Presenting a Category Modulo a Rewriting System

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by the means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the objects are considered modulo an equivalence relation (in the spirit of rewriting modulo), which is described by equational generators. When those form a convergent (abstract) rewriting system on objects, there are three very natural constructions that can be used to define the category which is described by the presentation: one is based on restricting to objects which are normal forms, one consists in turning equational generators into identities (i.e. considering a quotient category), and one consists in formally adding inverses to equational generators (i.e. localizing the category). We show that, under suitable coherence conditions on the presentation, the three constructions coincide, thus generalizing celebrated results on presentations of groups. We illustrate our techniques on a non-trivial example, and hint at a generalization for 2-categories

PAC-Bayesian Generalization Bounds for Adversarial Generative Models

We extend PAC-Bayesian theory to generative models and develop generalization bounds for models based on the Wasserstein distance and the total variation distance. Our first result on the Wasserstein distance assumes the instance space is bounded, while our second result takes advantage of dimensionality reduction. Our results naturally apply to Wasserstein GANs and Energy-Based GANs, and our bounds provide new training objectives for these two. Although our work is mainly theoretical, we perform numerical experiments showing non-vacuous generalization bounds for Wasserstein GANs on synthetic datasets

Pointless learning

Bayesian inversion is at the heart of probabilistic programming and more generally machine learning. Understanding inversion is made difficult by the pointful (kernel-centric) point of view usually taken in the literature. We develop a pointless (kernel-free) approach to inversion. While doing so, we revisit some foundational objects of probability theory, unravel their category-theoretical underpinnings and show how pointless Bayesian inversion sits naturally at the centre of this construction

Pointless learning (long version)

International audienceBayesian inversion is at the heart of probabilistic programming and more generally machine learning. Understanding inversion is made difficult by the pointful (kernel-centric) point of view usually taken in the literature. We develop a pointless (kernel-free) approach to inversion. While doing so, we revisit some foundational objects of probability theory, unravel their category-theoretical underpinnings and show how pointless Bayesian inversion sits naturally at the centre of this construction

Pointless learning (long version)

International audienceBayesian inversion is at the heart of probabilistic programming and more generally machine learning. Understanding inversion is made difficult by the pointful (kernel-centric) point of view usually taken in the literature. We develop a pointless (kernel-free) approach to inversion. While doing so, we revisit some foundational objects of probability theory, unravel their category-theoretical underpinnings and show how pointless Bayesian inversion sits naturally at the centre of this construction

Comparison of Characteristics of Neuropathic and Non-neuropathic Pruritus to Develop a Tool for the Diagnosis of Neuropathic Pruritus: The NP5

The diagnosis of neuropathic pruritus (NP) may be difficult. The aim of this study was to compare the characteristics of both neuropathic pruritus and non-neuropathic pruritus (NNP) in order to elaborate a tool to help the diagnosis of NP without clinical examination. One hundred and seven patients were included: Fifty three in the NP group and Fifty four in the NNP group. In multiple regression, presence of twinges, absence of burning, worsening with activity, no worsening with stress, and relief with cold ambient temperature were independent factors that were associated with NP. A score of two criteria out of five was optimal to discriminate NP from NNP with a sensitivity of 76% and a specificity of 77%. Alloknesis, hyperknesis, or the ice cube test were not included because their evaluation is based on clinical examination. Future high-powered studies are needed to confirm the results of the present study

The Athena X-ray Integral Field Unit: a consolidated design for the system requirement review of the preliminary definition phase

