Geometric compression of invariant manifolds in neural nets

We study how neural networks compress uninformative input space in models where data lie in $d$ dimensions, but whose label only vary within a linear manifold of dimension $d_\parallel < d$. We show that for a one-hidden layer network initialized with infinitesimal weights (i.e. in the \textit{feature learning} regime) trained with gradient descent, the uninformative $d_\perp=d-d_\parallel$ space is compressed by a factor $\lambda\sim \sqrt{p}$, where $p$ is the size of the training set. We quantify the benefit of such a compression on the test error $\epsilon$. For large initialization of the weights (the \textit{lazy training} regime), no compression occurs and for regular boundaries separating labels we find that $\epsilon \sim p^{-\beta}$, with $\beta_\text{Lazy} = d / (3d-2)$. Compression improves the learning curves so that $\beta_\text{Feature} = (2d-1)/(3d-2)$ if $d_\parallel = 1$ and $\beta_\text{Feature} = (d + d_\perp/2)/(3d-2)$ if $d_\parallel > 1$. We test these predictions for a stripe model where boundaries are parallel interfaces ($d_\parallel=1$) as well as for a cylindrical boundary ($d_\parallel=2$). Next we show that compression shapes the Neural Tangent Kernel (NTK) evolution in time, so that its top eigenvectors become more informative and display a larger projection on the labels. Consequently, kernel learning with the frozen NTK at the end of training outperforms the initial NTK. We confirm these predictions both for a one-hidden layer FC network trained on the stripe model and for a 16-layers CNN trained on MNIST, for which we also find $\beta_\text{Feature}>\beta_\text{Lazy}$. The great similarities found in these two cases support that compression is central to the training of MNIST, and puts forward kernel-PCA on the evolving NTK as a useful diagnostic of compression in deep nets

Procalcitonin levels during pregnancy, delivery and postpartum

Aims: To determine the normal value ranges of procalcitonin (PCT) in women with uncomplicated pregnancies. Methods: This prospective cohort study was conducted between May 2009 and February 2010 among 60 women without signs of clinical infection (31 vaginal deliveries, 29 cesarean sections) attending the maternity unit of the University of Geneva Hospitals. Sequential follow-up of PCT levels was performed at 24-28 weeks (n=7), 36-40 weeks (n=60), at delivery (n=59), and at days 2-3 (n=58) and 10 (n=53) postpartum using a sensitive PCT assay with a functional sensitivity of 0.06 μg/L. Results: Median levels of PCT were: 24-28 weeks: 0.043 μg/L (range 0.010-0.080); 36-40 weeks: 0.061 μg/L (range 0.010-0.110); at delivery: 0.068 μg/L (range 0.010-0.170); days 2-3: 0.200 μg/L (range 0.030-5.00); and day 10: 0.060 μg/L (range 0.020-0.120). At days 2-3 postpartum, three women had a PCT level between 0.25 μg/L and 0.5 μg/L and two women had a level higher than 0.5 μg/L. Conclusions: This study provides reference values for PCT during the third trimester, at delivery and at the immediate postpartum period. A cut-off PCT level of 0.25 μg/L can be used during the third trimester, at delivery, and at the immediate postpartum period to rule out infectio

Uncooperative Rendezvous and Docking for MicroSats

This paper proposes a solution to perform active debris removal with a cost effective microsatellite. A complex aspect of debris removal in space is the detection and positive identification of the debris, medium to close approach as well as the orbital rendezvous and following on-site operations. These aspects will require a mix of several technologies, some of which already exist, and some of which will need to be miniaturized and adapted for programs such as CleanSpace One. The rendezvous phases in particular will require a good knowledge of the position of the chaser as well as that of the target. In the CleanSpace One concept, the approach and in-orbit maneuvering will be performed by a micropropulsion system based on miniature thrusters. This concept also proposes that grabbing will be done by means of a robotic claw, which will adapt itself to the form of a non-cooperating object. These are key technologies that currently being developed in EPFL laboratories. The overall microsatellite uses CubeSat and COTS technologies

Ki-Mouse: une application Windows permettant de contrôler sa souris en utilisant les membres de son corps

La fondation (FST) m’a demandé dans le cadre de ce travail de Bachelor de réaliser une application Windows en utilisant le capteur Kinect. Cette application permet à l’utilisateur de contrôler son ordinateur à l’aide des membres de son corps. En effet, un paramétrage permet à l’utilisateur de choisir les actions souris à effectuer et de les associer aux parties du corps. Pour réaliser ce travail, un apprentissage du Kinect et du kit de développement (SDK) mis à disposition par Microsoft a été nécessaire afin d’assimiler leur fonctionnement. Comme il y a très peu de documents et d’exemples à disposition, la recherche d’informations a été essentielle. L’application développée permet de configurer les actions et les mouvements à effectuer par chaque utilisateur. La gestion de profil permet de récupérer sa propre configuration lors d’une utilisation ultérieure