arXiv subjects

Quentin Barthélemy

Publications and source records attributed to Quentin Barthélemy.

At least 19 recordsLinked to original sources

arXiv2026

UNet-AF: Alias-free UNet architectures

The simplicity and effectiveness of UNet architectures make them ubiquitous in image restoration, segmentation, and diffusion models. They are often assumed to be equivariant to translations, yet they traditionally consist of layers that are known to be prone to aliasing, which hinders their equivariance in practice. To overcome this limitation, we show how to build sub-pixel translation-equivariant UNet architectures by appropriately choosing their main components (convolution, pooling, downsampling, activation, and normalization layers) to be alias-free. We evaluate the proposed equivariant architectures against non-equivariant baselines on image restoration tasks and observe competitive performance with a significant increase in measured equivariance. Through extensive ablation studies, we also demonstrate the importance of every architectural choice to achieve high equivariance. Our implementation is available at https://github.com/jscanvic/UNet-AF

cs.CV↗

arXiv2026

Anomalously high quasiparticle thermal conductivity in the underdoped cuprate superconductor HgBa$_{2}$CuO$_{4+δ}$

The single-layer cuprate superconductor HgBa$_{2}$CuO$_{4+δ}$ (Hg1201) is an ideal candidate for investigating many properties of cuprates with minimal disorder and without the complication of multiple CuO$_2$ layers. Here we measure the in-plane longitudinal thermal conductivity $κ$ of underdoped Hg1201 ($T_c$ = 76 K, $p$ = 0.11) at dilution refrigerator temperatures to extract the nodal quasiparticle velocity ratio $v_F/v_Δ$. Assuming contributions from only a single line node per quadrant on the Fermi surface leads to a value of $v_F/v_Δ$ = $23 \pm 3$, anomalously large compared to other cuprates at similar dopings. In conjunction with the anomalously high quasiparticle specific heat of Hg1201 in the normal state reported previously at a similar doping, this points to more than one Fermi surface sheet crossing the nodal line, suggesting the presence of more than the single small electron pocket detected by quantum oscillations.

cond-mat.supr-con↗

arXiv2026

Equivariant Splitting: Self-supervised learning from incomplete data

Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for training is expensive or even impossible. In this paper, we propose a new self-supervised learning strategy devised for the challenging setting where measurements are observed via a single incomplete observation model. We introduce a new definition of equivariance in the context of reconstruction networks, and show that the combination of self-supervised splitting losses and equivariant reconstruction networks results in unbiased estimates of the supervised loss. Through a series of experiments on image inpainting, accelerated magnetic resonance imaging, sparse-view computed tomography, and compressive sensing, we demonstrate that the proposed loss achieves state-of-the-art performance in settings with highly rank-deficient forward models. The code is available at https://github.com/vsechaud/Equivariant-Splitting

cs.CV↗

arXiv2025

Improved Riemannian potato field: an Automatic Artifact Rejection Method for EEG

Electroencephalography (EEG) signal cleaning has long been a critical challenge in the research community. The presence of artifacts can significantly degrade EEG data quality, complicating analysis and potentially leading to erroneous interpretations. While various artifact rejection methods have been proposed, the gold standard remains manual visual inspection by human experts-a process that is time-consuming, subjective, and impractical for large-scale EEG studies. Existing techniques are often hindered by a strong reliance on manual hyperparameter tuning, sensitivity to outliers, and high computational costs. In this paper, we introduce the improved Riemannian Potato Field (iRPF), a fast and fully automated method for EEG artifact rejection that addresses key limitations of current approaches. We evaluate iRPF against several state-of-the-art artifact rejection methods, using two publicly available EEG databases, labeled for various artifact types, comprising 226 EEG recordings. Our results demonstrate that iRPF outperforms all competitors across multiple metrics, with gains of up to 22% in recall, 102% in specificity, 54% in precision, and 24% in F1-score, compared to Isolation Forest, Autoreject, Riemannian Potato, and Riemannian Potato Field, respectively. Statistical analysis confirmed the significance of these improvements (p < 0.001) with large effect sizes (Cohen's d > 0.8) in most comparisons. Additionally, on a typical EEG recording iRPF performs artifact cleaning in under 8 milliseconds per epoch using a standard laptop, highlighting its efficiency for large-scale EEG data processing and real-time applications. iRPF offers a robust and data-driven artifact rejection solution for high-quality EEG pre-processing in brain-computer interfaces and clinical neuroimaging applications.

eess.SP↗

arXiv2025

Thermal Hall conductivity in the strongest cuprate superconductor: Estimate of the mean free path in the trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8 + δ}$

