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Leveraging topology, geometry, and symmetries for efficient Machine Learning

Michaël Defferrard

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

EPFL2022

Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties

Michele Ceriotti, Jigyasa Nigam, Michael John Willatt

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each structure. In most ...

AIP Publishing2022

Low-scale leptogenesis with flavour and CP symmetries

Marco Drewes, Juraj Klaric, Yannis Georis

We consider a type-I seesaw framework endowed with a flavour symmetry, belonging to the series of non-abelian groups increment (3 n(2)) and increment (6 n(2)), and a CP symmetry. Breaking these symmetries in a non-trivial way results in the right-handed ne ...

Springer Nature2022

The Dimension of the Body in Higher Education: Matrix of Meanings in Students’ Diaries

Simon Nessim Henein, Ramiro Tau

In this paper, we attempt to show some consequences of bringing the body back into higher education, through the use of performing arts in the curricular context of scientific programs. We start by arguing that dominant traditions in higher education repro ...

2022

Construction of optimal spectral methods in phase retrieval

Florent Gérard Krzakala, Lenka Zdeborová

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

Virtual Capacitor Concept for Effective Real-Time MMC Simulations

Drazen Dujic, Stefan Milovanovic, Min Luo

In this paper, the real-time simulation model of the modular multilevel converter was split into several independent parts through the use of the virtual capacitor concept. As a result, the number of state-space matrices the real-time solver needs to take ...

2021

Virtual Capacitor Concept for Computationally Efficient and Flexible Real-Time MMC Model

Drazen Dujic, Stefan Milovanovic, Min Luo

This paper demonstrates the splitting of the modular multilevel converter real-time simulation model into several independent parts through the use of the virtual capacitor concept. As a result, the number of state-space matrices the real-time solver needs ...

2021

Reversible and Broad-Range Oxygen Sensing Based on Purely Organic Long-Lived Photoemitters

Esther Amstad, René M. Rossi, Efe Armagan

The detection of oxygen (O-2) by optical sensors is of growing importance, for example, in biology, life science, environmental science, and aerodynamics, where the composition of gases is crucial for many applications. Purely organic optical O-2 sensors a ...

2021

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

Pascal Fua, Mathieu Salzmann, Zheng Dang, Kwang Moo Yi, Fei Wang, Yinlin Hu

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...

IEEE COMPUTER SOC2021

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