Publications

2025

• Reconstruction 3D depuis des couples SAR ascendant/descendant
  
  • Barbier--Renard Emile
  • Tupin Florence
  • Denis Loïc
  , 2025, pp.1-4. Afin d'exploiter les disparités géométriques entre des images SAR acquises sous différents points de vue, nous présentons une méthode de reconstruction de surface par rendu inverse inspirée de NeRF. Elle optimise une carte d'élévation et une carte de coefficients de rétrodiffusion à partir d'un minimum de deux images, et s'appuie sur un modèle de rendu différentiable adapté à cette représentation en carte d'élévation ainsi qu'une stratégie multi-échelles assurant une convergence rapide. Nous validons les capacités de reconstruction sur des données synthétiques réalistes générées par le simulateur EMPRISE ® de l'ONERA.
• Ordonnancement et ACM conjoint sur canal aléatoire basé sur un transformer entrainé par apprentissage profond par renforcement
  
  • Nérondat Sylvain
  • Leturc Xavier
  • Le Martret Christophe
  • Ciblat Philippe
  , 2025. Nous proposons une solution conjointe d'ordonnancement et de sélection du schéma de modulation et codage pour un système de communications sans fil sur un canal aléatoire. Les trafics de chaque lien sont "contraints en délai" ou "best effort". Les paquets sont stockés dans des files d'attente de taille finie, et les paquets arrivant alors que la file est pleine sont supprimés. Les pertes de paquets peuvent être aussi dues au canal ou à un dépassement de délai. L'allocation des ressources se fait par bloc sur une trame, chaque bloc étant dédié à un type de trafic pour un lien donné. La solution repose sur un réseau de neurones profond de type "transformer", combiné à une ramification d'action et entraîné par apprentissage par renforcement afin de minimiser la perte de paquets.
• Détection non supervisée de changements radiométriques en imagerie radar à synthèse d'ouverture
  
  • Bultingaire Thomas
  • Kervazo Christophe
  • Denis Loïc
  • Tupin Florence
  , 2025, pp.1-4. L'imagerie radar à synthèse d'ouverture est un mode d'imagerie clé pour la détection de changements en télédétection. Cette tâche est difficile à cause du phénomène de chatoiement, un phénomène qui nécessite de réaliser une étape de débruitage pour y être davantage robuste. Cependant, il est nécessaire de prendre en compte les incertitudes de débruitage pour contrôler la probabilité de fausse alarme des changements détectés car les instabilités de débruitage doivent être distinguées des changements. Nous proposons donc un réseau, entraîné de manière auto-supervisée, pour prédire les incertitudes de débruitage menant à une détection de changements radiométriques dont la performance est évaluée sur des images du satellite TerraSAR-X.
• Generalizability and sample complexity of quadratic shallow neural networks under low-rank learning
  
  • Wang Xiaolin
  • Rioul Olivier
  • Mokraoui Anissa
  • Duhamel Pierre
  • Benesty Jacob
  , 2025. We investigate the interplay between sample complexity and model complexity in low-rank learning of quadratic shallow neural networks (QSNN), within a novel doubly-correlated teacher-student framework that incorporates parameter correlations to reflect real-world data properties. This framework generalizes existing theories for QSNN by analyzing the impact of sample size on generalization loss for models under low-rank learning or exhibiting inherent bias. We observe a two-regime behavior in the scaling law of generalization ability with respect to sample size and show that parameter correlations in the teacher model significantly enhance the generalization of rank-reduced models. Extensive numerical simulations confirm the results and offer theoretical insights and practical guidance for designing efficient neural network architectures under low-rank learning.
• Une distance de style stochastique pour la synthèse de textures multispectrales
  
  • Ollivier Sélim
  • Gousseau Yann
  • Lefebvre Sidonie
  , 2025, pp.985-988/2025-1702. In this paper, we propose a novel multispectral style distance that relies on a RGB network. It consists in the stochastic evaluation of a classical style distance, over images formed by random triplets of spectral bandes. It constitutes a simple and efficient extension of state-of-the-art methods for multispectral texture synthesis, while avoiding the additional training of a multispectral network.
• Modèle physique variationnel pour l’estimation de réponses impulsionnelles de salles
  