The thermal Hall conductivity of the trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ (Hg1223) - the superconductor with the highest critical temperature $T_c$ at ambient pressure - was measured at temperatures down to 2 K for three dopings in the underdoped regime ($p$ = 0.09, 0.10, 0.11). By combining a previously introduced simple model and prior theoretical results, we derive a formula for the inverse mean free path, $1 / \ell$, which allows us to estimate the mean free path of $d$-wave quasiparticles in Hg1223 below $T_c$. We find that $1 / \ell$ grows as $T^3$, in agreement with the theoretical expectation for a clean $d$-wave superconductor. Measurements were also conducted on the single layer mercury-based cuprate HgBa$_2$CuO$_{6+δ}$ (Hg1201), revealing that the mean free path in this compound is roughly half that of its three-layered counterpart at the same doping ($p$ = 0.10). This observation is be attributed to the protective role of the outer planes in Hg1223, which results in a more pristine inner plane. We also report data in an ultraclean crystal of YBa$_2$Cu$_3$O$_y$ (YBCO) with full oxygen content $p$ = 0.18, believed to be the cleanest of any cuprate, and find that $\ell$ is not longer than in Hg1223.

cond-mat.supr-con↗

arXiv2025

Translation-Equivariance of Normalization Layers and Aliasing in Convolutional Neural Networks

The design of convolutional neural architectures that are exactly equivariant to continuous translations is an active field of research. It promises to benefit scientific computing, notably by making existing imaging systems more physically accurate. Most efforts focus on the design of downsampling/pooling layers, upsampling layers and activation functions, but little attention is dedicated to normalization layers. In this work, we present a novel theoretical framework for understanding the equivariance of normalization layers to discrete shifts and continuous translations. We also determine necessary and sufficient conditions for normalization layers to be equivariant in terms of the dimensions they operate on. Using real feature maps from ResNet-18 and ImageNet, we test those theoretical results empirically and find that they are consistent with our predictions.

cs.CV↗

arXiv2025

Bridging the Theoretical Gap in Randomized Smoothing

Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper introduces a new framework that bridges this gap by leveraging Lipschitz continuity for certification and proposing a novel, less conservative method for computing confidence intervals in randomized smoothing. Our approach tightens the bounds of certified robustness, offering a more accurate reflection of model robustness in practice. Through rigorous experimentation we show that our method improves the robust accuracy, compressing the gap between empirical findings and previous theoretical results. We argue that investigating local Lipschitz constants and designing ad-hoc confidence intervals can further enhance the performance of randomized smoothing. These results pave the way for a deeper understanding of the relationship between Lipschitz continuity and certified robustness.

cs.LG↗

arXiv2024

The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However how to design an efficient classifier with an associated certified radius? Randomized smoothing provides a promising framework by relying on noise injection into the inputs to obtain a smoothed and robust classifier. In this paper, we first show that the variance introduced by the Monte-Carlo sampling in the randomized smoothing procedure estimate closely interacts with two other important properties of the classifier, \textit{i.e.} its Lipschitz constant and margin. More precisely, our work emphasizes the dual impact of the Lipschitz constant of the base classifier, on both the smoothed classifier and the empirical variance. To increase the certified robust radius, we introduce a different way to convert logits to probability vectors for the base classifier to leverage the variance-margin trade-off. We leverage the use of Bernstein's concentration inequality along with enhanced Lipschitz bounds for randomized smoothing. Experimental results show a significant improvement in certified accuracy compared to current state-of-the-art methods. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.

cs.LG↗

arXiv2024

Spectral Norm of Convolutional Layers with Circular and Zero Paddings

This paper leverages the use of \emph{Gram iteration} an efficient, deterministic, and differentiable method for computing spectral norm with an upper bound guarantee. Designed for circular convolutional layers, we generalize the use of the Gram iteration to zero padding convolutional layers and prove its quadratic convergence. We also provide theorems for bridging the gap between circular and zero padding convolution's spectral norm. We design a \emph{spectral rescaling} that can be used as a competitive $1$-Lipschitz layer that enhances network robustness. Demonstrated through experiments, our method outperforms state-of-the-art techniques in precision, computational cost, and scalability. The code of experiments is available at https://github.com/blaisedelattre/lip4conv.

