7 papers
A necessary condition for the existence of solutions of singular linear-quadratic vector equations
Rishikesh Yadav, Axel Flinth
We study the existence of solutions for systems of linear-quadratic vector equations with singular linear parts. We derive a sufficient condition for small right hand sides.
Equivariance and Augmentation for Bayesian Neural Networks
Miaowen Dong, Axel Flinth, Jan E. Gerken
Symmetries are important for many deep learning tasks, ranging from applications in the sciences to medical imaging. However, there is an ongoing debate about whether to impose sym…
Conservation Laws from Data Symmetry in Neural Networks
Jakob Galley, Vahid Shahverdi, Axel Flinth
We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks. Under the assumption that the loss funct…
On the fibers and semi-algebraicity of ReLU neuromanifolds
Axel Flinth, Stefano Mereta, Michele Pernice
We study the semi-algebraicity of the neuromanifold of a feedforward ReLU neural network and its symmetries. We prove that is not…
Ensembles provably learn equivariance through data augmentation
Oskar Nordenfors, Axel Flinth
Recently, it was proved that group equivariance emerges in ensembles of neural networks as the result of full augmentation in the limit of infinitely wide neural networks (neural t…
Bilinear Compressive Security
Axel Flinth, Hubert Orlicki, Semira Einsele +1
Beyond its widespread application in signal and image processing, \emph{compressed sensing} principles have been greatly applied to secure information transmission (often termed 'c…