  • Lalay Louis
  • Fontaine Mathieu
  • Badeau Roland
  , 2025. Estimer la réponse impulsionnelle d’une salle est essentiel pour des tâches comme la déréverbération, qui améliore la reconnaissance automatique de la parole. La plupart des méthodes existantes reposent soit sur du traitement du signal statistique, soit sur des réseaux de neurones profonds s’inspirant du traitement du signal. Cependant, la combinaison des modélisations statistique et physique reste largement inexploré en estimation de réponse impulsionnelle de salle. Cet article propose une approche novatrice intégrant les deux aspects à travers un modèle physique. La réponse de salle est décomposée en paramètres interprétables : un bruit blanc gaussien modulé par une décroissance exponentielle dépendante de la fréquence (modélisant l’absorption des murs) et un filtre autorégressif (modélisant par exemple la réponse du microphone). L’optimisation d’une fonction d’énergie libre variationnelle permet une estimation pratique des paramètres. Nous montrons que, connaissant les signaux secs et réverbérants, la méthode proposée surpasse la déconvolution classique dans des environnements bruités, comme le confirment les mesures objectives.
• Vers une axiomatique minimale de l'information quantique : Schrödinger ex-nihilo
  
  • Rioul Olivier
  , 2025. Partant de deux simples postulats quantiques, on peut retrouver l’équation de Schrödinger qui modélise l’évolution d’un système quelconque en dimension finie. Cette équation de la physique fondamentale, qui peut sembler absconse pour la communauté du traitement du signal, n’est en effet qu’une conséquence de propriétés d’orthogonalité dans un espace de Hilbert et d’une hypothèse probabiliste sur la mesure quantique. Sa preuve mathématique utilise des versions simplifiées des théorèmes de Wigner et de Stone.
• Quelques éléments historiques portant sur la cyclostationnarité et son application en télécommunications
  
  • Ciblat Philippe
  , 2025. Dans ce papier, nous donnons quelques grandes dates sur la théorie de signaux cyclostationnaires, la première étant en 1958 du côté des Etats-Unis et la deuxième étant 1959 du côté de l'Union Soviétique suivi de quelques autres des deux côtés de l'Océan Atlantique. Nous nous attardons ensuite sur deux applications-phares de la cyclostationnarité que sont la synchronisation et l'égalisation autodidacte pour lesquelles la communauté française a joué un rôle conséquent dans les années 1990.
• SigN: SIMBox Activity Detection Through Latency Anomalies at the Cellular Edge
  
  • Kouam Anne Josiane
  • Carneiro Viana Aline
  • Martins Philippe
  • Adjih Cédric
  • Tchana Alain
  , 2025. Despite their widespread adoption, cellular networks face growing vulnerabilities due to their inherent complexity and the integration of advanced technologies. One of the major threats in this landscape is Voice over IP (VoIP) to GSM gateways, known as SIMBox devices. These devices use multiple SIM cards to route VoIP traffic through cellular networks, enabling international bypass fraud with losses of up to $3.11 billion annually. Beyond financial impact, SIMBox activity degrades network performance, threatens national security, and facilitates eavesdropping on communications. Existing detection methods for SIMBox activity are hindered by evolving fraud techniques and implementation complexities, limiting their practical adoption in operator networks. This paper addresses the limitations of current detection methods by introducing SigN , a novel approach to identifying SIMBox activity at the cellular edge. The proposed method focuses on detecting remote SIM card association, a technique used by SIMBox appliances to mimic human mobility patterns. The method detects latency anomalies between SIMBox and standard devices by analyzing cellular signaling during network attachment. Extensive indoor and outdoor experiments demonstrate that SIMBox devices generate significantly higher attachment latencies, particularly during the authentication phase, where latency is up to 23 times greater than that of standard devices. We attribute part of this overhead to immutable factors such as LTE authentication standards and Internet-based communication protocols. Therefore, our approach offers a robust, scalable, and practical solution to mitigate SIMBox activity risks at the network edge. (10.1145/3708821.3733902)
  DOI : 10.1145/3708821.3733902
• Déréverbération non-supervisée de la parole par modèle hybride
  
  • Bahrman Louis
  • Fontaine Mathieu
  • Richard Gaël
  , 2025, pp.1-4. Cet article introduit une nouvelle stratégie d'apprentissage pour améliorer des systèmes de déréverbération de la parole de manière non-supervisée en n'utilisant que des signaux réverbérants. La plupart des algorithmes existants nécessitent des paires de signaux (sec, réverbérant), qui sont difficiles à obtenir. Notre approche utilise en revanche des informations acoustiques limitées, comme le temps de réverbération (RT60), pour entraîner un système de déréverbération. Les résultats expérimentaux démontrent que notre méthode permet d'obtenir des performances plus cohérentes que l'état de l'art sur différentes mesures objectives.
• La borne bayesienne de Schützenberger-van Trees : Un principe d'incertitude sur l'a posteriori
  