cs.LG↗

arXiv2023

Planar thermal Hall effect from phonons in a Kitaev candidate material

Kitaev materials are a promising platform for the realization of quantum spin liquid states. The thermal Hall effect has emerged as a potential probe of exotic excitations within such states. In the Kitaev candidate material $α$-RuCl$_{3}$, however, the thermal Hall conductivity $κ_{xy}$ has been attributed not only to exotic Majorana fermions or chiral magnons, but also to phonons. It has been shown theoretically that the former two types of heat carriers can generate a "planar" thermal Hall effect, whereby the magnetic field is parallel to the heat current, as observed experimentally, but it is unknown whether phonons also could. Here we show that a planar thermal Hall effect is present in another Kitaev candidate material, Na$_{2}$Co$_{2}$TeO$_{6}$. On the basis of a striking similarity between the temperature and field dependence of $κ_{xy}$ and that of the phonon-dominated thermal conductivity $κ_{xx}$, we argue that the planar thermal Hall effect in Na$_{2}$Co$_{2}$TeO$_{6}$ is generated by phonons. The phonon contributed planar $κ_{xy}$ also shows a strong sample dependence, which indicates an extrinsic origin of the mechanism. By conducting a complete study with different in-plane configurations of heat current $J$ and magnetic field $H$, $i.e.$ $H$ $\|$ $J$ and $H$ $\bot$ $J$, we observe a large difference in $κ_{xy}$ between these two configurations, which reveals that the direction of the heat current $J$ may play an important role in determining the planar thermal Hall effect. Our observation calls for a re-evaluation of the planar thermal Hall effect observed in $α$-RuCl$_{3}$.

cond-mat.str-el↗

arXiv2023

Planar parallel phonon Hall effect and local symmetry breaking

Y-kapellasite [Y3Cu9(OH)19Cl8] is a frustrated antiferromagnetic insulator which remains paramagnetic down to a remarkably low Néel temperature of about 2 K. Having studied this material in the paramagnetic regime, in which phonons are the only possible heat carriers, we report the observation of a planar parallel thermal Hall effect coming unambiguously from phonons. This is an advantage over the Kitaev quantum spin liquid candidates α-RuCl3 and Na2Co2TeO6 where in principle other heat carriers can be involved [1-4]. As it happens, Y-kapellasite undergoes a structural transition attributed to the positional freezing of a hydrogen atom below about 33 K. Above this transition, the global crystal symmetry forbids the existence of a planar parallel signal - the same situation as in Na2Co2TeO6 and cuprates [3-5]. This points to the notion of a local symmetry breaking at the root of the phonon Hall effect. In this context, the advantage of Y-kapellasite over Na2Co2TeO6 (with high levels of Na disorder and stacking faults) and cuprates (with high levels of disorder coming from dopants and oxygen vacancies) is its clean structure, where the only degree of freedom available for local symmetry breaking is this hydrogen atom randomly distributed over six equivalent positions above 33 K. This provides a specific and concrete case for the general idea of local symmetry breaking leading to the phonon Hall effect in a wide range of insulators.

cond-mat.str-el↗

arXiv2023

Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration

Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a precise, fast, and differentiable upper bound for the spectral norm of convolutional layers using circulant matrix theory and a new alternative to the Power iteration. Called the Gram iteration, our approach exhibits a superlinear convergence. First, we show through a comprehensive set of experiments that our approach outperforms other state-of-the-art methods in terms of precision, computational cost, and scalability. Then, it proves highly effective for the Lipschitz regularization of convolutional neural networks, with competitive results against concurrent approaches. Code is available at https://github.com/blaisedelattre/lip4conv.

cs.LG↗

arXiv2023

Oscillations in the magnetothermal conductivity of $\boldsymbolα$-RuCl$_3$: Evidence of transition anomalies

The 2D layered insulator $α$-RuCl$_3$ is a candidate material for a quantum spin-liquid state, which may be realized when a magnetic field suppresses the antiferromagnetic order present at low temperature. Oscillations in the field dependence of the thermal conductivity, observed for an in-plane magnetic field $B$ up to a critical field $B^{\star}$, have been attributed to exotic charge-neutral fermions, viewed as evidence of a quantum spin-liquid state between the critical field $B_{c}$ $\simeq 7$ T at which the antiferromagnetic phase ends and $B^{\star}$. Here we report measurements of the thermal conductivity of $α$-RuCl$_3$ as a function of magnetic field up to 15 T applied in two distinct in-plane directions: parallel and perpendicular to the Ru-Ru bond. We find that the number of oscillations between $B_{c}$ and $B^{\star}$ is the same for the two field directions even though the field interval between $B_{c}$ and $B^{\star}$ is different. In other words, the period of the oscillations is controlled by the transition fields $B_{c}$ and $B^{\star}$. We conclude that these are not true oscillations -- coming from putative fermions in a spin-liquid state -- but anomalies associated with a sequence of magnetic transitions.

cond-mat.str-el↗

arXiv2022

End-to-end P300 BCI using Bayesian accumulation of Riemannian probabilities

In brain-computer interfaces (BCI), most of the approaches based on event-related potential (ERP) focus on the detection of P300, aiming for single trial classification for a speller task. While this is an important objective, existing P300 BCI still require several repetitions to achieve a correct classification accuracy. Signal processing and machine learning advances in P300 BCI mostly revolve around the P300 detection part, leaving the character classification out of the scope. To reduce the number of repetitions while maintaining a good character classification, it is critical to embrace the full classification problem. We introduce an end-to-end pipeline, starting from feature extraction, and is composed of an ERP-level classification using probabilistic Riemannian MDM which feeds a character-level classification using Bayesian accumulation of confidence across trials. Whereas existing approaches only increase the confidence of a character when it is flashed, our new pipeline, called Bayesian accumulation of Riemannian probabilities (ASAP), update the confidence of each character after each flash. We provide the proper derivation and theoretical reformulation of this Bayesian approach for a seamless processing of information from signal to BCI characters. We demonstrate that our approach performs significantly better than standard methods on public P300 datasets.

