Jan E. Gerken
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Equivariant Neural Tangent Kernels Open
Little is known about the training dynamics of equivariant neural networks, in particular how it compares to data augmented training of their non-equivariant counterparts. Recently, neural tangent kernels (NTKs) have emerged as a powerful …
Emergent Equivariance in Deep Ensembles Open
We show that deep ensembles become equivariant for all inputs and at all training times by simply using data augmentation. Crucially, equivariance holds off-manifold and for any architecture in the infinite width limit. The equivariance is…
Diffeomorphic Counterfactuals With Generative Models Open
Counterfactuals can explain classification decisions of neural networks in a human interpretable way. We propose a simple but effective method to generate such counterfactuals. More specifically, we perform a suitable diffeomorphic coordin…
View article: HEAL-SWIN: A Vision Transformer On The Sphere
HEAL-SWIN: A Vision Transformer On The Sphere Open
High-resolution wide-angle fisheye images are becoming more and more important for robotics applications such as autonomous driving. However, using ordinary convolutional neural networks or vision transformers on this data is problematic d…
Diffeomorphic Counterfactuals with Generative Models Open
Counterfactuals can explain classification decisions of neural networks in a human interpretable way. We propose a simple but effective method to generate such counterfactuals. More specifically, we perform a suitable diffeomorphic coordin…
View article: Equivariance versus Augmentation for Spherical Images
Equivariance versus Augmentation for Spherical Images Open
We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with…
View article: Geometric Deep Learning and Equivariant Neural Networks
Geometric Deep Learning and Equivariant Neural Networks Open
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using p…
Towards closed strings as single-valued open strings at genus one Open
We relate the low-energy expansions of world-sheet integrals in genus-one amplitudes of open- and closed-string states. The respective expansion coefficients are elliptic multiple zeta values (eMZVs) in the open-string case and non-holomor…
Modular Graph Forms and Scattering Amplitudes in String Theory Open
In this thesis, we investigate the low-energy expansion of scattering amplitudes of closed strings at one-loop level (i.e. at genus one) in a ten-dimensional Minkowski background using a special class of functions called modular graph form…