  • Rioul Olivier
  • Renaux Alexandre
  , 2025. Cette communication propose une perspective historique sur la borne de Cramér-Rao bayésienne (BCRB), généralement attribuée à van Trees qui l’a découverte en 1968. Selon la loi de Stigler sur l’éponymie, aucune découverte scientifique ne porte le nom de son premier découvreur. C’est non seulement le cas de la borne Cramér-Rao elle-même – due notamment aux mathématiciens français Fréchet et Darmois – mais aussi de l’inégalité de van Trees. En effet, le médecin, généticien, épidémiologiste et mathématicien français Marcel-Paul (Marco) Schützenberger, dans un petit article d’une quinzaine de lignes seulement, écrit en 1956 – plus d’une décennie avant van Trees – avait non seulement démontré la BCRB, mais comme le montre une lecture approfondie de sa preuve, l’avait fait avec une démarche très originale en la reliant au principe d’incertitude de Weyl-Heisenberg sur l’a posteriori. Nous passons en revue et comparons les contributions de Schützenberger et de van Trees ainsi que celles de Gart en 1959. L’équivalence générale entre BCRB et principe d’incertitude sur l’a posteriori ouvre de nouvelles perspectives.
• Super-résolution non supervisée d'images hyperspectrales de télédétection utilisant un entraînement entièrement synthétique
  
  • Xu Xinxin
  • Gousseau Yann
  • Kervazo Christophe
  • Ladjal Saïd
  , 2025. Hyperspectral single-image super-resolution (SISR) aims to improve the spatial resolution of images while preserving their spectral richness. Most current methods rely on supervised learning that requires high-resolution reference data, which are often unavailable in practice. To overcome this limitation, we propose an unsupervised learning approach based on the generation of synthetic data. The hyperspectral image is first decomposed into materials and abundances using a hyperspectral unmixing algorithm. A neural network is then trained to super-resolve the abundance maps from synthetic data generated through a dead leaves model, which imitates the statistical properties of real abundances. The high-resolution hyperspectral image is finally reconstructed by recombining the super-resolved abundance maps with the materials. Experimental results validate the effectiveness of this approach and highlight the usefulness of synthetic data for training.
• Unified Variational and Physics-aware Model for Room Impulse Response Estimation
  
  • Lalay Louis
  • Fontaine Mathieu
  • Badeau Roland
  , 2025. Room impulse response estimation is essential for tasks like speech dereverberation, which improves automatic speech recognition. Most existing methods rely on either statistical signal processing or deep neural networks designed to replicate signal processing principles. However, combining statistical and physical modeling for RIR estimation remains largely unexplored. This paper\footnote{This paper was submitted to Interspeech 2025} proposes a novel approach integrating both aspects through a theoretically grounded model. The RIR is decomposed into interpretable parameters: white Gaussian noise filtered by a frequency-dependent exponential decay (e.g. modeling wall absorption) and an autoregressive filter (e.g. modeling microphone response). A variational free-energy cost function enables practical parameter estimation. As a proof of concept, we show that given dry and reverberant speech signals, the proposed method outperforms classical deconvolution in noisy environments, as validated by objective metrics.
• Emotional speech markers of psychiatric disturbance in Huntington’s disease
  
