hyper-parameter optimization experiments involving several thousands of variables.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Efficient Kernel UCB for Contextual Bandits

In this paper, we tackle the computational efficiency of kernelized UCB algorithms in contextual bandits. While standard methods require a O(CT^3) complexity where T is the horizon and the constant C is related to optimizing the UCB rule, we propose an efficient contextual algorithm for large-scale problems. Specifically, our method relies on incremental Nystrom approximations of the joint kernel embedding of contexts and actions. This allows us to achieve a complexity of O(CTm^2) where m is the number of Nystrom points. To recover the same regret as the standard kernelized UCB algorithm, m needs to be of order of the effective dimension of the problem, which is at most O(\sqrt(T)) and nearly constant in some cases.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

High Dynamic Range and Super-Resolution from Raw Image Bursts

Photographs captured by smartphones and mid-range cameras have limited spatial resolution and dynamic range, with noisy response in underexposed regions and color artefacts in saturated areas. This paper introduces the first approach (to the best of our knowledge) to the reconstruction of high-resolution, high-dynamic range color images from raw photographic bursts captured by a handheld camera with exposure bracketing. This method uses a physically-accurate model of image formation to combine an iterative optimization algorithm for solving the corresponding inverse problem with a learned image representation for robust alignment and a learned natural image prior. The proposed algorithm is fast, with low memory requirements compared to state-of-the-art learning-based approaches to image restoration, and features that are learned end to end from synthetic yet realistic data. Extensive experiments demonstrate its excellent performance with super-resolution factors of up to $\times 4$ on real photographs taken in the wild with hand-held cameras, and high robustness to low-light conditions, noise, camera shake, and moderate object motion.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On the Benefits of Large Learning Rates for Kernel Methods

This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that a phenomenon can be precisely characterized in the context of kernel methods, even though the resulting optimization problem is convex. Specifically, we consider the minimization of a quadratic objective in a separable Hilbert space, and show that with early stopping, the choice of learning rate influences the spectral decomposition of the obtained solution on the Hessian's eigenvectors. This extends an intuition described by Nakkiran (2020) on a two-dimensional toy problem to realistic learning scenarios such as kernel ridge regression. While large learning rates may be proven beneficial as soon as there is a mismatch between the train and test objectives, we further explain why it already occurs in classification tasks without assuming any particular mismatch between train and test data distributions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Self Supervised Learning for Few Shot Hyperspectral Image Classification

Deep learning has proven to be a very effective approach for Hyperspectral Image (HSI) classification. However, deep neural networks require large annotated datasets to generalize well. This limits the applicability of deep learning for HSI classification, where manually labelling thousands of pixels for every scene is impractical. In this paper, we propose to leverage Self Supervised Learning (SSL) for HSI classification. We show that by pre-training an encoder on unlabeled pixels using Barlow-Twins, a state-of-the-art SSL algorithm, we can obtain accurate models with a handful of labels. Experimental results demonstrate that this approach significantly outperforms vanilla supervised learning.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Self-Supervised Models are Continual Learners

Self-supervised models have been shown to produce comparable or better visual representations than their supervised counterparts when trained offline on unlabeled data at scale. However, their efficacy is catastrophically reduced in a Continual Learning (CL) scenario where data is presented to the model sequentially. In this paper, we show that self-supervised loss functions can be seamlessly converted into distillation mechanisms for CL by adding a predictor network that maps the current state of the representations to their past state. This enables us to devise a framework for Continual self-supervised visual representation Learning that (i) significantly improves the quality of the learned representations, (ii) is compatible with several state-of-the-art self-supervised objectives, and (iii) needs little to no hyperparameter tuning. We demonstrate the effectiveness of our approach empirically by training six popular self-supervised models in various CL settings.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

The Spectral Bias of Polynomial Neural Networks

Polynomial neural networks (PNNs) have been recently shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies have revealed that neural networks demonstrate a $\textit{spectral bias}$ towards low-frequency functions, which yields faster learning of low-frequency components during training. Inspired by such studies, we conduct a spectral analysis of the Neural Tangent Kernel (NTK) of PNNs. We find that the $Π$-Net family, i.e., a recently proposed parametrization of PNNs, speeds up the learning of the higher frequencies. We verify the theoretical bias through extensive experiments. We expect our analysis to provide novel insights into designing architectures and learning frameworks by incorporating multiplicative interactions via polynomials.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention

We address the problem of learning on sets of features, motivated by the need of performing pooling operations in long biological sequences of varying sizes, with long-range dependencies, and possibly few labeled data. To address this challenging task, we introduce a parametrized representation of fixed size, which embeds and then aggregates elements from a given input set according to the optimal transport plan between the set and a trainable reference. Our approach scales to large datasets and allows end-to-end training of the reference, while also providing a simple unsupervised learning mechanism with small computational cost. Our aggregation technique admits two useful interpretations: it may be seen as a mechanism related to attention layers in neural networks, or it may be seen as a scalable surrogate of a classical optimal transport-based kernel. We experimentally demonstrate the effectiveness of our approach on biological sequences, achieving state-of-the-art results for protein fold recognition and detection of chromatin profiles tasks, and, as a proof of concept, we show promising results for processing natural language sequences. We provide an open-source implementation of our embedding that can be used alone or as a module in larger learning models at https://github.com/claying/OTK.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Unsupervised Learning of Visual Features by Contrasting Cluster Assignments

