2025​Activity reportProject-TeamCELESTE​‌

7.1.1 acanag​‌

• Keyword:
  Anomaly detection
• Functional​​ Description:
  La bibliothèque Python​​​‌ acanag ou Active Anomaly​ Detection apprend à détecter​‌ les anomalies dans les​​ données multidimensionnelles de type​​​‌ bags, lots, ou séries​ temporelles.
• Contact:
  Kevin Bleakley​‌
• Partners:
  CNRS, IRT SystemX,​​ IRT Saint Exupéry

7.1.2​​ sanssouci

• Keyword:
  Multiple testing​​​‌
• Functional Description:
  In a‌ multiple testing context, sanssouci‌​‌ provides statistical guarantees on​​ possibly user-defined and/or data-driven​​​‌ sets of hypotheses. Typical‌ use cases include differential‌​‌ gene expression studies in​​ genomics and fMRI studies​​​‌ in neuroimaging. New contributions‌ include overall optimization and‌​‌ documentation improvements, and, above​​ all, the implementation of​​​‌ the new algorithms described‌ in 11.
• Contact:‌​‌
  Guillermo Durand
• Partner:
  Pierre​​ Neuvial (CNRS, Université de​​​‌ Toulouse)

7.1.3 KCPD

• Name:‌
  Kernel Change Point Detection‌​‌
• Keyword:
  Change-point detection
• Functional​​ Description:
  The library is​​​‌ based on the kernel‌ change point detection methods‌​‌ described in Sylvain Arlot​​ and co-authors (2012,2017).
• URL:​​​‌
  https://­github.­com/­etaia/­kernel-change-point-detection
• Contact:
  Kevin Bleakley‌
• Partner:
  IRT SystemX

8.1.1‌ Conformal prediction for hierarchical‌​‌ data

Participants: Guillaume Principato​​, Gilles Stoltz,​​​‌ Jean-Michel Poggi.

In‌ collaboration with colleagues from‌​‌ EDF (Yvenn Amara-Ouali, Yannig​​ Goude, and Bachir Hamrouche)​​​‌ we study in 45‌ conformal prediction for multivariate‌​‌ data, and more precisely,​​ focus on hierarchical data,​​​‌ where some components are‌ linear combinations of others.‌​‌ Intuitively, the hierarchical structure​​ can be leveraged to​​​‌ reduce the size of‌ prediction regions for the‌​‌ same coverage level. We​​ implement this intuition by​​​‌ including a projection step‌ (also called a reconciliation‌​‌ step) in the split​​ conformal prediction (SCP) procedure,​​​‌ and prove that the‌ resulting prediction regions are‌​‌ indeed globally smaller. We​​ do so both under​​​‌ the classic goal of‌ joint coverage, and under‌​‌ a new and challenging​​ task: component-wise coverage, for​​​‌ which efficiency results are‌ more difficult to obtain.‌​‌ The associated strategies and​​ their analyses are based​​​‌ both on the literature‌ of SCP and of‌​‌ forecast reconciliation, which we​​ connect. We also illustrate​​​‌ the theoretical findings, for‌ different scales of hierarchies,‌​‌ on simulated data.

8.1.2​​ Optimal transport-based conformal prediction​​​‌

Participants: Claire Boyer.‌

This joint work 25‌​‌ with Gauthier Thurin (ENS​​ Paris) and Kimia Nadjahi​​​‌ (ENS Paris) proposes a‌ novel conformal prediction framework‌​‌ for multivariate outputs based​​ on optimal transport. By​​​‌ leveraging Monge–Kantorovich vector ranks‌ and quantiles, the method‌​‌ constructs flexible, potentially non-convex​​ prediction regions that better​​​‌ capture the geometry of‌ complex uncertainty patterns, while‌​‌ retaining finite-sample, distribution-free coverage​​ guarantees.

8.2.1 Modeling of passenger‌​‌ movements in trains with​​ communicating coaches

Participants: Christine​​​‌ Keribin, Gilles Stoltz‌.

In collaboration with‌​‌ colleagues from SNCF, namely,​​ Mélissa Baietto and Rémi​​​‌ Coulaud, we model in‌ 6 passenger movements within‌​‌ communicating coaches equipped with​​ infra-red sensors at each​​​‌ door, counting the numbers‌ of passengers boarding and‌​‌ alighting at that door.​​ The business objective is​​​‌ to better estimate the‌ real occupancy rate of‌​‌ each coach instead of​​ solely using boarding counts​​​‌ and discarding passenger movements.‌ To do so, we‌​‌ propose modelings based on​​ stochastic transition matrices that​​​‌ are specific to each‌ station in the most‌​‌ complex modeling. The latter,​​ called local modeling, also​​​‌ has to estimate alighting‌ counts, which it does‌​‌ through data-based alighting rates​​​‌ rather than with origin-destination​ matrices. This piece of​‌ the methodology is of​​ independent interest. The local​​​‌ modeling may actually be​ seen as a neural​‌ network (a recurrent neural​​ network with a many-to-many​​​‌ architecture featuring one hidden​ layer). All modelings are​‌ fit through least-squares minimizations.​​ We evaluate them both​​​‌ qualitatively and quantitatively, on​ data from line H​‌ of the suburban railway​​ network of the Greater​​​‌ Paris area. The qualitative​ evaluation consists of successfully​‌ interpreting the outcomes of​​ the models (transition matrices,​​​‌ alighting rates) based on​ the geographies of the​‌ platforms of the boarding​​ or alighting stations. The​​​‌ quantitative evaluation consists of​ using the models constructed​‌ to forecast alighting counts:​​ modeling passenger movements improves​​​‌ the forecasting performance by​ about at least $\mathrm{15‌}\%$ compared to ignoring​​ the existence of such​​​‌ movements. All in all,​ this study backs up​‌ upgrading the passenger-movement modeling​​ layer in the real-time​​​‌ crowding information deployed in​ the greater-Paris area from​‌ the global modeling currently​​ used to local modeling.​​​‌

8.2.2 Forecasting time series​ with constraints

Participants: Claire​‌ Boyer.

The collaborative​​ work 36 with colleagues​​​‌ from EDF proposes a​ unified framework for time​‌ series forecasting that systematically​​ integrates linear constraints into​​​‌ learning algorithms. The framework​ encompasses and combines existing​‌ approaches such as generalized​​ additive models and hierarchical​​​‌ forecasting, and shows that​ the exact minimizer of​‌ the constrained empirical risk​​ can be computed efficiently​​​‌ using only linear algebra​ operations. This formulation enables​‌ highly scalable implementations optimized​​ for GPU architectures. Extensive​​​‌ empirical evaluations on real-world​ applications, including electricity demand​‌ and tourism forecasting, demonstrate​​ state-of-the-art performance of the​​​‌ proposed approach.

8.2.3 Randomized​ multi-class classification under system​‌ constraints: a unified approach​​ via post-processing

Participants: Evgenii​​​‌ Chzhen, Gayane Taturyan​.

In collaboration with​‌ M. Hebiri, in 35​​ we study the problem​​​‌ of multi-class classification under​ system-level constraints expressible as​‌ linear functionals over randomized​​ classifiers. We propose a​​​‌ post-processing approach that adjusts​ a given base classifier​‌ to satisfy general constraints​​ without retraining. Our method​​​‌ formulates the problem as​ a linearly constrained stochastic​‌ program over randomized classifiers,​​ and leverages entropic regularization​​​‌ and dual optimization techniques​ to construct a feasible​‌ solution. We provide finite-sample​​ guarantees for the risk​​​‌ and constraint satisfaction for​ the final output of​‌ our algorithm under minimal​​ assumptions. The framework accommodates​​​‌ a broad class of​ constraints, including fairness, abstention,​‌ and churn requirements.

8.2.4​​ Prediction-aware learning in multi-agent​​​‌ systems

Participants: Etienne Boursier​.

The work 19​‌ proposes a prediction-aware learning​​ framework for uncoupled online​​​‌ learning in time-varying multiplayer​ games, where agents exploit​‌ forecasts of future payoffs​​ to adapt their strategies.​​​‌ While classical regret guarantees​ degrade rapidly in dynamic​‌ environments, this approach explicitly​​ incorporates prediction to obtain​​​‌ tighter performance bounds when​ payoff variations are predictable.​‌ We introduce POMWU, a​​ contextual extension of the​​​‌ Optimistic Multiplicative Weight Update​ algorithm, and show that,​‌ under bounded prediction errors,​​ it achieves convergence and​​​‌ social welfare guarantees comparable​ to those in static​‌ games, up to terms​​ depending on the prediction​​ quality.

8.2.5 Detecting rare​​​‌ anomalies in multidimensional data‌ using active and supervised‌​‌ learning

Participants: Kevin Bleakley​​.

Detecting rare anomalies​​​‌ in batches of multidimensional‌ data is challenging. We‌​‌ have proposed an original​​ supervised active-learning framework 7​​​‌ that sends a small‌ number of data points‌​‌ from each batch to​​ an expert for labeling​​​‌ as ‘anomaly’ or ‘nominal’‌ via two mechanisms: (i)‌​‌ points most likely to​​ be anomalies in the​​​‌ eyes of a supervised‌ classifier trained on previously-labeled‌​‌ data; and (ii) points​​ suggested by an active​​​‌ learner. Instead of training‌ the supervised classifier directly‌​‌ on currently-labeled raw data,​​ we treat the scores​​​‌ calculated by an ensemble‌ of $M$ user-defined unsupervised‌​‌ anomaly detectors as if​​ they were the learner’s​​​‌ input features. Our approach‌ generalizes earlier attempts to‌​‌ linearly aggregate unsupervised anomaly​​ detector scores, and broadens​​​‌ the scope of these‌ methods from unordered bags‌​‌ of data to ordered​​ data such as time​​​‌ series. Simulated and real‌ data trials suggest that‌​‌ this method usually outperforms—often​​ significantly—linear strategies. The Python​​​‌ library acanag implements our‌ proposed method. This 2025‌​‌ work, in collaboration with​​ Benjamin Auder (LMO Orsay),​​​‌ Martin Royer (IRT System‌ X), and Mouhcine Mendhil‌​‌ (IRT Saint Exupéry), was​​ subsequently published early 2026​​​‌ in TMLR.

