Publications related to Pseudo-Euclidean space

Geometric Learning: Leveraging differential geometry for learning and control

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

EPFL2024

Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Haoye Qin, Aleksi Antoine Bossart, Zhechen Zhang

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

2024

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Thanh Trung Huynh, Quoc Viet Hung Nguyen, Thành Tâm Nguyên

The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entiti ...

London2023

A structured prediction approach for robot imitation learning

Aude Billard, Iason Batzianoulis, Anqing Duan

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

London2023

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks

Sabine Süsstrunk, Mathieu Salzmann, Yulun Jiang, Chen Liu, Zhuoyi Huang

We address the problem of stably and efficiently training a deep neural network robust to adversarial perturbations bounded by an

l_1

norm. We demonstrate that achieving robustness against

l_1

-bounded perturbations is more challenging than in the

l_2

...

2023

Discount models

Damir Filipovic

Discount is the difference between the face value of a bond and its present value. We propose an arbitrage-free dynamic framework for discount models, which provides an alternative to the Heath-Jarrow-Morton framework for forward rates. We derive general c ...

Heidelberg2023

Relative, local and global dimension in complex networks

Alexis Arnaudon

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogenei ...

NATURE PORTFOLIO2022

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

EPFL2022

On discrete Fourier uniqueness sets in Euclidean space

Maryna Viazovska

In this paper we present a new construction of a discrete Fourier uniqueness set in Euclidean space. ...

ICM2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

Pseudo-Euclidean space

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Geometric Learning: Leveraging differential geometry for learning and control

Anomalous and Chern topological waves in hyperbolic networks

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

A structured prediction approach for robot imitation learning

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks

Discount models

Relative, local and global dimension in complex networks

Fourier uniqueness and interpolation in Euclidean space

On discrete Fourier uniqueness sets in Euclidean space

Collapse-invariant properties of spaces equipped with signals or directions

Collapse-invariant properties of spaces equipped with signals or directions

Geometric Learning: Leveraging differential geometry for learning and control

Relative, local and global dimension in complex networks

Fourier uniqueness and interpolation in Euclidean space

On discrete Fourier uniqueness sets in Euclidean space

Anomalous and Chern topological waves in hyperbolic networks

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks

A structured prediction approach for robot imitation learning

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Discount models