  • Chenain Lucie
  • Fabre Audrey
  • Titeux Hadrien
  • Morgado Graça
  • Youssov Katia
  • Clavel Chloé
  • Bachoud-Lévi Anne-Catherine
  Frontiers in Psychiatry, Frontiers, 2025, 16, pp.1633492-1:1633492-20. Introduction: Psychiatric disorders and difficulties in emotional expression represent a major problem in the management of Huntington's Disease (HD). To improve patient follow-up, we propose to investigate the link between emotional expression and psychiatric symptoms, measured by the Problem Behaviors Assessment (PBA) scale. To this aim we developed the first emotional/psychiatric speech corpus, emoHD. Methods: We included 102 HD gene carriers and 35 healthy controls (HC). Psychiatric symptoms were assessed using PBA sub-scales for Depression, Irritability/aggressivity, Apathy, and Obsessive/compulsive symptoms. Speech was annotated using three emotional descriptors: primary emotions, affective phenomena, and activation levels. Affective phenomena labels were selected based on PBA statements by external participants unaware of the study's aims. We analyzed (1) emotional descriptors' relationships, (2) emotional expression differences between HD and HC, and (3) the associations between emotions and psychiatric symptoms. Results: HD patients showed reduced emotional expressiveness than HC with more neutral activation levels (=0). Only the primary emotion "angry" was less expressed in HD compared to HC. In contrast they expressed more affective phenomena states like apathetic, confused, "depressed", "disoriented", "frustrated", and "pessimistic" than HC, whereas they expressed less "other" and "irritable" than HC. Expressed emotions were congruent with psychiatric symptoms (e.g., "anxious" and "nervous" are positively associated with Depression PBA sub-scale; "frustrated" with Irritability/aggressivity PBA sub-scale). (10.3389/fpsyt.2025.1633492)
  DOI : 10.3389/fpsyt.2025.1633492
• Enhancing Plasticity for First Session Adaptation Continual Learning
  
  • Marouf Imad Eddine
  • Roy Subhankar
  • Lathuilière Stéphane
  • Tartaglione Enzo
  , 2025. The integration of large pre-trained models (PTMs) into Class-Incremental Learning (CIL) has fa- cilitated the development of computationally efficient strategies such as First-Session Adaptation (FSA), which fine-tunes the model solely on the first task while keeping it frozen for subsequent tasks. Although effective in homogeneous task sequences, these approaches struggle when faced with the heterogeneity of real-world task distributions. We introduce Plasticity-Enhanced Test-Time Adaptation in Class-Incremental Learning (PLASTIC), a method that reinstates plasticity in CIL while preserving model stability. PLASTIC leverages Test-Time Adaptation (TTA) by dynamically fine-tuning LayerNorm parameters on unlabeled test data, enabling adaptability to evolving tasks and improving robustness against data corruption. To prevent TTA-induced model divergence and maintain stable learning across tasks, we introduce a teacher-student distillation framework, ensur- ing that adaptation remains controlled and generalizable. Extensive experiments across multiple benchmarks demonstrate that PLASTIC consistently outperforms both conventional and state-of- the-art PTM-based CIL approaches, while also exhibiting inherent robustness to data corruptions. Code is available at: https://github.com/IemProg/PLASTIC.
• Efficient Negative Weight Realization for Analog Resistive Neural Networks
  
  • Kiraz Zulal
  • Pham Dang-Kièn Germain
  • Desgreys Patricia
  , 2025. Most analog nonlinear resistive neural networks for machine learning training use doubling input and output neuron nodes to implement negative weights. However, this approach increases network size, modifies the gradient computation, and complicates circuit design. We propose an alternative circuit topology that retains a one-to-one correspondence between neurons in the original model and their analog counterparts. Our design employs a emph{single} input source for all first-layer weights, a emph{single} resistor per weight, and a bidirectional amplifier for the rest of the layers' weight to handle negative connections without duplicating neurons. We validate our design on a binary XOR classification task over SI{100}{} training epochs and SI{100}{} randomized initializations. Our textbf{single-resistor} approach achieved an average final error of SI{-6.6}{dB} and required approximately SI{568}{} minutes of total CPU time. In comparison, the textbf{doubled-node} design reached SI{-4.6}{dB} error and consumed around SI{1104}{} minutes of CPU time. This equates to nearly 49% less computation for the single-resistor circuit while preserving the standard gradient update procedure—demonstrating that negative weights can be realized more efficiently without doubling input/output neurons.
• Immersed boundary–lattice Boltzmann mesoscale method for wetting problems
  
  • Bellantoni Elisa
  • Guglietta Fabio
  • Pelusi Francesca
  • Desbrun Mathieu
  • Um Kiwon
  • Nicolaou Mihalis
  • Savva Nikos
  • Sbragaglia Mauro
  Physical Review E, American Physical Society (APS), 2025, 112 (2), pp.025305 (1-15). We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: the former is used to model the non-ideal sharp interface of the droplet coupled with the inner and outer fluids, simulated with the lattice Boltzmann scheme. We further introduce an interaction force to model the wetting interactions of the droplet with the solid at mesoscale: this interaction force is designed with the key computational advantage of providing a regularization of the interface profile close to the contact line, avoiding abrupt curvature changes that could otherwise cause numerical instabilities. The proposed model substantially improves earlier immersed boundary - lattice Boltzmann models for wetting in that it allows a description of an ample variety of wetting interactions, ranging from hydrophobic to hydrophilic cases, without the need for any pre-calibration study on model parameters to be used. Model validations against theoretical results for droplet shape at equilibrium and scaling laws for droplet spreading dynamics are addressed. (10.1103/mp3p-8j22)
  DOI : 10.1103/mp3p-8j22
• Time-resolved second-order autocorrelation function of parametric down-conversion
  