8.2.6 Physics-informed‌ kernel learning

Participants: Claire‌​‌ Boyer.

The article​​ 37 introduces physics-informed kernel​​​‌ learning (PIKL), a principled‌ alternative to physics-informed neural‌​‌ networks that integrates physical​​ priors through a kernel-based​​​‌ formulation. By approximating the‌ underlying kernel using Fourier‌​‌ methods, the authors derive​​ a tractable estimator that​​​‌ minimizes a physics-informed risk‌ combining data fidelity and‌​‌ PDE constraints. The framework​​ comes with theoretical guarantees​​​‌ that quantify the impact‌ of the physical prior‌​‌ on convergence rates. Numerical​​ experiments demonstrate that PIKL​​​‌ can outperform physics-informed neural‌ networks in both accuracy‌​‌ and computational efficiency, and​​ in some settings even​​​‌ surpass classical PDE solvers,‌ particularly in the presence‌​‌ of noisy boundary conditions.​​ This is a joint​​​‌ work with Nathan Doumèche‌ (EDF & Sorbonne Université),‌​‌ Francis Bach (Inria), and​​ Gérard Biau (Sorbonne Université),​​​‌ accepted for publication in‌ JMLR in 2025.

8.2.7‌​‌ Fast kernel methods: Sobolev,​​ physics-informed, and additive models​​​‌

Participants: Claire Boyer.‌

The work 37 addresses‌​‌ the scalability limitations of​​ kernel methods by introducing​​​‌ a GPU-accelerated framework for‌ kernel regression with $\mathrm{O‌‌}(nlog\mathrm{n})$ computational complexity. Leveraging​​​‌ Fourier representations of kernels‌ together with non-uniform fast‌​‌ Fourier transforms (NUFFT), the​​ proposed approach enables exact,​​​‌ fast, and memory-efficient computations‌ at scale. The framework‌​‌ is instantiated for Sobolev​​ kernel regression, physics-informed regression,​​​‌ and additive models, and‌ the resulting estimators are‌​‌ shown—when applicable—to achieve minimax​​ convergence rates consistent with​​​‌ classical kernel theory. Extensive‌ experiments demonstrate the ability‌​‌ to process datasets with​​ tens of billions of​​​‌ samples within minutes, combining‌ strong statistical guarantees with‌​‌ unprecedented computational scalability.

8.3.1 Early‌ alignment in two-layer networks‌​‌ training is a two-edged​​ sword

Participants: Etienne Boursier​​​‌.

The work 8‌ characterizes the early-stage optimization‌​‌ dynamics of two-layer neural​​​‌ networks with (leaky) ReLU​ activations. In a general​‌ setting, it provides a​​ precise description and quantitative​​​‌ analysis of an early​ alignment phase, during which​‌ neurons align with a​​ small number of key​​​‌ directions determined by the​ critical points of a​‌ data-dependent function. Throughout this​​ phase, the learned function​​​‌ remains close to zero,​ while the representation becomes​‌ increasingly sparse. This sparsification​​ is typically preserved throughout​​​‌ training and ultimately yields​ a final estimator that​‌ is effectively equivalent to​​ a much smaller network.​​​‌ Building on this alignment​ phenomenon, we also present​‌ an example with three​​ data points showing that,​​​‌ in the small-initialization regime,​ arbitrarily large overparameterized networks​‌ may fail to interpolate​​ the data. This result​​​‌ highlights that the seminal​ convergence guarantees for infinitely​‌ wide networks critically depend​​ on the smoothness of​​​‌ the activation function and​ do not extend to​‌ networks with ReLU activations.​​

8.3.2 Simplicity bias and​​​‌ optimization threshold in two-layer​ ReLU networks

Participants: Etienne​‌ Boursier.

Building on​​ the early alignment characterization​​​‌ of 8, the​ work 17 shows that,​‌ when sufficient data are​​ available, trained two-layer ReLU​​​‌ networks often converge to​ simpler solutions that do​‌ not fully interpolate the​​ training data yet generalize​​​‌ better. In particular, for​ a specific linear data​‌ model, we show that​​ the trained network converges​​​‌ to a solution that​ closely matches the least-squares​‌ linear estimator, and is​​ therefore optimal on unseen​​​‌ data. This simple example​ illustrates the transition from​‌ memorization to generalization—an effect​​ observed in in-context learning​​​‌ and diffusion model training—where,​ beyond a certain number​‌ of training samples, the​​ optimization dynamics fail to​​​‌ reach an interpolating global​ minimum. Instead, they converge​‌ to a spurious local​​ minimum of the training​​​‌ loss that nonetheless achieves​ minimal test error.

8.3.3​‌ A theoretical framework for​​ grokking: interpolation followed by​​​‌ Riemannian norm minimisation

Participants:​ Etienne Boursier.

Grokking​‌ is a training phenomenon​​ characterized by two distinct​​​‌ phases: an initial overfitting​ regime with near-zero training​‌ loss and high test​​ loss, followed—after a long​​​‌ delay—by a generalization phase​ in which both training​‌ and test losses become​​ small. The work 18​​​‌ provides a rigorous and​ general characterization of the​‌ two-stage optimization dynamics underlying​​ the grokking phenomenon. In​​​‌ overparameterized settings, the critical​ points of the training​‌ loss form manifolds. Under​​ suitable smoothness assumptions, we​​​‌ establish a two-stage convergence​ of the parameter trajectory​‌ as the weight-decay parameter​​ $\lambda \to 0$.​​​‌ During the first phase,​ the dynamics follow the​‌ unregularized gradient flow, which​​ may lead to poor​​​‌ generalization, for instance in​ large-initialization regimes. In the​‌ second phase, occurring on​​ a time scale of​​​‌ order $1/\mathrm{\lambda }$, the trajectory converges​‌ to a Riemannian flow​​ that minimizes the parameter​​​‌ norm over the critical​ manifold of the training​‌ loss. This phase induces​​ a decrease in parameter​​​‌ norm while preserving training​ performance, a mechanism typically​‌ associated with improved generalization​​ and responsible for the​​​‌ emergence of grokking.

8.3.4​ Policy optimization via adversarial​‌ learning on advantage functions​​

Participants: Chiara Mignacco,​​ Gilles Stoltz.

In​​​‌ collaboration with Matthieu Jonckheere‌ (LAAS–CNRS, Toulouse), We revisit‌​‌ in 14 the reduction​​ of learning in adversarial​​​‌ Markov decision processes (MDPs)‌ to adversarial learning based‌​‌ on Q-values; this reduction​​ has been considered in​​​‌ a number of recent‌ articles as one building‌​‌ block to perform policy​​ optimization. Namely, we first​​​‌ consider and extend this‌ reduction in an ideal‌​‌ setting where an oracle​​ provides value functions: it​​​‌ may involve any adversarial‌ learning strategy (not just‌​‌ exponential weights) and it​​ may be based indifferently​​​‌ on Q-values or on‌ advantage functions. We then‌​‌ present two extensions: first,​​ convergence of the last​​​‌ iterate for a vast‌ class of adversarial learning‌​‌ strategies (again, not just​​ exponential weights), satisfying a​​​‌ property called monotonicity of‌ weights; and second, stronger‌​‌ regret criteria for learning​​ in MDPs, inherited from​​​‌ the stronger regret criteria‌ of adversarial learning named‌​‌ strongly adaptive regret and​​ tracking regret. Then,​​​‌ we demonstrate how adversarial‌ learning, also referred to‌​‌ as aggregation of experts,​​ relates to aggregation (orchestration)​​​‌ of expert policies: we‌ obtain stronger forms of‌​‌ performance guarantees in this​​ setting than existing ones,​​​‌ via yet another, simple‌ reduction. Finally, we discuss‌​‌ the impact of the​​ reduction of learning in​​​‌ adversarial MDPs to adversarial‌ learning in practical scenarios‌​‌ where transition kernels are​​ unknown and value functions​​​‌ must be learned. In‌ particular, we review the‌​‌ literature and note that​​ many strategies for policy​​​‌ optimization feature a policy-improvement‌ step based on exponential‌​‌ weights with estimated Q-values.​​ Our main message is​​​‌ that this step may‌ be replaced by the‌​‌ application of any adversarial​​ learning strategy on estimated​​​‌ Q-values or on estimated‌ advantage functions.

The empirical‌​‌ evaluation of this methodology,​​ together with other twists,​​​‌ is conducted in the‌ companion article 42.‌​‌

8.4.1 An​​​‌ analysis of the noise‌ schedule for score-based generative‌​‌ models

Participants: Claire Boyer​​.

