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Using Small Language Models to Reverse-Engineer Machine Learning Pipelines Structures
No full textSANER 2026 ReportBackground: Extracting the stages that structure Machine Learning (ML) pipelines from source code is key for gaining a deeper understanding of data science practices. However, the diversity caused by the constant evolution of the ML ecosystem (e.g., algorithms, libraries, datasets) makes this task challenging. Existing approaches either depend on non-scalable, manual labeling, or on ML classifiers that do not properly support the diversity of the domain. These limitations highlight the need for more flexible and reliable solutions.Objective: We evaluate whether Small Language Models (SLMs) can leverage their code understanding and classification abilities to address these limitations, and subsequently how they can advance our understanding of data science practices.Method: We conduct a confirmatory study based on two reference works selected for their relevance regarding current state-of-the-art's limitations. First, we compare several SLMs using Cochran's Q test. The best-performing model is then evaluated against the reference studies using two distinct McNemar's tests. We further analyze how variations in taxonomy definitions affect performance through an additional Cochran's Q test. Finally, a goodness-of-fit analysis is conducted using Pearson's chi-squared tests to compare our insights on data science practices with those from prior studies
Training for Mixed-Precision Integer Weights, Activations and Embeddings in BERT
No full textInternational audiencePre-trained language models (LMs) deliver strong performance across a wide range of Natural Language Processing (NLP) tasks but remain costly to deploy on embedded devices due to their high memory and compute requirements. A widely used strategy for adapting LMs to resource-constrained devices is aggressive quantization. At low bit-widths, mixed-precision schemes, where different components of the model use different numerical precisions, offer an effective balance between compression and accuracy. In this work, we evaluate the impact of mixed-precision quantization for inference on the BERT language model. Unlike prior studies that often overlook activation quantization, our evaluation systematically explores mixed-precision configurations for both weights and activations. We also examine the effects of quantizing the embedding layer, which is commonly limited to token-weight quantization. Evaluated on the SQuAD and GLUE benchmarks, our approach achieves substantial reductions in memory and computational cost without sacrificing accuracy
Most incompatible measurements and sum-of-squares optimisation
No full textMeasurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a long-standing problem. In this work, we exhibit analytical universal parent measurements giving access to bounds that beat the state of the art. In particular, we can show that, for relevant robustnesses, sets of anticommuting observables give rise to the most incompatible dichotomic measurements. We also formalise the construction of such universal parent measurements in the framework of sum-of-squares optimisation and obtain preliminary numerical results demonstrating the power of the method by improving on our own analytical values. All results find direct application for demonstrating genuine high-dimensional steering, that is, certifying the dimensionality of a quantum system in a one-sided device-independent manner
Uncertainty estimation in marker-based motion capture of the tennis serve
No full textInternational audienceMarker-based motion capture (MoCap) systems are widely used to analyse human movement. However, they are affected by measurement uncertainties, particularly marker placement errors (MPE) and soft tissue artefacts (STA). Here, we quantify the individual and combined effects of these two sources of uncertainty on joint angles and angular velocities in the case of the tennis serve. A Monte-Carlo approach was used to simulate 3000 perturbed marker trajectories for each uncertainty source and their combination. We applied a random offset for MPE, while sinusoidal perturbations were used to simulate for STA. The resulting joint kinematics were compared across all degrees of freedom. Confidence intervals (5-95 %), root mean square deviation (RMSD) and Minimal Detectable Changes (MDC) were calculated for key biomechanical variables. Results showed that STA predominantly affected angular velocities, while MPE had a greater impact on joint angles. The combined simulation consistently produced the largest variability, with mean confidence intervals ranging from 5.1° to 30.8° for joint angles and from 70.5°.s-1 to 248.5°.s-1 for joint angular velocities, and RMSD values ranging from 1.6° to 8.4° for joint angles and from 16.8°.s-1 to 68.0°.s-1 for joint angular velocities. To our knowledge, this is the first quantification of MPE and STA effects on ballistic movement kinematics. These results provide critical reference values, enabling more accurate comparisons across subjects and studies while accounting for measurement uncertainties
High-Dimensional Analysis of Gradient Flow for Extensive-Width Quadratic Neural Networks
No full textWe study the high-dimensional training dynamics of a shallow neural network with quadratic activation in a teacher-student setup. We focus on the extensive-width regime, where the teacher and student network widths scale proportionally with the input dimension, and the sample size grows quadratically. This scaling aims to describe overparameterized neural networks in which feature learning still plays a central role. In the high-dimensional limit, we derive a dynamical characterization of the gradient flow, in the spirit of dynamical mean-field theory (DMFT). Under l2-regularization, we analyze these equations at long times and characterize the performance and spectral properties of the resulting estimator. This result provides a quantitative understanding of the effect of overparameterization on learning and generalization, and reveals a double descent phenomenon in the presence of label noise, where generalization improves beyond interpolation. In the small regularization limit, we obtain an exact expression for the perfect recovery threshold as a function of the network widths, providing a precise characterization of how overparameterization influences recovery
Degree bounds for linear differential equations and recurrences
