Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Gerken, Jan"'
Equivariant neural networks have in recent years become an important technique for guiding architecture selection for neural networks with many applications in domains ranging from medical image analysis to quantum chemistry. In particular, as the mo
Externí odkaz:
http://arxiv.org/abs/2406.06504
Autor:
Gerken, Jan E., Kessel, Pan
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 emergent i
Externí odkaz:
http://arxiv.org/abs/2403.03103
Autor:
Carlsson, Oscar, Gerken, Jan E., Linander, Hampus, Spieß, Heiner, Ohlsson, Fredrik, Petersson, Christoffer, Persson, Daniel
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 due to proje
Externí odkaz:
http://arxiv.org/abs/2307.07313
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 coordinate transfo
Externí odkaz:
http://arxiv.org/abs/2206.05075
Autor:
Gerken, Jan E., Carlsson, Oscar, Linander, Hampus, Ohlsson, Fredrik, Petersson, Christoffer, Persson, Daniel
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 an increas
Externí odkaz:
http://arxiv.org/abs/2202.03990
Autor:
Gerken, Jan Erik
In dieser Dissertation untersuchen wir die Niedrigenergieentwicklung von Streuamplituden geschlossener Strings auf Einschleifenniveau (d.h. auf Genus eins) in einem zehndimensionalen Minkowski-Hintergrund mit Hilfe einer speziellen Klasse von Funktio
Externí odkaz:
http://edoc.hu-berlin.de/18452/22571
Autor:
Gerken, Jan E., Aronsson, Jimmy, Carlsson, Oscar, Linander, Hampus, Ohlsson, Fredrik, Petersson, Christoffer, Persson, Daniel
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 principal bu
Externí odkaz:
http://arxiv.org/abs/2105.13926
Autor:
Gerken, Jan E.
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 forms. These al
Externí odkaz:
http://arxiv.org/abs/2011.08647
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 in the open-string case and non-holomorphic modular forms
Externí odkaz:
http://arxiv.org/abs/2010.10558
Autor:
Gerken, Jan E.
Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy numerous
Externí odkaz:
http://arxiv.org/abs/2007.05476