The Athena X-ray Integral Unit (X-IFU) is the high resolution X-ray spectrometer, studied since 2015 for flying in the mid-30s on the Athena space X-ray Observatory, a versatile observatory designed to address the Hot and Energetic Universe science theme, selected in November 2013 by the Survey Science Committee. Based on a large format array of Transition Edge Sensors (TES), it aims to provide spatially resolved X-ray spectroscopy, with a spectral resolution of 2.5 eV (up to 7 keV) over an hexagonal field of view of 5 arc minutes (equivalent diameter). The X-IFU entered its System Requirement Review (SRR) in June 2022, at about the same time when ESA called for an overall X-IFU redesign (including the X-IFU cryostat and the cooling chain), due to an unanticipated cost overrun of Athena. In this paper, after illustrating the breakthrough capabilities of the X-IFU, we describe the instrument as presented at its SRR, browsing through all the subsystems and associated requirements. We then show the instrument budgets, with a particular emphasis on the anticipated budgets of some of its key performance parameters. Finally we briefly discuss on the ongoing key technology demonstration activities, the calibration and the activities foreseen in the X-IFU Instrument Science Center, and touch on communication and outreach activities, the consortium organisation, and finally on the life cycle assessment of X-IFU aiming at minimising the environmental footprint, associated with the development of the instrument. Thanks to the studies conducted so far on X-IFU, it is expected that along the design-to-cost exercise requested by ESA, the X-IFU will maintain flagship capabilities in spatially resolved high resolution X-ray spectroscopy, enabling most of the original X-IFU related scientific objectives of the Athena mission to be retained. (abridged).Comment: 48 pages, 29 figures, Accepted for publication in Experimental Astronomy with minor editin

The Athena X-ray Integral Field Unit: a consolidated design for the system requirement review of the preliminary definition phase

The Athena X-ray Integral Unit (X-IFU) is the high resolution X-ray spectrometer studied since 2015 for flying in the mid-30s on the Athena space X-ray Observatory. Athena is a versatile observatory designed to address the Hot and Energetic Universe science theme, as selected in November 2013 by the Survey Science Committee. Based on a large format array of Transition Edge Sensors (TES), X-IFU aims to provide spatially resolved X-ray spectroscopy, with a spectral resolution of 2.5 eV (up to 7 keV) over a hexagonal field of view of 5 arc minutes (equivalent diameter). The X-IFU entered its System Requirement Review (SRR) in June 2022, at about the same time when ESA called for an overall X-IFU redesign (including the X-IFU cryostat and the cooling chain), due to an unanticipated cost overrun of Athena. In this paper, after illustrating the breakthrough capabilities of the X-IFU, we describe the instrument as presented at its SRR (i.e. in the course of its preliminary definition phase, so-called B1), browsing through all the subsystems and associated requirements. We then show the instrument budgets, with a particular emphasis on the anticipated budgets of some of its key performance parameters, such as the instrument efficiency, spectral resolution, energy scale knowledge, count rate capability, non X-ray background and target of opportunity efficiency. Finally, we briefly discuss the ongoing key technology demonstration activities, the calibration and the activities foreseen in the X-IFU Instrument Science Center, touch on communication and outreach activities, the consortium organisation and the life cycle assessment of X-IFU aiming at minimising the environmental footprint, associated with the development of the instrument. Thanks to the studies conducted so far on X-IFU, it is expected that along the design-to-cost exercise requested by ESA, the X-IFU will maintain flagship capabilities in spatially resolved high resolution X-ray spectroscopy, enabling most of the original X-IFU related scientific objectives of the Athena mission to be retained. The X-IFU will be provided by an international consortium led by France, The Netherlands and Italy, with ESA member state contributions from Belgium, Czech Republic, Finland, Germany, Poland, Spain, Switzerland, with additional contributions from the United States and Japan.The French contribution to X-IFU is funded by CNES, CNRS and CEA. This work has been also supported by ASI (Italian Space Agency) through the Contract 2019-27-HH.0, and by the ESA (European Space Agency) Core Technology Program (CTP) Contract No. 4000114932/15/NL/BW and the AREMBES - ESA CTP No.4000116655/16/NL/BW. This publication is part of grant RTI2018-096686-B-C21 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. This publication is part of grant RTI2018-096686-B-C21 and PID2020-115325GB-C31 funded by MCIN/AEI/10.13039/501100011033