In collaboration with​​​‌ Stanislas Strasman (Sorbonne Université),‌ Antonio Ocello (ENSAE), Sylvain‌​‌ Le Corff (Sorbonne Université),​​ and Vincent Lemaire (Sorbonne​​​‌ Université), the article 15‌ provides a theoretical analysis‌​‌ of score-based generative models,​​ deriving explicit upper bounds​​​‌ on the Kullback–Leibler divergence‌ between the target and‌​‌ learned distributions that depend​​ on the noise schedule.​​​‌ Under additional regularity assumptions,‌ we obtain improved Wasserstein‌​‌ error bounds by exploiting​​ contraction properties of the​​​‌ underlying dynamics. These results‌ yield practical insights into‌​‌ the choice of training​​ hyperparameters, notably the noise​​​‌ schedule, and are illustrated‌ through numerical experiments on‌​‌ synthetic data and CIFAR-10,​​ highlighting an optimal regime​​​‌ within a parametric family‌ of schedules.

8.4.2 Taking‌​‌ a big step: large​​ learning rates in denoising​​​‌ score matching prevent memorization‌

Participants: Claire Boyer.‌​‌

The conference proceedings 27​​, conducted in collaboration​​​‌ with Yu-Han Wu (Google‌ DeepMind), Pierre Marion (Inria)‌​‌ and Gérard Biau (Sorbonne​​ Université), investigate the origin​​​‌ of memorization in diffusion-based‌ generative models and explain‌​‌ why this is often​​ limited in practice despite​​​‌ the absence of explicit‌ regularization. Focusing on denoising‌​‌ score matching, we show​​​‌ that the empirical optimal​ score is highly irregular​‌ in the small-noise regime​​ and leads to memorization​​​‌ of the training data.​ We then identify an​‌ implicit regularization mechanism induced​​ by sufficiently large learning​​​‌ rates in stochastic gradient​ descent, proving that such​‌ training dynamics prevent stable​​ convergence toward arbitrarily low-risk​​​‌ local minima. As a​ result, the learned score​‌ cannot closely match the​​ empirical optimum, thereby mitigating​​​‌ memorization. The theoretical analysis,​ conducted in a simplified​‌ one-dimensional setting with two-layer​​ neural networks, is supported​​​‌ by numerical experiments demonstrating​ the central role of​‌ the learning rate in​​ controlling memorization effects.

8.4.3​​​‌ Optimal stopping in latent​ diffusion models

Participants: Claire​‌ Boyer.

The collaborative​​ work 46 with researchers​​​‌ from Google, Sorbonne Université​ and Inria, investigates an​‌ unexpected phenomenon in latent​​ diffusion models (LDMs), namely​​​‌ that the final steps​ of the diffusion process​‌ can deteriorate sample quality.​​ Going beyond standard numerical​​​‌ arguments for early stopping,​ the authors show that​‌ this effect is intrinsic​​ to the dimensionality reduction​​​‌ inherent in LDMs. Within​ a Gaussian setting with​‌ linear autoencoders, they provide​​ a theoretical characterization of​​​‌ the interplay between latent​ dimension and optimal stopping​‌ time, demonstrating that lower-dimensional​​ latent representations benefit from​​​‌ earlier stopping, while higher-dimensional​ ones require later termination.​‌ The analysis further reveals​​ interactions between latent dimensionality​​​‌ and other key hyperparameters,​ such as constraints in​‌ score matching. These findings​​ are supported by experiments​​​‌ on both synthetic and​ real datasets, establishing early​‌ stopping as a critical​​ hyperparameter for controlling generative​​​‌ quality in LDMs.

8.5.1 Computational lower​​ bounds in latent models:​​​‌ clustering, sparse-clustering, biclustering

Participants:​ Bertrand Even, Christophe​‌ Giraud.

In collaboration​​ with Bertrand Even and​​​‌ Nicolas Verzelen, we investigate​ in 39 computational lower​‌ bounds in latent models.​​ In many high-dimensional problems,​​​‌ like sparse-PCA, planted clique,​ and clustering, the best​‌ known algorithms with polynomial​​ time complexity fail to​​​‌ reach the statistical performance​ provably achievable by algorithms​‌ free of computational constraints.​​ This observation has given​​​‌ rise to the conjecture​ of the existence, for​‌ some problems, of gaps—so​​ called statistical-computational gaps—between the​​​‌ best possible statistical performance​ achievable without computational constraints,​‌ and the best performance​​ achievable with poly-time algorithms.​​​‌ A powerful approach to​ assess the best performance​‌ achievable in poly-time is​​ to investigate the best​​​‌ performance achievable by polynomials​ with low-degree. We build​‌ on the seminal paper​​ of Schramm and Wein​​​‌ 52 and propose a​ new scheme to derive​‌ lower bounds on the​​ performance of low-degree polynomials​​​‌ in some latent space​ models. By better leveraging​‌ the latent structures, we​​ obtain new and sharper​​​‌ results, with simplified proofs.​ We then instantiate our​‌ scheme to provide computational​​ lower bounds for the​​​‌ problems of clustering, sparse​ clustering, and biclustering. We​‌ also prove matching upper-bounds​​ and some additional statistical​​​‌ results, in order to​ provide a comprehensive description​‌ of the statistical-computational gaps​​ occurring in these three​​​‌ problems.

8.5.2 Computational barriers​ for permutation-based problems, and​‌ cumulants of weakly dependent​​ random variables

Participants: Bertrand​​ Even, Christophe Giraud​​​‌.

In collaboration with‌ Bertrand Even and Nicolas‌​‌ Verzelen, we investigate in​​ 38 computational barriers for​​​‌ permutation-based problems. In many‌ high-dimensional problems, polynomial-time algorithms‌​‌ fall short of achieving​​ the statistical limits attainable​​​‌ without computational constraints. A‌ powerful approach to probe‌​‌ the limits of polynomial-time​​ algorithms is to study​​​‌ the performance of low-degree‌ polynomials. Low-degree lower bounds‌​‌ are tightly related to​​ multivariate cumulants. Prior works​​​‌ leverage independence among latent‌ variables to bound cumulants.‌​‌ However, such approaches break​​ down for problems with​​​‌ latent structure lacking independence,‌ such as those involving‌​‌ random permutations. To address​​ this important restriction, we​​​‌ develop a technique to‌ upper-bound cumulants under weak‌​‌ dependencies—such as those arising​​ from sampling without replacement​​​‌ or random permutations. To‌ showcase the effectiveness of‌​‌ our approach, we uncover​​ evidence of statistical–computational gaps​​​‌ in multiple feature matching‌ and in seriation problems.‌​‌

8.5.3 Low-degree lower bounds​​ via almost orthonormal bases​​​‌

Participants: Simone Maria Giancola‌, Christophe Giraud.‌​‌

In collaboration with Alexandra​​ Carpentier, and Nicolas Verzelen,​​​‌ S.M. Giancola and C.‌ Giraud investigate in 33‌​‌ low-degree lower bounds via​​ almost orthonormal bases. Low-degree​​​‌ polynomials have emerged as‌ a powerful paradigm for‌​‌ providing evidence of statistical-computational​​ gaps across a variety​​​‌ of high-dimensional statistical models.‌ For detection problems—where the‌​‌ goal is to test​​ a planted distribution ${\mathrm{\mathbb{P}‌}}^{\text{'}}$ against a null‌ distribution $\mathbb{P}$ with independent‌​‌ components—the standard approach is​​ to bound the advantage​​​‌ using an $L^{\mathrm{2‌}}\left(\mathbb{P}\right)$-orthonormal‌​‌ family of polynomials. However,​​ this method breaks down​​​‌ for estimation tasks or‌ more complex testing problems‌​‌ where $\mathbb{P}$ has some​​ planted structure, so that​​​‌ no simple $L^{\mathrm{2‌}}\left(\mathbb{P}\right)$-orthogonal‌​‌ polynomial family is available.​​ To address this challenge,​​​‌ several technical workarounds have‌ been proposed, though their‌​‌ implementation can be tricky.​​

In this work, we​​​‌ propose a more direct‌ proof strategy. Focusing on‌​‌ random graph models, we​​ construct a basis of​​​‌ polynomials that is almost‌ orthonormal under $\mathbb{P}$,‌​‌ in precisely those regimes​​ where statistical-computational gaps arise.​​​‌ This almost orthonormal basis‌ not only yields a‌​‌ direct route to establishing​​ low-degree lower bounds, but​​​‌ also allows us to‌ explicitly identify the polynomials‌​‌ that optimize the low-degree​​ criterion. This, in turn,​​​‌ provides insights into the‌ design of optimal polynomial-time‌​‌ algorithms. We illustrate the​​ effectiveness of our approach​​​‌ by recovering known low-degree‌ lower bounds, and establishing‌​‌ new ones for problems​​ such as hidden subcliques,​​​‌ stochastic block models, and‌ seriation models.

8.5.4 Phase‌​‌ transitions for stochastic block​​ models with more than​​​‌ sqrt(n) communities

Participants: Christophe‌ Giraud.

.

