From the 1 of 10 linked papers with an AI index.
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Introduction to Regularization and Learning Methods for Inverse Problems
Danielle Bednarski, Tim Roith
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolutio…
Adversarial flows: A gradient flow characterization of adversarial attacks
Lukas Weigand, Tim Roith, Martin Burger
A popular method to perform adversarial attacks on neuronal networks is the so-called fast gradient sign method and its iterative variant. In this paper, we interpret this method a…
MirrorCBO: A consensus-based optimization method in the spirit of mirror descent
Leon Bungert, Franca Hoffmann, Dohyeon Kim +1
In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For…
Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies
Tim Roith, Leon Bungert, Philipp Wacker
Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence…
Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization
Martin Burger, Samira Kabri, Yury Korolev +2
The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns…