Caroline Chaux

Mai Quyen Pham, Laurent Duval, Caroline Chaux et al.

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data.

Elizabeth Z. C. Tan, Caroline Chaux, Emmanuel Soubies et al.

We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating projection algorithm which aims to solve RPCA in its nonconvex form. The proposed procedure combines benefits of deep neural networks and the interpretability of the original algorithm and it automatically learns hyperparameters. We demonstrate the unrolled algorithm's effectiveness on synthetic datasets and also on a face modeling problem, where it leads to both better numerical and visual performances.

Mimoun Mohamed, François Malgouyres, Valentin Emiya et al.

The {\it straight-through estimator} (STE) is commonly used to optimize quantized neural networks, yet its contexts of effective performance are still unclear despite empirical successes.To make a step forward in this comprehension, we apply STE to a well-understood problem: {\it sparse support recovery}. We introduce the {\it Support Exploration Algorithm} (SEA), a novel algorithm promoting sparsity, and we analyze its performance in support recovery (a.k.a. model selection) problems. SEA explores more supports than the state-of-the-art, leading to superior performance in experiments, especially when the columns of $A$ are strongly coherent.The theoretical analysis considers recovery guarantees when the linear measurements matrix $A$ satisfies the {\it Restricted Isometry Property} (RIP).The sufficient conditions of recovery are comparable but more stringent than those of the state-of-the-art in sparse support recovery. Their significance lies mainly in their applicability to an instance of the STE.

Maxime Meyer, Mario Michelessa, Caroline Chaux et al.

We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on the length of the prompt, which we show empirically to be tight up to a factor less than 10, across architectures and model sizes. Our analysis also provides a theoretical explanation for previously observed empirical failures of transformers on simple sequence tasks, such as copying and cramming. Formally, we prove that (i) the maximal length of accessible sequences (those that the transformer can output for some prompt) grows linearly with the prompt length, (ii) beyond a critical threshold, the proportion of accessible sequences decays exponentially with sequence length, and (iii) the linear coefficient relating prompt length to accessible sequence length admits a theoretical upper bound. Notably, these results hold even with unbounded context and computation time.

Elad Sofer, Tomer Shaked, Caroline Chaux et al.

Machine learning (ML) models are often sensitive to carefully crafted yet seemingly unnoticeable perturbations. Such adversarial examples are considered to be a property of ML models, often associated with their black-box operation and sensitivity to features learned from data. This work examines the adversarial sensitivity of non-learned decision rules, and particularly of iterative optimizers. Our analysis is inspired by the recent developments in deep unfolding, which cast such optimizers as ML models. We show that non-learned iterative optimizers share the sensitivity to adversarial examples of ML models, and that attacking iterative optimizers effectively alters the optimization objective surface in a manner that modifies the minima sought. We then leverage the ability to cast iteration-limited optimizers as ML models to enhance robustness via adversarial training. For a class of proximal gradient optimizers, we rigorously prove how their learning affects adversarial sensitivity. We numerically back our findings, showing the vulnerability of various optimizers, as well as the robustness induced by unfolding and adversarial training.

Maxime Meyer, Mario Michelessa, Caroline Chaux et al.

Despite the empirical success of prompt tuning in adapting pretrained language models to new tasks, theoretical analyses of its capabilities remain limited. Existing theoretical work primarily addresses universal approximation properties, demonstrating results comparable to standard weight tuning. In this paper, we explore a different aspect of the theory of transformers: the memorization capability of prompt tuning. We provide two principal theoretical contributions. First, we prove that the amount of information memorized by a transformer cannot scale faster than linearly with the prompt length. Second, and more importantly, we present the first formal proof of a phenomenon empirically observed in large language models: performance degradation in transformers with extended contexts. We rigorously demonstrate that transformers inherently have limited memory, constraining the amount of information they can retain, regardless of the context size. This finding offers a fundamental understanding of the intrinsic limitations of transformer architectures, particularly their ability to handle long sequences.

Caroline Chaux, Laurent Duval, Jean-Christophe Pesquet

We propose a 2D generalization to the $M$-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (\textit{i}) the construction of the dual basis and (\textit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the $M$-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed $M$-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various $M$-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.