In‌​‌ collaboration with Alexandra Carpentier,​​ and Nicolas Verzelen, C.​​​‌ Giraud investigated in 34‌ the problem of community‌​‌ recovery in stochastic block​​ models (SBM) with many​​​‌ communities. Predictions from statistical‌ physics postulate that recovery‌​‌ of the communities in​​ SBM is possible in​​​‌ polynomial time above, and‌ only above, the Kesten-Stigum‌​‌ (KS) threshold. This conjecture​​ has given rise to​​​‌ a rich literature, proving‌ that non-trivial community recovery‌​‌ is indeed possible in​​​‌ SBM above the KS​ threshold. Failure of low-degree​‌ polynomials below the KS​​ threshold was also proven,​​​‌ as long as the​ number $K$ of communities​‌ remains smaller than $\sqrt{\mathrm{n}}$, where $n$ is​​​‌ the number of nodes​ in the observed graph.​‌

In this work, we​​ postulate a new threshold​​​‌ below the KS threshold​ for $K\ge \sqrt{\mathrm{n‌}}$, and we prove​​ that:

• 1.
  For any​​​‌ graph density, low-degree​ polynomials fail to recover​‌ communities below the postulated​​ threshold.
• 2.
  Community recovery​​​‌ is possible in polynomial​ time above the postulated​‌ threshold, essentially by counting​​ occurrences of some specific​​​‌ motifs, based on the​ blow-up of a cycle.​‌

In particular, counting self-avoiding​​ paths of length $log‌\left(n\right)$—which​ is closely related to​‌ spectral algorithms based on​​ the non-backtracking operator—is optimal​​​‌ only in the sparse​ regime. Other motif counts—unrelated​‌ to spectral properties—must be​​ considered in denser regimes.​​​‌

8.6.1​ Attention layers provably solve​‌ single-location regression

Participants: Claire​​ Boyer.

The conference​​​‌ proceedings 20, conducted​ in collaboration with Pierre​‌ Marion (Inria), Gérard Biau​​ (Sorbonne Université,) and Raphaël​​​‌ Berthier (Inria), contributes to​ the theoretical understanding of​‌ attention-based models by analyzing​​ their ability to recover​​​‌ sparse, token-level information and​ internal linear representations. We​‌ introduce the single-location regression​​ task, in which only​​​‌ one token at a​ random and unknown location​‌ in a sequence determines​​ the output. We propose​​​‌ a dedicated predictor, interpretable​ as a simplified non-linear​‌ self-attention mechanism, and establish​​ its asymptotic Bayes optimality.​​​‌ Despite the non-convexity of​ the training problem, the​‌ analysis shows that the​​ model successfully learns the​​​‌ underlying structure, providing theoretical​ insight into the effectiveness​‌ of attention mechanisms in​​ settings with sparse and​​​‌ structured token dependencies.

8.6.2​ Attention-based clustering

Participants: Claire​‌ Boyer.

In collaboration​​ with Rodrigo Maulen (Sorbonne​​​‌ Université) and Pierre Marion​ (Inria), the conference proceedings​‌ 22 provides a theoretical​​ analysis of the ability​​​‌ of transformer architectures to​ uncover latent structure in​‌ data in an unsupervised​​ manner. Focusing on data​​​‌ generated from Gaussian mixture​ models, the authors show​‌ that a simplified two-head​​ attention layer can effectively​​​‌ perform clustering: by minimizing​ a suitably defined population​‌ risk using unlabeled data,​​ the attention head parameters​​​‌ provably align with the​ true mixture centroids. The​‌ study further demonstrates that​​ even an attention layer​​​‌ with fixed key, query,​ and value matrices set​‌ to the identity—thus involving​​ no trainable parameters—can perform​​​‌ in-context quantization. These results​ highlight the intrinsic capacity​‌ of attention mechanisms to​​ adapt to input-dependent distributions​​​‌ and to capture underlying​ structural properties of the​‌ data.

8.6.3 Statistical advantage​​ of softmax attention: insights​​​‌ from single location regression​

Participants: Claire Boyer.​‌

The work 28,​​ conducted in collaboration with​​​‌ colleagues from Inria Paris,​ ENS and EPFL, provides​‌ a theoretical investigation of​​ attention mechanisms in large​​​‌ language models, with a​ particular focus on understanding​‌ the role of the​​ softmax activation. Through the​​​‌ study of a single-location​ regression task, the authors​‌ analyze attention-based predictors in​​ a high-dimensional regime using​​ tools from statistical physics.​​​‌ They show that, at‌ the population level, softmax‌​‌ attention achieves the Bayes-optimal​​ risk, whereas linear attention​​​‌ is intrinsically suboptimal. The‌ analysis further identifies key‌​‌ properties of activation functions​​ required for optimal performance.​​​‌ In the finite-sample regime,‌ the authors derive an‌​‌ asymptotic characterization of the​​ test error, demonstrating that​​​‌ although softmax is no‌ longer strictly Bayes-optimal, it‌​‌ consistently outperforms linear attention.​​ These results shed light​​​‌ on the fundamental advantages‌ of softmax attention and‌​‌ its connection to gradient-based​​ optimization dynamics.

8.7.1 Fast confidence bounds​​ for the false discovery​​​‌ proportion over a path‌ of hypotheses

Participants: Guillermo‌​‌ Durand.

In the​​ work 11, in​​​‌ a multiple testing context,‌ we present a new‌​‌ algorithm (and an additional​​ trick) that allows one​​​‌ to quickly compute an‌ entire curve of confidence‌​‌ bounds for the false​​ discovery proportion when the​​​‌ underlying bound $V_{\mathrm{\Re ‌}}^{*}$ construction is based‌​‌ on a reference family​​ $\Re$ with a forest​​​‌ structure like in 50‌. By an entire‌​‌ curve, we mean the​​ values $V_{\Re }^{*‌}(S_1)‌,\cdots ,{\mathrm{V‌‌}}_{\Re }^{*}\left({\mathrm{S}}_m\right)$ computed on​​​‌ a path of increasing‌ selection sets $S_{\mathrm{1‌‌}}⊊\cdots ⊊{\mathrm{S}}_m$, $|{\mathrm{S‌}}_t|=\mathrm{t‌}$. The new algorithm‌​‌ leverages the fact that​​ going from $S_{\mathrm{t‌}}$ to $S_{t+‌1}$ is done by‌​‌ adding only one hypothesis.​​ Compared to a more​​​‌ naive approach, the new‌ algorithm has a complexity‌​‌ in $𝒪(|𝒦|m)‌$ instead of $O(‌\left|𝒦{|}^{\mathrm{2‌‌}}\right)$, where $|𝒦|$ is the​​​‌ cardinality of the family.‌

8.7.2 Robust estimation and‌​‌ outlier detection for stochastic​​ block models

Participants: Leonardo​​​‌ Martins Bianco, Christine‌ Keribin.

In this‌​‌ joint work with Zacharie​​ Naulet (INRAE-MaIAGE), we study​​​‌ robust estimation of graph‌ clustering 21. We‌​‌ first prove a bound​​ for the estimation error​​​‌ of stochastic block model‌ (SBM) parameters which generalizes‌​‌ the bound appearing in​​ Acharya et al. 49​​​‌ for Erdös-Renyi graphs to‌ the case of graphs‌​‌ with multiple communities. Interpreting​​ this bound, we then​​​‌ propose SubSearch, an‌ algorithm for robustly estimating‌​‌ SBM parameters by exploring​​ the space of subgraphs​​​‌ in search of one‌ that closely aligns with‌​‌ the model's assumptions. Our​​ approach also functions as​​​‌ an outlier detection method,‌ identifying nodes responsible for‌​‌ the graph's deviation from​​ the model and going​​​‌ beyond simple techniques like‌ pruning high-degree nodes. Extensive‌​‌ experiments on both synthetic​​ and real-world datasets demonstrate​​​‌ the effectiveness of our‌ method.

8.7.3 Pink discoloration‌​‌ defects associated with microbial​​ structure and metabolome changes​​​‌ in commercial bloomy cheeses‌

Participants: Christine Keribin.‌​‌

In this joint work​​ 13 with F. Irlinger,​​​‌ S. Helinck and A.-S.‌ Sarthou (Paris-Saclay Food and‌​‌ Bioproduct Engineering) and B.​​ Laroche (INRAE MaIAGE), we​​​‌ investigate pink discoloration defects‌ in French bloomy rind‌​‌ soft cheeses, which can​​​‌ negatively affect product appearance​ and lead to economic​‌ losses. Two batches of​​ cheese from the same​​​‌ processing plant were analyzed:​ one with pink defects​‌ and one without, allowing​​ for comparative analysis. A​​​‌ multi-omics approach was applied​ combining microbial profiling (16S​‌ rRNA and ITS2 sequencing)​​ and metabolomics (GC–MS and​​​‌ LC-MS) to identify the​ factors linked to the​‌ defect. We performed a​​ Gaussian latent block model​​​‌ (LBM) co-clustering (Nadif and​ Govaert 51) in​‌ order to detect associations​​ between groups of OTUs​​​‌ and groups of metabolites.​ Based on the LBM​‌ results, a Multiblock sPLS-DA​​ analysis was run to​​​‌ determine if the observed​ associations were also related​‌ to the spoilage status.​​ We found interesting correlations​​​‌ and notably with P.​ gangotriensis that had never​‌ previously been detected in​​ cheese. Its role was​​​‌ tested with a dedicated​ inoculation experiment. The results​‌ strongly suggest that P.​​ gangotriensis is responsible for​​​‌ the pink defect.

8.7.4​ Model selection

Participants: Pascal​‌ Massart, Vincent Rivoirard​​.

In this joint​​​‌ work 40 with Claire​ Lacour, we addressed the​‌ problem of model selection​​ in the sequence model​​​‌ $Y=\theta +\xi$, when $\mathrm{\xi ‌}$ is sub-Gaussian, for non-Euclidian​​ loss functions. In this​​​‌ model, the penalized comparison​ to overfitting procedure was​‌ studied for the ${\mathrm{\ell }}_p$-loss, $p\ge ‌1.$ Several oracle​ inequalities were derived from​‌ concentration inequalities for sub-Weibull​​ variables. Using judicious collections​​​‌ of models and penalty​ terms, minimax rates of​‌ convergence were stated for​​ Besov bodies ${ℬ}_{\mathrm{r‌},\infty }^s$.​ These results were applied​‌ to the functional model​​ of nonparametric regression.