  • Horoshko Dmitri
  • Srivastava Shivang
  • Sośnicki Filip
  • Mikołajczyk Michał
  • Karpiński Michał
  • Brecht Benjamin
  • Kolobov Mikhail
  Physical Review A, American Physical Society, 2025, 112 (2), pp.023703-1:023703-13. We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale. (10.1103/7ckm-tm3r)
  DOI : 10.1103/7ckm-tm3r
• SpectreShield: Design and Analysis of Spectre Countermeasures on RISC-V Using gem5
  
  • Khan Mahreen
  • Mushtaq Maria
  • Pacalet Renaud
  • Apvrille Ludovic
  , 2025. <div><p>Speculative execution attacks like Spectre exploit microarchitectural side effects to leak sensitive data during transient execution. While various software and hardware countermeasures have been proposed for x86 and ARM architectures, their effectiveness and microarchitectural impact remain underexplored on RISC-V platforms. To study such attacks and evaluate these countermeasures, simulation tools like the gem5 simulator provide detailed insights into microarchitectural state changes during speculation. In this paper, we present the first comprehensive evaluation of Spectre-v1 countermeasures on the RISC-V architecture using the gem5 full-system simulator. We implement and assess four Spectre-v1 mitigations: index masking (CM1), randomized offset (CM2), fence-based serialization (CM3), and bitwise selection (CM4). Our experiments reveal that, in the absence of mitigations, Spectre-v1 enables 100% secret key recovery. In contrast, all proposed countermeasures reduce the recovery rate to below 1%, with branch mispredictions decreasing by 41.7%-46.3%. The paper analyzes the securityperformance trade-offs of each approach. Beyond demonstrating their effectiveness, we quantify their microarchitectural impact, measuring reductions in squashed instructions, DRAM latency variability, and return address stack mispredictions. This paper provides a practical framework for evaluating transient execution defenses and advances secure-by-design RISC-V processors.</p></div>
• Bayesian Stream Tuner: Dynamic Hyperparameter Optimization for Real-Time Data Streams
  
  • Verma Nilesh
  • Bifet Albert
  • Pfahringer Bernhard
  • Bahri Maroua
  , 2025, 2, pp.2871-2882. Hyperparameter optimization is crucial for maximizing machine learning model performance, yet most existing algorithms are designed for batch or offline scenarios and assume static data distributions. Such assumptions fall short in data stream settings, where models must adapt to evolving inputs in real time. To address these limitations, we propose the Bayesian Stream Tuner (BST), a novel framework for online hyperparameter optimization in nonstationary data streams. BST maintains a dynamic set of candidate hyperparameter configurations and periodically refines them using an incremental Bayesian model, which estimates configuration performance based on recent data statistics and hyperparameter values. This systematic exploration and refinement strategy allows BST to detect and respond to concept drift by resetting its adaptation mechanisms whenever necessary, ensuring strong performance under changing distributions. Our theoretical analysis establishes sublinear regret bounds for BST in dynamic environments, and extensive experiments on classification and regression tasks demonstrate that BST consistently outperforms state-of-the-art online hyperparameter optimization methods in both predictive accuracy and adaptability, making it a powerful solution for real-time hyperparameter tuning in evolving data streams. (10.1145/3711896.3736852)
  DOI : 10.1145/3711896.3736852
• Satellite Image Time-Series Data Augmentation Using an Attention Mechanism Variational Recurrent Autoencoder
  
