Bilinear Generalized Approximate Message Passing—Part I: Derivation

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(S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

Nicolas Henri Bernard Flammarion, Scott William Pesme

In this paper, we investigate the impact of stochasticity and large stepsizes on the implicit regularisation of gradient descent (GD) and stochastic gradient descent (SGD) over diagonal linear networks. We prove the convergence of GD and SGD with macroscop ...

2023

On a Finite-Size Neuronal Population Equation

Tilo Schwalger, Valentin Marc Schmutz

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

SIAM PUBLICATIONS2023

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Rafael Vazquez Hernandez

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2023

Positive Definite Completions and Continuous Graphical Models

Kartik Waghmare

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

EPFL2023

DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices

Olga Fink, Ismail Nejjar

Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gap between a labeled source dataset and an unlabelled target dataset for regression problems. Recent works mostly focus on learning a deep feature encoder by minimizing the discrepa ...

IEEE2023

Higher Order Asymptotics: Applications to Satellite Conjunction and Boundary Problems

Soumaya Elkantassi

Higher-order asymptotics provide accurate approximations for use in parametric statistical modelling. In this thesis, we investigate using higher-order approximations in two-specific settings, with a particular emphasis on the tangent exponential model. ...

EPFL2023

espm: A Python library for the simulation of STEM-EDXS datasets

Adrien Maxime Louis Teurtrie, Cécile Hébert, Duncan Thomas Lindsay Alexander, Nathanaël Perraudin, Hui Chen, Guillaume Romain Obozinski, Hui Chen

We present two open-source Python packages: "electron spectro-microscopy"(espm) and "electron microscopy tables"(emtables). The espm software enables the simulation of scanning transmission electron microscopy energy-dispersive X-ray spectroscopy datacubes ...

ELSEVIER2023

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation

Alfio Quarteroni, Andrea Manzoni

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as th ...

Wiley2023

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Fabrizio Minganti

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

AMER PHYSICAL SOC2023

Acute TNF alpha levels predict cognitive impairment 6-9 months after COVID-19 infection

Dimitri Nestor Alice Van De Ville, Alessandra Griffa, Idris Guessous, Alexandre Cionca

Background: A neurocognitive phenotype of post-COVID-19 infection has recently been described that is characterized by a lack of awareness of memory impairment (i.e., anosognosia), altered functional connectivity in the brain's default mode and limbic netw ...

PERGAMON-ELSEVIER SCIENCE LTD2023