8.7.5​​​‌ Concentration inequalities and cut-off​ phenomena for penalized model​‌ selection within a basic​​ Rademacher framework

Participants: Pascal​​​‌ Massart, Vincent Rivoirard​.

The work 41​‌ was conceived as a​​ tribute to Patrick Cattiaux.​​​‌ One of the authors​ has known Patrick Cattiaux​‌ for many years and​​ is deeply indebted to​​​‌ him. If one wished​ to illustrate the adage​‌ that life is shaped​​ by chance encounters, what​​​‌ better example could there​ be than the meeting,​‌ in the 1980s, of​​ two young people who​​​‌ both fell in love​ with the mathematics of​‌ randomness—one of whom profoundly​​ changed the other’s life​​​‌ by sharing a simple​ but decisive secret: if​‌ you truly believe in​​ it, a passion can​​​‌ become a profession. By​ another fortunate coincidence, this​‌ tribute appeared at a​​ particularly fitting moment, as​​​‌ Michel Talagrand has just​ been awarded the Abel​‌ Prize. The temptation to​​ pay a double homage​​​‌ was therefore irresistible. Following​ one of the many​‌ paths opened by mathematics,​​ we first established a​​​‌ connection between the work​ of Patrick Cattiaux and​‌ that of Michel Talagrand.​​ We then showed how​​​‌ the abstract probabilistic tools​ related to the concentration​‌ of product measures, revisited​​ in this light, can​​​‌ be used to illuminate​ cut-off phenomena in our​‌ own field of expertise,​​ namely mathematical statistics. There​​​‌ is nothing revolutionary here:​ the influence of Talagrand’s​‌ work on the development​​ of mathematical statistics since​​ the late 1990s is​​​‌ well known. Our contribution‌ rather lies in the‌​‌ choice of a very​​ simple framework, allowing the​​​‌ ideas to be presented‌ with minimal technicalities and‌​‌ letting the main concepts​​ stand out clearly.

10.1.1 Visits to international​​​‌ teams

10.2.1 ANR

Sylvain​​​‌ Arlot, Evgenii Chzhen, Luca‌ Ganssali, Christophe Giraud and‌​‌ Gilles Stoltz are part​​ of the PEPR-IA grant​​​‌ CAUSALI-T-AI (CAUSALIty Teams up‌ with Artificial Intelligence), which‌​‌ is led by Marianne​​ Clausel (Univ. de Lorraine),​​​‌ during the period 2023-2028.‌

Sylvain Arlot, Christophe Giraud‌​‌ and Guillermo Durand are​​ part of the ANR​​​‌ Chair-IA grant Biscotte,‌ which is led by‌​‌ Gilles Blanchard (Université Paris​​ Saclay), for the period​​​‌ 2019-2026.

Guillermo Durand is‌ part of the ANR‌​‌ BACKUP: BAyesian nonparametrics,​​ Complex models and Kernels,​​​‌ Uncertainty quantification and deeP‌ methods, with Sorbonne Université‌​‌ and Université de Toulouse.​​ Period: 2023-2028. See here​​​‌.

Christophe Giraud and‌ Guillermo Durand are part‌​‌ of ANR ASCAI:​​ Active and batch segmentation,​​​‌ clustering, and seriation: toward‌ unified foundations in AI,‌​‌ with Potsdam University, Munich​​ University, Montpellier INRAE (Period​​​‌ 2022-2026). See here.‌

11.1.1 Scientific​​ events: organisation

11.1.2 Scientific​‌ events: selection

11.1.3​​​‌ Journal

11.1.4 Invited​​ talks

• B. Even, ASCAI,​​​‌ Orsay, June 2025
• C.​ Boyer, Data science seminar,​‌ Oxford Mathematical Institute (UK),​​ February 2025
• C. Boyer,​​​‌ Seminar, Halicioglu Data Science​ Institute, San Diego, March​‌ 2025
• C. Boyer, Summer​​ School CRM Montreal, May​​ 2025
• C. Boyer, Summer​​​‌ School EDF-INRIA, June 2025‌
• C. Boyer, LMS-Bath Symposia‌​‌ on Inverse Problems and​​ Artificial Intelligence in Medicine​​​‌ Bath (UK), June 2025‌
• C. Boyer, 1W-MINDS seminar,‌​‌ September 2025
• C. Boyer,​​ Colloquium, University of Vienna,​​​‌ October 2025
• C. Boyer,‌ Lecture on generative models,‌​‌ Université d'Aix-Marseille, Novembre 2025​​
• C. Giraud, NITMB, Chicago,​​​‌ April 2025
• C. Giraud,‌ Institute Mathematical Science, Singapore,‌​‌ May 2025
• C. Giraud,​​ ENSAE, November 2025
• C.​​​‌ Giraud, LSE, London, December‌ 2025
• E. Boursier, Inria‌​‌ Lille, March, 2025
• E.​​ Boursier, 10e journée statistique,​​​‌ IHES, Bures-sur-Yvette, April, 2025‌
• E. Boursier, Inria Grenoble,‌​‌ March, 2025
• G. Durand,​​ CBIO team seminar, École​​​‌ des Mines de Paris,‌ March 2025
• G. Durand,‌​‌ Séminaire de modélisation mathématique​​ en sciences de la​​​‌ vie et santé, Univ‌ Paris-Cité, November 2025
• R.‌​‌ Périer, BACKUP meeting, Paris,​​ June 2025
• R. Périer,​​​‌ ASCAI meeting, Orsay, June‌ 2025
• R. Périer, Séminaire‌​‌ parisien de statistique, Paris,​​ September 2025
• J.-M. Poggi,​​​‌ JDSSV Special Invited Paper‌ Session, ISI World Statistics‌​‌ Congress, The Hague, the​​ Netherlands, October 2025
• H.​​​‌ Cui, Séminaire parisien de‌ statistique, Paris, Novembre 2025‌​‌
• H. Cui, ENS Paris,​​ November 2025
• C. Keribin,​​​‌ CFE-CMStatistics, Londres, December 2025‌

11.1.5 Research administration

• S.‌​‌ Arlot is a member​​ of the council of​​​‌ the Computer Science Graduate‌ School (GS ISN) of‌​‌ University Paris-Saclay.
• S. Arlot​​ is a member of​​​‌ the council of the‌ Computer Science Doctoral School‌​‌ (ED STIC) of University​​ Paris-Saclay.
• C. Boyer is​​​‌ a member of the‌ scientific committee of the‌​‌ PGMO (Programme Gaspard Monge​​ pour l'Optimisation) program.
• C.​​​‌ Boyer is an elected‌ member of the liaison‌​‌ committee of SMAI-MODE group.​​
• C. Giraud is a​​​‌ member of the Scientific‌ Committee of labex IRMIA+,‌​‌ Strasbourg.
• C. Giraud is​​ deputy director of the​​​‌ Mathematics Graduate School of‌ University Paris-Saclay.
• C. Giraud‌​‌ is in charge of​​ the whole Masters program​​​‌ in mathematics for University‌ Paris-Saclay.
• C. Giraud is‌​‌ a member of the​​ local Scientific Committee of​​​‌ Institut Pascal.
• C. Giraud‌ is a member of‌​‌ the council of the​​ Mathematics Doctoral School (EDMH)​​​‌ of Université Paris-Saclay.
• C.‌ Keribin is member of‌​‌ the board of the​​ Computer Science Doctoral School​​​‌ (ED MSTIC) of Paris-Est‌ Sup.
• C. Keribin is‌​‌ deputy director of Laboratoire​​ de mathématiques d'Orsay, director​​​‌ since 1/1/2026.
• C. Keribin‌ is in charge of‌​‌ the M2-Math and IA​​ program master of the​​​‌ mathematical school
• P. Massart‌ is director of the‌​‌ Fondation Mathématique Jacques Hadamard​​.

11.1.6 Service to​​​‌ the academic community

• Kevin‌ Bleakley : Maintains the‌​‌ English version of the​​ LMO's website dedicated to​​​‌ research activities
• E. Boursier:‌ member of Inria Saclay‌​‌ scientific committee
• E. Chzhen:​​ member of Bibliothèque Jacques​​​‌ Hadamard scientific committee
• C.‌ Giraud: coordinator of computing‌​‌ resources at the Institut​​ Mathématiques d'Orsay (10 engineers)​​​‌
• C. Giraud: senior member‌ of CCUPS (Commission Consultative‌​‌ Université Paris Saclay)
• G​​ . Durand: member of​​​‌ CCUPS
• G . Durand:‌ member of the Teaching‌​‌ Council of the maths​​ department of Orsay
• C.​​​‌ Giraud: recruting committee for‌ Data-AI associate professor positions‌​‌
• C. Keribin is co-president​​​‌ of the scholarship allocation​ committee MixtAI of the​‌ SaclAI school.
• C. Keribin​​ is member of the​​​‌ committee for awarding the​ Sophie Germain excellence scholarships​‌ (FMJH)
• C. Keribin: member​​ of the follow-up committee​​​‌ for PhD student Sara​ Madad (UTT)
• C. Keribin:​‌ member of the follow-up​​ committee for PhD student​​​‌ Anderson Augusma (Laboratoire d'informatique​ de Grenoble)
• C. Keribin:​‌ member of the follow-up​​ committee for PhD student​​​‌ Augustin Pion (Laboratoire des​ Signaux et Systèmes, CentraleSupelec)​‌
• C. Keribin: member of​​ the follow-up committee for​​​‌ PhD student Lucie Arts​ (LPSM)
• C. Keribin: member​‌ of the follow-up committee​​ for PhD student Samy​​​‌ Vilhes (Insa Rouen)
• G.​ Durand: member of the​‌ follow-up committee for PhD​​ student Nicola De Simone​​​‌ (CEA Grenoble)

11.2.1 Teaching

Most of​​ the team members (especially​​​‌ Professors, Associate Professors and​ Ph.D. students) teach several​‌ courses at University Paris-Saclay,​​ as part of their​​​‌ teaching duty. We mention​ below some of the​‌ classes in which we​​ teach.

