7 papers
The Symmetries of Three-Layer ReLU Networks
Johanna Marie Gegenfurtner, Moritz Grillo, Guido Montúfar
We develop a framework for analyzing parameter symmetries in deep ReLU networks and obtain a complete characterization of the generic parameter fibers for three-layer bottleneck ar…
Don't Stop Me Yet: Sampling Loss Minima via Dissipative Riemannian Mechanics
Albert Kjøller Jacobsen, Leo Uhre Jakobsen, Johanna Marie Gegenfurtner +1
The minima of modern neural network loss functions are typically not isolated, rather they form connected components of reparameterization invariant solutions on the training data.…
Reducing Memorisation in Generative Models via Riemannian Bayesian Inference
Johanna Marie Gegenfurtner, Albert Kjøller Jacobsen, Naima Elosegui Borras +2
Modern generative models can produce realistic samples, however, balancing memorisation and generalisation remains an open problem. We approach this challenge from a Bayesian persp…
Staying on the Manifold: Geometry-Aware Noise Injection
Albert Kjøller Jacobsen, Johanna Marie Gegenfurtner, Georgios Arvanitidis
It has been shown that perturbing the input during training implicitly regularises the gradient of the learnt function, leading to smoother models and enhancing generalisation. How…
Minimal Submanifolds of the Classical Compact Riemannian Symmetric Spaces
Johanna Marie Gegenfurtner
Minimal submanifolds constitute a central area within the realm of differential geometry, due to their many applications in various branches of physics. In this thesis we will empl…
Compact minimal submanifolds of the Riemannian symmetric spaces , , , via complex-valued eigenfunctions
Johanna Marie Gegenfurtner, Sigmundur Gudmundsson
In this work we construct new multi-dimensional families of compact minimal submanifolds, of the classical Riemannian symmetric spaces , , an…