Geometry, Algebra and Physics in Deep Neural Networks
The research group on Geometry, Algebra and Physics in Deep Neural Networks (GAPinDNNs) is based at the Department for Mathematical Sciences at Chalmers University of Technology and the University of Gothenburg. Our vision is to develop a mathematical foundation for deep learning which elevates the field into a theoretically well-grounded science.
News
New Version of PEAR Paper on the arXiv
A substantially updated version of our paper PEAR: Equal Area Weather Forecasting on the Sphere by Hampus Linander, Christoffer Petersson, Daniel Persson and Jan Gerken is now available on the arXiv. The new version shows that PEAR outperforms a much wider range of baseline architectures than previously evaluated, demonstrates that PEAR performs well in climate model emulation, and presents new results on the symmetry properties of PEAR.
The new results on symmetry properties and climate modeling are thanks to the work of our master’s students Pietro Rosso and Tage Tykesson. Congratulations to both!
New Preprint on Comparing Neural Representations via Diffusion Geometry
A new preprint From Layers to Networks: Comparing Neural Representations via Diffusion Geometry is now available on the arXiv. The paper brings tools from diffusion geometry and multi-view learning to the comparison of neural representations, showing that a broad class of representational similarity measures can be reformulated via row-stochastic Markov matrices. This yields multi-scale variants of Centered Kernel Alignment and Distance Correlation and enables network-to-network comparisons, achieving state-of-the-art results on the Representational Similarity (ReSi) benchmark.
First author is our master’s student Atharva Khandait, together with Jan Gerken. Congratulations to Atharva on his first publication!
New Preprint on Steerable Neural ODEs on Homogeneous Spaces
Daniel Persson, together with collaborators Emma Andersdotter and Fredrik Ohlsson at Umeå University, have published a new preprint on Steerable Neural ODEs on Homogeneous Spaces. The paper introduces a novel geometric framework for equivariant neural ODEs on homogeneous spaces, using parallel transport to steer feature vectors transforming under local symmetry groups.
New Preprint on Criticality and Saturation in Orthogonal Neural Networks
Max Guillen and Jan Gerken have published a new preprint on Criticality and Saturation in Orthogonal Neural Networks. The paper derives layer-wise recursion relations for the finite-width statistics of networks with orthogonal weight initialization and extends the recently-introduced Feynman diagram framework to this setting, providing a theoretical explanation for the depth-stability of orthogonally-initialized nonlinear networks.
Paper accepted at ICML 2026
Our paper Finite-Width Neural Tangent Kernels from Feynman Diagrams by Max Guillen, Philipp Misof and Jan Gerken has been accepted at ICML 2026! The paper introduces a Feynman diagram framework for computing finite-width corrections to NTK statistics, enabling layer-wise recursive relations for preactivations, NTKs and higher-derivative tensors required to predict training dynamics at leading order.
Invited talk at AI4Physics Workshop, Uppsala University
Daniel Persson gave an invited talk on Geometric Deep Learning - From equivariance to weather predictions at the AI4Physics Workshop at Uppsala University. Slides are available here.
New Preprint on The Geometry of Polynomial Group Convolutional Neural Networks
Daniel Persson, together with collaborators Yacoub Hendi and Magdalena Larfors, have published a new preprint on The Geometry of Polynomial Group Convolutional Neural Networks.
Elias in Boston
Our PhD student Elias will spend the spring in Boston on a WASP-funded research visit, working with Maurice Weiler at MIT and Robin Walters at Northeastern University on equivariant neural scaling laws.
Poster session at NeurIPS 2025
Lots of interesting discussion at the poster session here on the first day of NeurIPS 2025 in San Diego! Hampus Linander presented our paper Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks by Longde Huang, Oleksandr Balabanov, Hampus Linander, Mats Granath, Daniel Persson and Jan Gerken.