• Masters: S. Arlot,​​​‌ Statistical learning and resampling,​ 30h, M2, Université Paris-Saclay​‌
• Masters: S. Arlot, Preparation​​ for French mathematics agrégation​​​‌ (statistics), 25h, M2, Université​ Paris-Saclay
• Masters: C. Boyer,​‌ Refresher courses in statistics,​​ 15h, M2, Université Paris-Saclay​​​‌
• Masters: C. Boyer, Optimization​ meets generalization, mathematics of​‌ neural networks, 20h, M2,​​ Université Paris-Saclay
• Masters: C.​​​‌ Boyer, Guidelines in Machine​ Learning, 20h, M2, Université​‌ Paris-Saclay
• Masters: C. Giraud,​​ High-Dimensional Probability and Statistics,​​​‌ 45h, M2, Université Paris-Saclay​
• Masters: C. Giraud, Mathematics​‌ for AI, 75h, M1,​​ Université Paris-Saclay
• Masters: C.​​​‌ Keribin, unsupervised and supervised​ learning, M1, 42h, Université​‌ Paris-Saclay/ENSTA
• Masters: C. Keribin,​​ Unsupervised learning, M1, 15h,​​​‌ Université Paris-Saclay
• Masters: C.​ Keribin, Advanced Unsupervised Learning,​‌ M2, 24h, Université Paris-Saclay​​
• Masters: C. Keribin, Internship​​​‌ supervision for M2-Maths &​ IA, Université Paris-Saclay
• Masters:​‌ G. Durand, Deep Learning​​ Project, 16h, M1-Maths &​​​‌ AI, Université Paris-Saclay
• Masters:​ G. Durand, Internship supervision,​‌ M1-Maths & AI, Université​​ Paris-Saclay
• Masters: G. Durand,​​​‌ pré-requis de statistique, 6h,​ M1-Maths & AI, Université​‌ Paris-Saclay
• Licence: G. Durand,​​ Statistical inference, 30h, L3​​​‌ mathématiques, Université Paris-Saclay
• Licence:​ G. Durand, Multivariate data​‌ analysis, 18h, L3 mathématiques,​​ Université Paris-Saclay
• Licence: G.​​​‌ Durand, Statistical tests for​ biology, 38h, L2 biology,​‌ Université Paris-Saclay
• Licence: G.​​ Durand, Probability and statistics,​​​‌ 24h, L2 mathématiques et​ sciences du vivant, Université​‌ Paris-Saclay
• Masters: G. Durand,​​ Mathematical statistics, 18h, mastères​​​‌ spécialisées, ENSAE
• Licence/Masters: E.​ Chzhen, PCC Polytechnique
• Masters:​‌ E. Chzhen, Statistical Theory​​ of Algorithmic Fairness, 20h,​​​‌ M2 Université Paris-Saclay
• Masters:​ E. Boursier, Sequential Learning,​‌ 24h, M2 Université Paris-Saclay​​

11.2.2 Supervision

11.2.3 Juries

We‌​‌ participated in many PhD​​ committees (too many to​​​‌ keep an exact record),‌ at University Paris-Saclay as‌​‌ well as at other​​ universities, and we refereed​​​‌ several of these PhDs.‌

11.3.1 Education‌​‌

• Christophe Giraud produces educational​​ videos on his YouTube​​​‌ channel “High-dimensional probability and‌ statistics”: see here.‌​‌
• Gilles Stoltz held a​​ MATh.en.JEANS workshop in 2024-25​​​‌ in Lycée Douanier Rousseau‌ of Laval.

11.3.2 Interventions‌​‌

• A perspective on statistics​​ and the summit for​​​‌ action on AI. See‌ here.