Unsupervised image representations have significantly reduced the gap with supervised pretraining, notably with the recent achievements of contrastive learning methods. These contrastive methods typically work online and rely on a large number of explicit pairwise feature comparisons, which is computationally challenging. In this paper, we propose an online algorithm, SwAV, that takes advantage of contrastive methods without requiring to compute pairwise comparisons. Specifically, our method simultaneously clusters the data while enforcing consistency between cluster assignments produced for different augmentations (or views) of the same image, instead of comparing features directly as in contrastive learning. Simply put, we use a swapped prediction mechanism where we predict the cluster assignment of a view from the representation of another view. Our method can be trained with large and small batches and can scale to unlimited amounts of data. Compared to previous contrastive methods, our method is more memory efficient since it does not require a large memory bank or a special momentum network. In addition, we also propose a new data augmentation strategy, multi-crop, that uses a mix of views with different resolutions in place of two full-resolution views, without increasing the memory or compute requirements much. We validate our findings by achieving 75.3% top-1 accuracy on ImageNet with ResNet-50, as well as surpassing supervised pretraining on all the considered transfer tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Convolutional Kernel Networks for Graph-Structured Data

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing graphs as a sequence of kernel feature maps, where each node carries information about local graph substructures. On the one hand, the kernel point of view offers an unsupervised, expressive, and easy-to-regularize data representation, which is useful when limited samples are available. On the other hand, our model can also be trained end-to-end on large-scale data, leading to new types of graph convolutional neural networks. We show that our method achieves competitive performance on several graph classification benchmarks, while offering simple model interpretation. Our code is freely available at https://github.com/claying/GCKN.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Estimate Sequences for Stochastic Composite Optimization: Variance Reduction, Acceleration, and Robustness to Noise

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of stochastic optimization methods as procedures that iteratively minimize a surrogate of the objective, which covers the stochastic gradient descent method and variants of the incremental approaches SAGA, SVRG, and MISO/Finito/SDCA. This point of view has several advantages: (i) we provide a simple generic proof of convergence for all of the aforementioned methods; (ii) we naturally obtain new algorithms with the same guarantees; (iii) we derive generic strategies to make these algorithms robust to stochastic noise, which is useful when data is corrupted by small random perturbations. Finally, we propose a new accelerated stochastic gradient descent algorithm and an accelerated SVRG algorithm with optimal complexity that is robust to stochastic noise.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Fully Trainable and Interpretable Non-Local Sparse Models for Image Restoration

Non-local self-similarity and sparsity principles have proven to be powerful priors for natural image modeling. We propose a novel differentiable relaxation of joint sparsity that exploits both principles and leads to a general framework for image restoration which is (1) trainable end to end, (2) fully interpretable, and (3) much more compact than competing deep learning architectures. We apply this approach to denoising, jpeg deblocking, and demosaicking, and show that, with as few as 100K parameters, its performance on several standard benchmarks is on par or better than state-of-the-art methods that may have an order of magnitude or more parameters.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Pruning Convolutional Neural Networks with Self-Supervision

Convolutional neural networks trained without supervision come close to matching performance with supervised pre-training, but sometimes at the cost of an even higher number of parameters. Extracting subnetworks from these large unsupervised convnets with preserved performance is of particular interest to make them less computationally intensive. Typical pruning methods operate during training on a task while trying to maintain the performance of the pruned network on the same task. However, in self-supervised feature learning, the training objective is agnostic on the representation transferability to downstream tasks. Thus, preserving performance for this objective does not ensure that the pruned subnetwork remains effective for solving downstream tasks. In this work, we investigate the use of standard pruning methods, developed primarily for supervised learning, for networks trained without labels (i.e. on self-supervised tasks). We show that pruned masks obtained with or without labels reach comparable performance when re-trained on labels, suggesting that pruning operates similarly for self-supervised and supervised learning. Interestingly, we also find that pruning preserves the transfer performance of self-supervised subnetwork representations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Screening Data Points in Empirical Risk Minimization via Ellipsoidal Regions and Safe Loss Functions

We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees. We derive loss functions that produce dual objectives with a sparse solution. We also show how to regularize convex losses to ensure such a dual sparsity-inducing property, and propose a general method to design screening tests for classification or regression based on ellipsoidal approximations of the optimal set. In addition to producing computational gains, our approach also allows us to compress a dataset into a subset of representative points.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Selecting Relevant Features from a Multi-domain Representation for Few-shot Classification

Popular approaches for few-shot classification consist of first learning a generic data representation based on a large annotated dataset, before adapting the representation to new classes given only a few labeled samples. In this work, we propose a new strategy based on feature selection, which is both simpler and more effective than previous feature adaptation approaches. First, we obtain a multi-domain representation by training a set of semantically different feature extractors. Then, given a few-shot learning task, we use our multi-domain feature bank to automatically select the most relevant representations. We show that a simple non-parametric classifier built on top of such features produces high accuracy and generalizes to domains never seen during training, which leads to state-of-the-art results on MetaDataset and improved accuracy on mini-ImageNet.

0 citations0 reviewsNo code linkedOpen access