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Breaking the curse of dimensionality for linear rules: optimal predictors over the ellipsoid
No full textIn this work, we address the following question: What minimal structural assumptions are needed to prevent the degradation of statistical learning bounds with increasing dimensionality? We investigate this question in the classical statistical setting of signal estimation from n independent linear observations Y i = X ⊤ i θ + ϵ i . Our focus is on the generalization properties of a broad family of predictors that can be expressed as linear combinations of the training labels, f (X) = n i=1 l i (X)Y i . This class -commonly referred to as linear prediction rules -encompasses a wide range of popular parametric and non-parametric estimators, including ridge regression, gradient descent, and kernel methods. Our contributions are twofold. First, we derive non-asymptotic upper and lower bounds on the generalization error for this class under the assumption that the Bayes predictor θ lies in an ellipsoid. Second, we establish a lower bound for the subclass of rotationally invariant linear prediction rules when the Bayes predictor is fixed. Our analysis highlights two fundamental contributions to the risk: (a) a variance-like term that captures the intrinsic dimensionality of the data; (b) the noiseless error, a term that arises specifically in the high-dimensional regime. These findings shed light on the role of structural assumptions in mitigating the curse of dimensionality
Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime
No full textNeural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and diagonal neural networks in the feature learning regime. Leveraging connections with matrix compressed sensing and LASSO, we derive a detailed phase diagram for the scaling exponents of the excess risk as a function of sample complexity and weight decay. This analysis uncovers crossovers between distinct scaling regimes and plateau behaviors, mirroring phenomena widely reported in the empirical neural scaling literature. Furthermore, we establish a precise link between these regimes and the spectral properties of the trained network weights, which we characterize in detail. As a consequence, we provide a theoretical validation of recent empirical observations connecting the emergence of power-law tails in the weight spectrum with network generalization performance, yielding an interpretation from first principles.</div
La lutte contre la torture, objectif majeur de la sauvegarde des droits humains
No full textInternational audienc
Metabarcoding and metagenomic data across aquatic environmental gradients along the coasts of France and Chile
No full textInternational audienceCoastal marine environments, such as lagoons, fjords or estuaries, experience pronounced environmental variability, with fluctuations in salinity, temperature and nutrient levels shaping microbial community structure and function. These gradients result in diverse habitats, which may harbour taxonomic and genetic novelty with biogeochemical and biotechnological relevance. To explore microbial diversity and functional potential across these dynamic ecosystems, we sampled 26 sites along the coasts of France and Chile, including lagoons, estuaries, fjords, harbours, as well as coastal and offshore marine sites. Surface waters were collected from all sites, with deeper layers included at three sites. Monthly sampling at six sites in France enabled the assessment of seasonal dynamics. In total, 116 samples were processed for both metabarcoding and metagenomic sequencing yielding over 53,000 amplicon sequence variants (ASVs) and 1,372 metagenome-assembled genomes (MAGs). This dataset further includes a comprehensive gene catalogue and environmental variables such as salinity, temperature, nutrient concentrations, productivity, as well as oxygen consumption metrics collected across the different ecosystems
Euclid: Early Release Observations -- The star-formation history of massive early-type galaxies in the Perseus cluster
No full textInternational audienceThe Euclid Early Release Observations (ERO) programme targeted the Perseus galaxy cluster in its central region over 0.7deg. We combined the exceptional image quality and depth of the ERO-Perseus with FUV and NUV observations from GALEX and AstroSat/UVIT, as well as data from MegaCam at the CFHT, to deliver FUV-to-NIR magnitudes of the 87 brightest galaxies within the Perseus cluster. We reconstructed the star-formation history (SFH) of 59 early-type galaxies (ETGs) within the sample, through the spectral energy distribution (SED) fitting code CIGALE and state-of-the-art stellar population (SP) models to reproduce the galactic UV emission from hot, old, low-mass stars (i.e. the UV upturn). In addition, for the six most massive ETGs in Perseus [stellar masses ], we analysed their spatially resolved SP through a radial SED fitting. In agreement with our previous work on Virgo ETGs, we found that (i) the majority of ETGs needs the presence of an UV upturn to explain their FUV emission, with temperatures ~33800 K; (ii) ETGs have grown their stellar masses quickly, with SF timescales Myr. We found that all ETGs in the sample have formed more than about 30% of their stellar masses at z~5, up to ~100%. At z~5, the stellar masses of the most massive nearby ETGs, which have present-day stellar masses , are then found to be comparable to those of the red quiescent galaxies observed by JWST at similar redshifts (z>4.6). This study can be extended to ETGs in the 14000 deg extragalactic sky that will soon be observed by Euclid, in combination with those from other major upcoming surveys (e.g. Rubin/LSST), and UV observations, to ultimately assess whether the nearby massive ETGs represent the progeny of the massive high-z JWST red quiescent galaxies
Hegel et le vitruvianisme. Sur le rapport entre philosophie et théorie de l'architecture
No full textInternational audienc
Near‐Inertial Wave Trapping Inside a Fine‐Scale Anticyclonic Eddy During the BioSWOT‐Med 2023 Cruise: Turbulence and Energy Flux
No full textInternational audienceAbstract Near‐inertial waves (NIWs) are an important source of turbulence for the ocean interior. Mesoscale anticyclonic eddies are known to facilitate their propagation at depth while trapping them. However, in situ observations have so far focused on large ( km radius), energetic eddies, whereas most of the ocean is populated by smaller, moderately energetic fine‐scale structures. Are these smaller structures efficient to trap NIWs and enhance turbulence? Here, we present in situ observations from the BioSWOT‐Med 2023 cruise addressing this issue by surveying a fine‐scale frontal area of the North Balearic front in the Mediterranean Sea, assisted by the first high‐resolution Sea Surface Height images of the new Surface Water and Ocean Topography (SWOT) satellite mission during its Calibration/Validation phase. We explore how fine scales modulate the evolution of turbulence below the mixed layer after experiencing two consecutive strong wind events. We show that turbulence remains low in the front and its cyclonic side, while being greatly enhanced in the anticyclonic side. The latter side is dominated by a fine‐scale anticyclone (12.8 km of radius, Rossby number of 0.5) that trapped NIWs, increasing turbulent dissipation level to several 10-8 W/kg . The NIW‐induced vertical kinetic energy flux reach up to 5.1 mW/m2 below the pycnocline and represent ~20 % of the wind power input into inertial motions, higher or similar to previous estimations outside and inside mesoscale anticyclones. Future work is needed to investigate whether these results extend to fine scales elsewhere in the world ocean, especially in regions with larger baroclinic Rossby radius of deformation