International​​ journals

• 5 articleF.​​​‌Fahd Al Qureshah,​ J.Jérémie Le Pen​‌, N.Nicole de​​ Weerd, M.Marcela​​​‌ Moncada-Velez, M.Marie​ Materna, D.Daniel​‌ Lin, B.Baptiste​​ Milisavljevic, F.Fernanda​​​‌ Vianna, L.Lucy​ Bizien, L.Lazaro​‌ Lorenzo, M.Marc​​ Lecuit, J.-D.Jean-David​​​‌ Pommier, S.Sevgi​ Keles, T.Tayfun​‌ Ozcelik, S.Sigifredo​​ Pedraza-Sanchez, N.Nicolas​​​‌ de Prost, L.​Loubna El Zein,​‌ H.Hassan Hammoud,​​ L. F.Lisa F.P.​​​‌ Ng, R.Rabih​ Halwani, N.Narjes​‌ Saheb Sharif-Askari, Y.​​ L.Yu Lung Lau​​​‌, A.Anthony Tam​, N.Neha Singh​‌, S.Sagar Bhattad​​, Y.Yackov Berkun​​​‌, W.Wasun Chantratita​, R.Raúl Aguilar-López​‌, M.Mohammad Shahrooei​​, L.Laurent Abel​​​‌, A.Alessandro Aiuti​, S.Saleh Al-Muhsen​‌, A. B.Ana​​ Bertha Alcántara-Garduño, E.​​​‌Evangelos Andreakos, A.​Andrés Arias, H.​‌ B.Hagit Baris Feldman​​, P.Paul Bastard​​​‌, A.Alexandre Bolze​, A.Alessandro Borghesi​‌, A.Ahmed Bousfiha​​, P.Petter Brodin​​​‌, J.John Christodoulou​, A.Aurélie Cobat​‌, R.Roger Colobran​​, A.Antonio Condino-Neto​​​‌, S.Sotiriјa Duvlis​, X.Xavier Duval​‌, M.Munis Dündar​​, S.Soha Fakhreddine​​​‌, J.Jacques Fellay​, C.Carlos Flores​‌, J. L.José​​ Luis Franco, G.​​​‌Guy Gorochov, P.​Peter Gregersen, D.​‌David Hagin, R.​​Rabih Halwani, M.​​​‌ T.María Teresa Herrera​, I.-N. F.Ivan​‌ Fan-Ngai Hung, E.​​Emmanuelle Jouanguy, Y.-L.​​​‌Yu-Lung Lau, D.​Daniel Leung, T.​‌Tom Le-Voyer, D.​​Davood Mansouri, J.​​​‌Jesús Mercado-García, I.​Isabelle Meyts, T.​‌Trine Mogensen, L.​​ F.Lisa F.P. Ng​​​‌, A.Antonio Novelli​, G.Giuseppe Novelli​‌, S.Satoshi Okada​​, F.Firat Ozcelik​​​‌, T.Tayfun Ozcelik​, R. P.Rebeca​‌ Perez de Diego,​​ J.Jordi Perez-Tur,​​​‌ G.Graziano Pesole,​ A.Anne Puel,​‌ L.Laurent Renia,​​ I.Igor Resnick,​​​‌ C.Carlos Rodríguez-Gallego,​ M.Manal Sbeity,​‌ S.Sahar Sedighzadeh,​​ M.Mohammad Shahrooei,​​ P.Pere Soler-Palacín,​​​‌ A.András Spaan,‌ S.Stuart Tangye,‌​‌ A. A.Ahmad Abou​​ Tayoun, Ş. G.​​​‌Şehime Gülsün Temel,‌ C.Christian Thorball,‌​‌ I.Ibrahim Torktaz,​​ S.Sophie Trouillet-Assant,​​​‌ S.Stuart Turvey,‌ F.Furkan Uddin,‌​‌ F. S.Fernanda Sales​​ Luiz Vianna, D.​​​‌Donald Vinh, O.‌Oscar Zabaleta-Martínez, Q.‌​‌Qian Zhang, S.-Y.​​Shen-Ying Zhang, J.-L.​​​‌Jean-Laurent Casanova, C.‌Chanreaksmey Eng, K.‌​‌Kimrong Bun, M.​​Mengheng Oum, P.​​​‌Patrice Piola, A.‌Arnaud Tarantola, M.‌​‌Mey Channa, V.​​Veasna Duong, P.​​​‌Philippe Buchy, C.‌Chris Gorman, J.-D.‌​‌Jean-David Pommier, Y.​​Yoann Crabol, P.​​​‌Philippe Dussart, M.‌M. Bunleat, M.‌​‌M. Panha, M.​​M.Kanarith Sim, E.​​​‌Em Bunnakea, D.‌Denis Laurent, H.‌​‌Heng Sothy, K.​​Ky Santy, A.​​​‌Anousone Douangnouvong, D.‌Danoy Chommanam, K.‌​‌Khansoudaphone Phakhounthong, M.​​Manivanh Vongsouvath, M.​​​‌Malee Seephone, B.‌Bountoy Sibounheunang, S.‌​‌Sayaphet Rattanavong, V.​​Viengmon Davong, M.​​​‌Malavanh Vongsouvath, M.‌Mayfong Mayxay, A.‌​‌Audrey Dubot-Pérès, P.​​Paul Newton, S.​​​‌Sommanikhone Phangmanixay, K.‌Khounthavy Phongsavath, D.‌​‌ D.Dang Duc Anh​​, D.Do Quyen​​​‌, T. T.Tran‌ Thi Mai Hung,‌​‌ N. T.Nguyen Thi​​ Thu Thuy, L.​​​‌ M.Luong Minh Tan‌, A. T.Anh‌​‌ Tuan Pham, N.​​Nguyen Hien, D.​​​‌ T.Do Thu Huong‌, L. T.Le‌​‌ Thanh Hai, N.​​ V.Nguyen Van Lam​​​‌, P. N.Pham‌ Nhat An, P.‌​‌ H.Phan Huu Phuc​​, P. B.Phung​​​‌ Bich Thuy, T.‌ T.Tran Thi Thu‌​‌ Huong, C. S.​​Chaw Su Hlaing,​​​‌ A. M.Aye Mya‌ Min Aye, C.‌​‌Cho Thair, K.​​Kyaw Linn, M.​​​‌May July, W.‌Win Thein, L.‌​‌ L.Latt Latt Kyaw​​, H. H.Htay​​​‌ Htay Tin, O.‌ S.Ommar Swe Tin‌​‌, K. Y.Khin​​ Yi Oo, Y.​​​‌Yoann Crabol, M.‌Magali Herrant, M.‌​‌Magali Lago, M.​​Maud Seguy, M.​​​‌Marc Jouan, L.‌Lukas Hafner, P.‌​‌Philippe Pérot, M.​​Marc Eloit, M.​​​‌Marc Lecuit, O.‌Olivier Lortholary, J.‌​‌Julien Capelle, B.​​Bruno Rosset, V.​​​‌Veronique Chevalier, J.‌Jérôme Honnorat, A.‌​‌ L.Anne Laurie Pinto​​, A.Auey Dubot-Peres​​​‌, X.Xavier de‌ Lamballerie, K.Kevin‌​‌ Bleakley, B.Bernadette​​ Murgue, C.Catherine​​​‌ Ferrant, C.Christian‌ Devaux, H.Hervé‌​‌ Tissot-Dupont, J.-P.Jean-Paul​​ Moatti, M.Mayfong​​​‌ Mayxay, P.Pascal‌ Bonnet, D.Didier‌​‌ Fontenille, J.-F.Jean-François​​ Delfraissy, P.Patrice​​​‌ Debré, B.Benoit‌ Durand, L.Laurent‌​‌ Abel, P.Paul​​ Bastard, E.Emmanuelle​​​‌ Jouanguy, V.Vivien‌ Béziat, P.Peng‌​‌ Zhang, C.Charles​​​‌ Rice, A.Aurélie​ Cobat, S.-Y.Shen-Ying​‌ Zhang, P.Paul​​ Hertzog, J.-L.Jean-Laurent​​​‌ Casanova and Q.Qian​ Zhang. A common​‌ form of dominant human​​ IFNAR1 deficiency impairs IFN-α​​​‌ and -ω but not​ IFN-β-dependent immunity.Journal​‌ of Experimental Medicine222​​2February 2025,​​​‌ e20241413HALDOI
• 6​ articleM.Mélissa Baietto​‌, R.Rémi Coulaud​​, C.Christine Keribin​​​‌ and G.Gilles Stoltz​. Improved real-time crowding​‌ information through the modeling​​ of passenger movements in​​​‌ trains with communicating coaches​.Data Science for​‌ Transportation2025HALback​​ to text
• 7 article​​​‌K.Kevin Bleakley,​ M.Mouhcine Mendil,​‌ M.Martin Royer and​​ B.Benjamin Auder.​​​‌ Supervised aggregation of anomaly​ score functions for active​‌ anomaly detection.Transactions​​ on Machine Learning Research​​​‌ Journal2026. In​ press. HALback to​‌ text
• 8 articleE.​​Etienne Boursier and N.​​​‌Nicolas Flammarion. Early​ alignment in two-layer networks​‌ training is a two-edged​​ sword.Journal of​​​‌ Machine Learning ResearchJuly​ 2025HALback to​‌ textback to text​​
• 9 articleS.Simon​​​‌ Briend, C.Christophe​ Giraud, G.Gábor​‌ Lugosi and D.Déborah​​ Sulem. Estimating the​​​‌ history of a random​ recursive tree.Bernoulli​‌2025. In press.​​ HAL
• 10 articleN.​​​‌Nathan Doumèche, G.​Gérard Biau and C.​‌Claire Boyer. On​​ the convergence of PINNs​​​‌.BernoulliVol. 31​2025, pp. 2127-2151​‌HAL
• 11 articleG.​​Guillermo Durand. Fast​​​‌ confidence bounds for the​ false discovery proportion over​‌ a path of hypotheses​​.ComputoOctober 2025​​​‌HALDOIback to​ textback to text​‌
• 12 articleS.Solenne​​ Gaucher, G.Gilles​​​‌ Blanchard and F.Frédéric​ Chazal. Supervised Contamination​‌ Detection, with Flow Cytometry​​ Application.Biometrika112​​​‌4August 2025HAL​DOI
• 13 articleF.​‌Françoise Irlinger, C.​​Christine Keribin, A.-S.​​​‌Anne-Sophie Sarthou, B.​Béatrice Laroche and S.​‌Sandra Helinck. Pink​​ discoloration defects associated with​​​‌ microbial structure and metabolome​ changes in commercial bloomy​‌ cheeses.International Journal​​ of Food Microbiology442​​​‌July 2025, 111363​HALDOIback to​‌ text
• 14 articleM.​​Matthieu Jonckheere, C.​​​‌Chiara Mignacco and G.​Gilles Stoltz. Policy​‌ Optimization via Adv2: Adversarial​​ Learning on Advantage Functions​​​‌.Transactions on Machine​ Learning Research JournalMay​‌ 2025, https://openreview.net/forum?id=Oyueig10EdHAL​​back to text
• 15​​​‌ articleS.Stanislas Strasman​, A.Antonio Ocello​‌, C.Claire Boyer​​, S.Sylvain Le​​​‌ Corff and V.Vincent​ Lemaire. An analysis​‌ of the noise schedule​​ for score-based generative models​​​‌.Transactions on Machine​ Learning Research JournalJanuary​‌ 2025HALback to​​ text

International peer-reviewed conferences​​​‌

• 16 inproceedingsA.Alex​ Barbier-Chebbah, C. L.​‌Christian L. Vestergaard,​​ J.-B.Jean-Baptiste Masson and​​​‌ E.Etienne Boursier.​ Approximate information maximization for​‌ bandit games.Proceedings​​ of Machine Learning Research​​​‌28th International Conference on​ Artificial Intelligence and Statistics​‌258Phuket, ThailandMay​​ 2025, 316-324HAL​​
• 17 inproceedingsE.Etienne​​​‌ Boursier and N.Nicolas‌ Flammarion. Simplicity bias‌​‌ and optimization threshold in​​ two-layer ReLU networks.​​​‌Proceedings of the 42nd‌ International Conference on Machine‌​‌ Learning, Vancouver, Canada. PMLR​​ 267, 2025ICML 2025​​​‌ - International Conference on‌ Machine Learning267Vancouver,‌​‌ CanadaJuly 2025HAL​​back to text
• 18​​​‌ inproceedingsE.Etienne Boursier‌, S.Scott Pesme‌​‌ and R.-A.Radu-Alexandru Dragomir​​. A Theoretical Framework​​​‌ for Grokking: Interpolation followed‌ by Riemannian Norm Minimisation‌​‌.Advances in Neural​​ Information Processing SystemsNeurIPS​​​‌ 2025 - Neural Information‌ Processing Systems38San‌​‌ Diego, United StatesDecember​​ 2025HALback to​​​‌ text
• 19 inproceedingsA.‌Aymeric Capitaine, E.‌​‌Etienne Boursier, E.​​Eric Moulines, M.​​​‌ I.Michael I. Jordan‌ and A.Alain Durmus‌​‌. Prediction-Aware Learning in​​ Multi-Agent Systems.Proceedings​​​‌ of the 42nd International‌ Conference on Machine Learning,‌​‌ Vancouver, Canada. PMLR 267,​​ 2025.ICML 2025 -​​​‌ 42nd International Conference on‌ Machine LearningPMLR 267‌​‌Vancouver, CanadaJuly 2025​​HALback to text​​​‌
• 20 inproceedingsP.Pierre‌ Marion, R.Raphaël‌​‌ Berthier, G.Gérard​​ Biau and C.Claire​​​‌ Boyer. Attention layers‌ provably solve single-location regression‌​‌.Proceedings of the​​ Thirteenth International Conference on​​​‌ Learning RepresentationsICLR 2025‌ - Thirteenth International Conference‌​‌ on Learning RepresentationsSingapore,​​ SingaporeFebruary 2025HAL​​​‌back to text
• 21‌ inproceedingsL.Leonardo Martins‌​‌ Bianco, C.Christine​​ Keribin and Z.Zacharie​​​‌ Naulet. SubSearch: Robust‌ Estimation and Outlier Detection‌​‌ for Stochastic Block Models​​ via Subgraph Search.​​​‌AISTATS 2025 - 28th‌ International Conference Artificial Intelligence‌​‌ and Statistics258Mai​​ Khao, ThailandMay 2025​​​‌, 1297-1305HALback‌ to text
• 22 inproceedings‌​‌R.Rodrigo Maulen-Soto,​​ P.Pierre Marion and​​​‌ C.Claire Boyer.‌ Attention-based clustering.Proceedings‌​‌ of The Thirty-ninth Annual​​ Conference on Neural Information​​​‌ Processing Systems (NeurIPS 2025)‌The Thirty-ninth Annual Conference‌​‌ on Neural Information Processing​​ Systems 2025San Diego,​​​‌ United States2025HAL‌back to text
• 23‌​‌ inproceedingsS.Stanislas Strasman​​, S.Sobihan Surendran​​​‌, C.Claire Boyer‌, S.Sylvain Le‌​‌ Corff, V.Vincent​​ Lemaire and A.Antonio​​​‌ Ocello. Wasserstein Convergence‌ of Critically Damped Langevin‌​‌ Diffusions.Proceedings of​​ The Thirty-ninth Annual Conference​​​‌ on Neural Information Processing‌ Systems (NeurIPS) 2025The‌​‌ Thirty-ninth Annual Conference on​​ Neural Information Processing Systems​​​‌ (NeurIPS 2025)San Diego,‌ United States2025HAL‌​‌
• 24 inproceedingsV.Victor​​ Thuot, A.Alexandra​​​‌ Carpentier, C.Christophe‌ Giraud and N.Nicolas‌​‌ Verzelen. Clustering with​​ bandit feedback: breaking down​​​‌ the computation/information gap.‌36. International Conference on‌​‌ Algorithmic Learning Theory, ALT​​ 2025272Proceedings of​​​‌ Machine Learning ResearchMilano,‌ ItalyPMLRFebruary 2025‌​‌, 1221 - 1284​​HAL
• 25 inproceedingsG.​​​‌Gauthier Thurin, K.‌Kimia Nadjahi and C.‌​‌Claire Boyer. Optimal​​ Transport-based Conformal Prediction.​​​‌Proceedings of International Conference‌ on Machine Learning (ICML‌​‌ 2025)International Conference on​​ Machine Learning (ICML 2025)​​​‌Vancouver, Canada2025HAL‌back to text
• 26‌​‌ inproceedingsD.Daniil Tiapkin​​​‌, E.Evgenii Chzhen​ and G.Gilles Stoltz​‌. Narrowing the Gap​​ between Adversarial and Stochastic​​​‌ MDPs via Policy Optimization​.The 28th International​‌ Conference on Artificial Intelligence​​ and Statistics (AISTATS)Mai​​​‌ Khao, ThailandMay 2025​HAL
• 27 inproceedingsY.-H.​‌Yu-Han Wu, P.​​Pierre Marion, G.​​​‌Gérard Biau and C.​Claire Boyer. Taking​‌ a Big Step: Large​​ Learning Rates in Denoising​​​‌ Score Matching Prevent Memorization​.Proceedings of Thirty​‌ Eighth Conference on Learning​​ Theory, PMLR (COLT 2025)​​​‌Proceedings of Thirty Eighth​ Conference on Learning Theory,​‌ PMLRLyon, France2025​​HALback to text​​​‌

