35 citations · 55 across the 12 of their papers we have counts for
12 papers
HEAL-SWIN: A Vision Transformer On The Sphere
Oscar Carlsson, Jan E. Gerken, Hampus Linander +4
High-resolution wide-angle fisheye images are becoming more and more important for robotics applications such as autonomous driving. However, using ordinary convolutional neural ne…
Optimization Dynamics of Equivariant and Augmented Neural Networks
Oskar Nordenfors, Fredrik Ohlsson, Axel Flinth
We investigate the optimization of neural networks on symmetric data, and compare the strategy of constraining the architecture to be equivariant to that of using data augmentation…
Energy translation symmetries and dynamics of separable autonomous two-dimensional ODEs
Johannes G. Borgqvist, Fredrik Ohlsson, Ruth E. Baker
We study symmetries in the phase plane for separable, autonomous two-state systems of ordinary differential equations (ODEs). We prove two main theoretical results concerning the e…
On the correspondence between symmetries of two-dimensional autonomous dynamical systems and their phase plane realisations
Fredrik Ohlsson, Johannes G. Borgqvist, Ruth E. Baker
We consider the relationship between symmetries of two-dimensional autonomous dynamical system in two common formulations; as a set of differential equations for the derivative of…
Symmetries of systems of first order ODEs: Symbolic symmetry computations, mechanistic model construction and applications in biology
Johannes Borgqvist, Fredrik Ohlsson, Ruth E. Baker
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and pro…
Equivariance versus Augmentation for Spherical Images
Jan E. Gerken, Oscar Carlsson, Hampus Linander +3
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 kno…
Geometric Deep Learning and Equivariant Neural Networks
Jan E. Gerken, Jimmy Aronsson, Oscar Carlsson +4
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional n…
(2,0) theory on Taub-NUT: A note on WZW models on singular fibrations
Fredrik Ohlsson
In this note we consider the gauge field equation of motion for the dimensional reduction of the (2,0) tensor multiplet on singular circle fibrations. The fibrations are characteri…
(2,0) theory on circle fibrations
Hampus Linander, Fredrik Ohlsson
We consider (2,0) theory on a manifold M_6 that is a fibration of a spatial S^1 over some five-dimensional base manifold M_5. Initially, we study the free (2,0) tensor multiplet wh…
BPS partition functions in N = 4 Yang-Mills theory on T^4
Måns Henningson, Fredrik Ohlsson
We consider N = 4 Yang-Mills theory on a flat four-torus with the R-symmetry current coupled to a flat background connection. The partition function depends on the coupling constan…
Finite energy shifts in SU(n) supersymmetric Yang-Mills theory on T^3xR at weak coupling
Fredrik Ohlsson
We consider a semi-classical treatment, in the regime of weak gauge coupling, of supersymmetric Yang-Mills theory in a space-time of the form T^3xR with SU(n)/Z_n gauge group and a…
The Weak Coupling Spectrum around Isolated Vacua in N=4 Super Yang-Mills on T^3 with any Gauge Group
Josef Lindman Hörnlund, Fredrik Ohlsson
The moduli space of flat connections for maximally supersymmetric Yang-Mills theories, in a space-time of the form T^3xR, contains isolated points, corresponding to normalizable ze…