  • Chaabane Ferdaous
  • Tupin Florence
  , 2025. Data scarcity presents a significant challenge in satellite image analysis, particularly for developing robust models in remote sensing applications. High-quality and abundant data are essential for accurate predictions; however, acquiring Satellite Image Time-Series (SITS) data is often constrained by factors such as limited temporal coverage and the high cost of Very High Resolution (VHR) acquisitions. To address this issue, we propose a novel Attention-based Variational Recurrent Autoencoder (AVRAE) designed for generating synthetic satellite image time-series data. This method extends the evidence lower bound (ELBO) of variational inference to incorporate the temporal dependencies essential for satellite data. A recurrent neural network-based autoencoder framework is employed, integrated with an attention mechanism to effectively capture both short-and long-term temporal relationships. The AVRAE framework synthesizes realistic and statistically representative satellite time-series data, enabling enhanced analysis for remote sensing applications. Evaluations using real-world satellite datasets demonstrate that AVRAE produces coherent and statistically valid synthetic data, thereby improving VHR SITS data quality for deep learning-based remote sensing applications.
• An Information Theoretic Proof of the Chernoff-Hoeffding Inequality
  
  • Rioul Olivier
  • Solé Patrick
  Information Processing Letters, Elsevier, 2025, 190, pp.106582. The Chernoff bound is a well-known upper bound on the tail of binomial distributions of parameter 1/2 involving the binary entropy function. Hoeffding's inequality (or the Chernoff-Hoeffding inequality) is a generalization for binomial distributions of parameter 1 -1/q, involving the q-ary entropy function (with q ≥ 2), which can be written in terms of the Kullback-Leibler divergence and is related to the bound in Fano's inequality. We give an information theoretic proof of that bound, and sketch some applications to channel and source coding. We also derive a refined bound which is always sharper. (10.1016/j.ipl.2025.106582)
  DOI : 10.1016/j.ipl.2025.106582
• CT Emphysema Subtypes and Cardiac Hemodynamics Estimated on MRI: The Multi-Ethnic Study of Atherosclerosis COPD Study
  
  • Hermann Emilia
  • Yang Jesse
  • Angelini Elsa
  • Balte Pallavi
  • Bluemke David
  • Carr James
  • Derlin Katja
  • Gomes Antoinette
  • Habibi Mohammadali
  • Hoffman Eric
  • Johns Chris
  • Kawut Steven
  • Kiely David
  • Laine Andrew
  • Lima Joao A.C.
  • Prince Martin
  • Smith Benjamin
  • Vogel-Claussen Jens
  • Watson Karol
  • Wild Jim
  • Swift Andrew
  • Barr R. Graham
  Chest, American College of Chest Physicians, 2025, 168 (2), pp.364-378. (10.1016/j.chest.2025.03.009)
  DOI : 10.1016/j.chest.2025.03.009
• Long run convergence of discrete-time interacting particle systems of the McKean-Vlasov type
  
  • Bianchi Pascal
  • Hachem Walid
  • Priser Victor
  Stochastic Processes and their Applications, Elsevier, 2025. We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the particles. We study the doubly asymptotic regime where both the number of iterations and the number n of particles tend to infinity, without any constraint on the relative rates of convergence of these two parameters. We establish that the empirical measure of the interpolated trajectories of the particles converges in probability, in an ergodic sense, to the set of recurrent Mc-Kean-Vlasov distributions. A first application example is the granular media equation, where the particles are shown to converge to a critical point of the Helmholtz energy. A second example is the convergence of stochastic gradient descent to the global minimizer of the risk, in a wide two-layer neural networks using random features.
• On the spectral decomposition of the complex Robin Laplacian
  
  • Badeau Roland
  Journal of the Acoustical Society of America, Acoustical Society of America, 2025, 158 (1), pp.838-848. The mathematical properties of the Laplacian on a bounded domain are well-known when the boundary condition is of the first type (Dirichlet) or second type (Neumann). In both cases, this operator is self-adjoint and, therefore, diagonalizable, its spectrum is discrete, and the set of eigenfunctions can be chosen to form an orthonormal basis of the Hilbert space of square-integrable functions on the domain. However, in the case of the third type (Robin) boundary condition, the same is true only when the parameter is real-valued. On the contrary, when this parameter is complex-valued, the Laplacian may not even be diagonalizable. In this paper, the spectral decomposition of the complex Robin Laplacian is investigated in the most general case possible, and a formula that decomposes any square-integrable function on the set of its (generalized) eigenfunctions is provided. This result is applied to the Green's function of the Helmholtz equation, whose existence, unicity, and closed-form expression are established in this general setting, and the statistical wave field theory, which provides the statistical laws of waves propagating in a bounded domain. (10.1121/10.0037233)
  DOI : 10.1121/10.0037233