Conferences without proceedings

• 28​ inproceedingsO.Odilon Duranthon​‌, P.Pierre Marion​​, C.Claire Boyer​​​‌, B.Bruno Loureiro​ and L.Lenka Zdeborová​‌. Statistical Advantage of​​ Softmax Attention: Insights from​​​‌ Single-Location Regression.ICLR​ 2026 - Fourteenth International​‌ Conference on Learning Representations​​Rio de Janeiro, Brazil​​​‌April 2026HALback​ to text
• 29 inproceedings​‌M.Maxime Megel,​​ G.Gilles Celeux,​​​‌ S. X.Serge X.​ Cohen, A.Agnès​‌ Grimaud and C.Christine​​ Keribin. Clustering of​​​‌ XRF spectral images using​ a dissimilarity based on​‌ likelihood loss.JdS​​ 2025 - 56ièmes Journées​​​‌ de StatistiqueMarseille, France​June 2025HAL
• 30​‌ inproceedingsP.-A.Pierre-André Mikem​​, C.Christine Keribin​​​‌ and P.Pascal Massart​. Weakly supervised learning​‌ methods for the classification​​ of patients from flow​​​‌ cytometry data.JDS​ 2025 - 56ème édition​‌ des Journées de Statistiques​​Marseille, FranceJune 2025​​​‌HAL
• 31 inproceedingsP.​Patrick Pamphile, S.​‌Sonia Lefeuvre, J.​​ O.Jacques Olivier Klein​​​‌ and I.Isabelle Bournaud​. Transition to the​‌ Competency-Based Approach: Teachers' Perception​​ in the Implementation of​​​‌ the BUT.Ecosystème​ de formations : pour​‌ quelles transformation(s) ?BREST,​​ FranceMay 2025HAL​​​‌

Reports & preprints

• 32​ miscG.Gérard Biau​‌ and C.Claire Boyer​​. A Note on​​​‌ k-NN Gating in RAG​.January 2026HAL​‌
• 33 miscA.Alexandra​​ Carpentier, S. M.​​​‌Simone Maria Giancola,​ C.Christophe Giraud and​‌ N.Nicolas Verzelen.​​ Low-degree lower bounds via​​​‌ almost orthonormal bases.​December 2025, 53p.​‌HALback to text​​
• 34 miscA.Alexandra​​​‌ Carpentier, C.Christophe​ Giraud and N.Nicolas​‌ Verzelen. Phase Transition​​ for Stochastic Block Model​​​‌ with more than $\sqrt{\mathrm{n}}$ Communities.September 2025​‌HALback to text​​back to text
• 35​​​‌ miscE.Evgenii Chzhen​, M.Mohamed Hebiri​‌ and G.Gayane Taturyan​​. Randomized multi-class classification​​​‌ under system constraints: a​ unified approach via post-processing​‌.December 2025HAL​​back to text
• 36​​​‌ miscN.Nathan Doumèche​, F.Francis Bach​‌, É.Éloi Bedek​​, G.Gérard Biau​​​‌, C.Claire Boyer​ and Y.Yannig Goude​‌. Forecasting time series​​ with constraints.February​​​‌ 2025HALback to​ text
• 37 miscN.​‌Nathan Doumèche, F.​​Francis Bach, G.​​​‌Gérard Biau and C.​Claire Boyer. Fast​‌ kernel methods: Sobolev, physics-informed,​​ and additive models.​​September 2025HALback​​​‌ to textback to‌ text
• 38 miscB.‌​‌Bertrand Even, C.​​Christophe Giraud and N.​​​‌Nicolas Verzelen. Computational‌ barriers for permutation-based problems,‌​‌ and cumulants of weakly​​ dependent random variables.​​​‌July 2025, 79‌ p.HALback to‌​‌ text
• 39 miscB.​​Bertrand Even, C.​​​‌Christophe Giraud and N.‌Nicolas Verzelen. Computational‌​‌ lower bounds in latent​​ models: clustering, sparse-clustering, biclustering​​​‌.June 2025HAL‌back to text
• 40‌​‌ miscC.Claire Lacour​​, P.Pascal Massart​​​‌ and V.Vincent Rivoirard‌. Is model selection‌​‌ possible for the ${}_{\mathrm{p}}$-loss? PCO estimation for​​​‌ regression models.April‌ 2025HALback to‌​‌ text
• 41 miscP.​​Pascal Massart and V.​​​‌Vincent Rivoirard. Concentration‌ inequalities and cut-off phenomena‌​‌ for penalized model selection​​ within a basic Rademacher​​​‌ framework.April 2025‌HALback to text‌​‌
• 42 miscC.Chiara​​ Mignacco, M.Matthieu​​​‌ Jonckheere and G.Gilles‌ Stoltz. Online Matching‌​‌ via Reinforcement Learning: An​​ Expert Policy Orchestration Strategy​​​‌.October 2025HAL‌back to text
• 43‌​‌ miscP.Patrick Pamphile​​ and I.Isabelle Bournaud​​​‌. Appropriation d'un dispositif‌ d'accompagnement méthodologique d'étudiants primoentrants‌​‌ à l'université : une​​ lecture par profils et​​​‌ postures.September 2025‌HAL
• 44 miscP.‌​‌Patrick Pamphile. Comprendre​​ la réussite étudiante :​​​‌ une comparaison méthodologique entre‌ régression multiple et analyse‌​‌ par profils.June​​ 2025HAL
• 45 misc​​​‌G.Guillaume Principato,‌ G.Gilles Stoltz,‌​‌ Y.Yvenn Amara-Ouali,​​ Y.Yannig Goude,​​​‌ B.Bachir Hamrouche and‌ J.Jean‐michel Poggi.‌​‌ Conformal Prediction for Hierarchical​​ Data.February 2025​​​‌HALback to text‌
• 46 miscY.-H.Yu-Han‌​‌ Wu, Q.Quentin​​ Berthet, G.Gérard​​​‌ Biau, C.Claire‌ Boyer, E.Elie‌​‌ Romuald and P.Pierre​​ Marion. Optimal stopping​​​‌ in latent diffusion models‌.October 2025HAL‌​‌back to text

Other​​ scientific publications

• 47 misc​​​‌C.Christophe Biernacki,‌ J.Julien Jacques and‌​‌ C.Christine Keribin.​​ Model based co-clustering: high​​​‌ dimension & estimation challenges‌.January 2025HAL‌​‌
• 48 miscL.Leonardo​​ Martins Bianco, C.​​​‌Christine Keribin and Z.‌Zacharie Naulet. Robust‌​‌ estimation and outlier detection​​ for Stochastic Block Models​​​‌ via subgraph search.‌December 2025HAL