cs.LG↗

arXiv2021

Minimizing subject-dependent calibration for BCI with Riemannian transfer learning

Calibration is still an important issue for user experience in Brain-Computer Interfaces (BCI). Common experimental designs often involve a lengthy training period that raises the cognitive fatigue, before even starting to use the BCI. Reducing or suppressing this subject-dependent calibration is possible by relying on advanced machine learning techniques, such as transfer learning. Building on Riemannian BCI, we present a simple and effective scheme to train a classifier on data recorded from different subjects, to reduce the calibration while preserving good performances. The main novelty of this paper is to propose a unique approach that could be applied on very different paradigms. To demonstrate the robustness of this approach, we conducted a meta-analysis on multiple datasets for three BCI paradigms: event-related potentials (P300), motor imagery and SSVEP. Relying on the MOABB open source framework to ensure the reproducibility of the experiments and the statistical analysis, the results clearly show that the proposed approach could be applied on any kind of BCI paradigm and in most of the cases to significantly improve the classifier reliability. We point out some key features to further improve transfer learning methods.

eess.SP↗

arXiv2019

Local study of the insulating quantum kagome antiferromagnets YCu3(OH)6OxCl3-x (x=0,1/3)

The quantum kagome antiferromagnets YCu3(OH)6OxCl3-x (x=0,1/3) are produced using a unified solid state synthesis route for polycrystalline samples. From structural refinements based on neutron diffraction data, we clarify the structure of the Y3Cu9(OH)18OCl8 (x=1/3) compound and provide a revised chemical formula. We use muon spin relaxation, as a local probe of magnetism, to investigate the exotic low temperature properties in the two compounds. In agreement with the low temperature neutron diffraction data, we find no evidence for long range ordering in both materials but they exhibit distinct ground states: while disordered static magnetism develops in the x=0 compound, we conclude on the stabilization of a quantum spin liquid in the x=1/3 one, since the local fields remain fully dynamical. Our findings are in contrast to previous reports based on thermodynamical measurements only. We then discuss their origin on the basis of structural details and specific heat measurements. In particular, the x=1/3 compound appears to realize an original spatially anisotropic kagome model.

cond-mat.str-el↗

arXiv2018

A framework for the comparison of different EEG acquisition solutions

The purpose of this work is to propose a framework for the benchmarking of EEG amplifiers, headsets, and electrodes providing objective recommendation for a given application. The framework covers: data collection paradigm, data analysis, and statistical framework. To illustrate, data was collected from 12 different devices totaling up to 6 subjects per device. Two data acquisition protocols were implemented: a resting-state protocol eyes-open (EO) and eyes-closed (EC), and an Auditory Evoked Potential (AEP) protocol. Signal-to-noise ratio (SNR) on alpha band (EO/EC) and Event Related Potential (ERP) were extracted as objective quantification of physiologically meaningful information. Then, visual representation, univariate statistical analysis, and multivariate model were performed to increase results interpretability. Objective criteria show that the spectral SNR in alpha does not provide much discrimination between systems, suggesting that the acquisition quality might not be of primary importance for spectral and specifically alpha-based applications. On the contrary, AEP SNR proved much more variable stressing the importance of the acquisition setting for ERP experiments. The multivariate analysis identified some individuals and some systems as independent statistically significant contributors to the SNR. It highlights the importance of inter-individual differences in neurophysiological experiments (sample size) and suggests some device might objectively be superior to others when it comes to ERP recordings. However, the illustration of the proposed benchmarking framework suffers from severe limitations including small sample size and sound card jitter in the auditory stimulations. While these limitations hinders a definite ranking of the evaluated hardware, we believe the proposed benchmarking framework to be a modest yet valuable contribution to the field.

q-bio.NC↗

arXiv2016

Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations

This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard $\ell_1$ regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-founded approach yields same accuracy as the other algorithms at the state-of-the-art, with significant gains in terms of convergence speed. Thirdly, the empirical validation of the approach on artificial and real-world problems demonstrates the generality and effectiveness of the method. On artificial problems, the proposed regularization subsumes the Total Variation minimization and recovers the expected decomposition. On the real-world problem of electro-encephalography brainwave decomposition, the approach outperforms similar approaches in terms of P300 evoked potentials detection, using structured spatial priors to guide the decomposition.

cs.DS↗