No full textLinear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing algorithms that compute such representations as a linear relation between the iterates of an elementary operator known as a pseudo-linear map. Algorithms of this form have been designed and used for solving various computational problems, in different contexts, including effective closure properties for linear differential or recurrence equations, the computation of a differential equation satisfied by an algebraic function, and many others. We propose a unified approach for establishing precise degree bounds on the solutions of all these problems. This approach relies on a common structure shared by all the specific instances of the class. For each problem, the obtained bound is tight. It either improves or recovers the previous best known bound that was derived by ad hoc methods
On the rectifiability of and spaces with unique tangents
No full textWe prove rectifiability results for and metric measure spaces with pointwise Ahlfors regular reference measure and with -almost everywhere unique metric tangents. In particular, we show rectifiability if (i) is for an arbitrary and has Hausdorff dimension n<5, or (ii) is and non-collapsed, namely it has Hausdorff dimension . Our strategy is based on the failure of the condition in sub-Finsler Carnot groups, on a new result on the failure of the non-collapsed on sub-Finsler Carnot groups, and on the recent breakthrough by Bate [Invent. Math., 230(3):995-1070, 2022]
Online Markov Decision Processes with Terminal Law Constraints
No full textTraditional reinforcement learning usually assumes either episodic interactions with resets or continuous operation to minimize average or cumulative loss. While episodic settings have many theoretical results, resets are often unrealistic in practice. The infinite-horizon setting avoids this issue but lacks non-asymptotic guarantees in online scenarios with unknown dynamics. In this work, we move towards closing this gap by introducing a reset-free framework called the periodic framework, where the goal is to find periodic policies: policies that not only minimize cumulative loss but also return the agents to their initial state distribution after a fixed number of steps. We formalize the problem of finding optimal periodic policies and identify sufficient conditions under which it is well-defined for tabular Markov decision processes. To evaluate algorithms in this framework, we introduce the periodic regret, a measure that balances cumulative loss with the terminal law constraint. We then propose the first algorithms for computing periodic policies in two multi-agent settings and show they achieve sublinear periodic regret of order Õ(T 3/4 ). This provides the first non-asymptotic guarantees for reset-free learning in the setting of M homogeneous agents, for M > 1.</div
Codes de calcul industriels pour la simulation des écoulements turbulents
No full textMasterLa simulation numérique en mécanique des fluides (ou CFD) est devenue un des outils standards à disposition des ingénieurs. Dans ce cours, on dressera un état de l’art des méthodes utilisées couramment dans les codes industriels et on donnera les pistes de recherche les plus actives qui constitueront les standards de demain. Ce cours n'a pas pour objet l'apprentissage pratique de l'utilisation d'un code CFD, mais donne toutes les clés pour comprendre ce que les codes contiennent et pour les utiliser de manière éclairée.Pré-requis : Ce cours ne nécessite comme base qu'un cours d’introduction à la turbulence.Contenu :Les principaux points qui seront abordés sont les suivants : 1. Introduction à la CFD (Computational Fluid Dynamics) ◦ Différents phases et points durs de la simulation : modélisation géométrique, maillage, modélisation physique, calcul, post-traitement, ◦ Évaluation des coûts de calcul liés à la turbulence, puissance de calcul disponible aujourd’hui et conclusions à en tirer pour la modélisation, ◦ Différentes méthodes disponibles (RANS, hybrides, LES, DNS) : objectifs, formalisme, modélisation, maturité, champs d’application, ◦ Panorama des codes de calculs : codes commerciaux (Fluent, StarCD, CFX, Powerflow…), codes industriels « maison », codes open-source (Open-Foam, Code_Saturne). 2. Méthode standard dans les projets industriels : la modélisation RANS (modélisation aux moyennes de Reynolds) : ◦ Problème de fermeture, différents niveaux de modélisation, rapide historique, ◦ Similitude avec la mécanique des milieux continus classique (lois de comportement), principes physiques guidant la modélisation, ◦ Modélisation au premier ordre : hypothèses, choix de la loi de comportement, k-epsilon, k-oméga, Spalart-Almaras, etc. : limitations, corrections, variantes, ◦ Modèles au second ordre : hypothèses, avantages, limitations, modélisation algébrique, ◦ La région de proche paroi : difficulté physique, choix du couple maillage/modèle, lois de paroi, modèles bas-Reynolds, 3. Les méthodes plus coûteuses : ◦ La simulation des grandes échelles (LES) : formalisme de filtrage, tensions de sous-maille, modélisation, champs d’application aujourd’hui, ◦ Les méthodes hybrides RANS/LES : • méthodes zonales : principe, modélisation aux interfaces, • méthodes continues : formalisme, URANS, OES, VLES, SNS, DES, SBES, SAS, PANS, PITM, HTLE
Internal tide loss of coherence in a realistic simulation of the North Atlantic
No full textInternational audienceAbstract. The loss of coherence of the semidiurnal internal tide is investigated using a high-resolution realistic numerical simulation over the North Atlantic. The analysis focuses on processes resulting from the interaction between the internal tide and the mesoscale background flow at time scales typically shorter than one month. To this end, a theoretical framework based on vertical mode decomposition and the splitting of the internal tide signal into coherent and incoherent components is developed and applied to the outputs of the numerical simulation. This framework enables the transfer terms between the coherent and incoherent parts, and between the different vertical modes – and therefore horizontal scales – of the internal tides to be evaluated. By focusing on three subdomains with contrasting dynamics, we demonstrate that coherent-to-incoherent energy transfers significantly impact the internal tide energy budget. These transfers are dominated by advection by slowly varying flows and mainly occur without changing the vertical mode of the internal tide involved. This is attributed to the dominance of the barotropic and first baroclinic modes in the mesoscale flow combined with the structure of the mesoscale flow/internal tide interaction terms. Typical energy transfer rates are of the order of a few tens of days in the Gulf Stream region and a few hundred days in the Azores for the mode 1 internal tide