Concept
Pseudo-Euclidean space
Related publications (98)
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EPFL2024Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks
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We address the problem of stably and efficiently training a deep neural network robust to adversarial perturbations bounded by an norm. We demonstrate that achieving robustness against -bounded perturbations is more challenging than in the ...
2023Discount models
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 ...
Heidelberg2023Relative, local and global dimension in complex networks
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 PORTFOLIO2022Fourier uniqueness and interpolation in Euclidean space
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 ...
EPFL2022Collapse-invariant properties of spaces equipped with signals or directions
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