News archive

Daniel Persson gave a talk on Beyond the chatbot - How I use AI in my mathematical research at the workshop New connections between physics and number theory, held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, July 13–17, 2026. Slides are available here.

Jan Gerken and Daniel Persson have been awarded a Proof-of-Concept grant from the Knut and Alice Wallenberg Foundation for the project AI-Assisted Ultrasound Guidance for Scalable Medical Training. This is a joint project with Carl Hallgren at Sahlgrenska University Hospital and Sebastian Bramberger at Sindrion Technologies. The Proof-of-Concept program bridges the gap between basic academic research and innovation, giving research groups the opportunity to develop early discoveries towards validated methods, products or processes and to prepare them for commercialization.

Jan Gerken presented our paper Finite-Width Neural Tangent Kernels from Feynman Diagrams, joint work with Max Guillen and Philipp Misof, as a poster at ICML 2026 in Seoul. The poster is available here.

A new preprint Equivariance and Augmentation for Bayesian Neural Networks by Miaowen Dong, Axel Flinth and Jan Gerken is now available on the arXiv. The paper studies data augmentation for Bayesian neural networks trained with variational inference, deriving conditions under which exact equivariance is reached, bounds on the equivariance error, and three novel symmetrization techniques. One of them, orbit expansion, outperforms the baseline in both equivariance and overall performance.

This is the first paper for our PhD student Miaowen Dong — congratulations, Miaowen!

Congratulations to our master’s students, who have all successfully defended their theses:

• Tage Tykesson: Deep Learning Climate Model Emulation with PEAR
• Atharva Khandait: Discrete Geometry for Comparing and Transferring Neural Representations
• Pietro Rosso: Equivariant Inductive Biases for Weather Prediction with PEAR
• Jonatan Larsen and Filip Nyman: SÄLEN and the Art of Metal Binding

Well done to all of them!

Daniel Persson gave an invited talk on Geometric Deep Learning - From equivariance to weather predictions at the Mathematical Foundations of AI workshop, held at Chalmers University of Technology (Palmstedtsalen), Gothenburg, June 8–10, 2026. Slides are available here.

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!

Daniel Persson is interviewed in the Swedish popular science magazine Forskning & Framsteg about the recent AI breakthrough in mathematics, where an AI model solved the 80-year-old Erdős unit distance problem. Daniel comments: “It is a very exciting breakthrough! It is remarkable that AI has been able to solve a problem at this level, with such advanced mathematics.”

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!

When Philipp Misof visited last year’s LOGML Summer School in London, the week-long group project sparked an idea for a new paper using Diffusion Geometry to learn geometric differential-forms from point clouds. This work was done together with Bruno Trentini, Jacob Hume, Vincenzo Antonio Isoldi, Katya Ivshina and Kelly Maggs and is now available as a preprint.

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.

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.

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.

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.

Daniel Persson, together with collaborators Yacoub Hendi and Magdalena Larfors, have published a new preprint on The Geometry of Polynomial Group Convolutional Neural Networks.

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.

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.

Our paper PEAR: Equal Area Weather Forecasting on the Sphere by Hampus Linander, Christoffer Petersson, Daniel Persson and Jan Gerken was accepted in the AI4Science workshop at NeurIPS 2025. In this paper we show how to do compute efficient global weather forecasting using the HEALPix grid.

Our paper on Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks has been accepted for a poster at NeurIPS 2025! In this paper, we combine lattice gauge equivariant networks with a novel training mechanism to learn topological invariants (Chern numbers) of topological insulators. This paper combines several beautiful topics in machine learning, physics and mathematics.

First author is our new PhD student Longde Huang. Congratulations to his first publication! From our group, Hampus Linander, Daniel Persson and Jan Gerken were also involved. Thanks to our phyiscs-collaborators Oleksandr Balabanov (then at Stockholm University) and Mats Granath (University of Gothenburg) for their expertise and a fun collaboration!

Today, Philipp is starting his 10-months internship at Genentech (Roche) in Switzerland. Under the supervision of Pan Kessel he will explore new ways of generative protein design. We wish him a successful start!

We are happy to announce that our group welcomes two new PhD students: Miaowen Dong and Longde Huang. They will both work under the supervision of Jan. Their respective research areas can be found at their linked profiles.

We proudly announce that Oscar successfully defended his thesis “Geometry and Symmetry in Deep Learning: From Mathematical Foundations to Vision Applications” in front of his opponent Remco Duits and the committee consisting of Kathlén Kohn, Fredrik Kahl, and Jun Yu. The whole group wishes him all the best on his future career path!

At Chalmers it is customary for PhD students to summarize their research after roughly the first half of their PhD. Philipp was successfully presenting his progress in form of a half-way seminar talk.

With the Swedish summer about to end, we came together for a memorable group excursion. Thanks to the surprisingly good weather, the exploration of Gothenburg’s archipelago with kayaks was a pleasant and exciting experience. A few capsizes added to the to the adventure- and are part of the learning process. To cap off the day, Daniel treated us to an authentic Mexican-themed BBQ evening.

Jan Gerken is part of the organizing committee for the GeUmetric Deep Learning Workshop in Umeå taking place 19-21 August. Our group also has strong representation among the contributed talks, including presentations from Longde, Max, Oscar, Philipp, Elias and Hampus.

Philipp Misof is presenting our paper Equivariant Neural Tangent Kernels written together with Pan Kessel and Jan Gerken at this year’s ICML in Vancouver. In this work, we extend the neural tangent kernel to equivariant neural networks and use it to draw an interesting connection between equivariant neural networks and data-augmented networks.

Elias Nyholm and Philipp Misof are attending the LOGML Summer School at the Imperial College London this week. They are both working in small groups on projects related to geometric deep learning, which they will summarize in a short presentation at the end of the week.

Our work PEAR: Equal Area Weather Forecasting on the Sphere by Hampus Linander, Christoffer Petersson, Daniel Persson and Jan Gerken, is now available on the arXiv. We use an equal area gridding (HEALPix) of the sphere to perform global weather forecasting with a volumetric transformer architecture, outperforming the same architecture on the standard Driscoll-Healy grid.

The preprint Equivariant Non-linear Maps for Neural Networks on Homogeneous Spaces is now available on the arXiv, with authors including Elias Nyholm, Oscar Carlsson and Daniel Persson. In this paper we define and study a family of equivariant neural network layers which unify convolution-based and attention-based architectures. We derive the generalised equivariance condition and show how it specialises in individual cases. The work is in collaboration with Maurice Weiler.

We have an open PhD position with Jan Gerken about symmetries in neural networks.

We seek a PhD student for a project at the intersection of mathematics and deep learning to work on theoretical aspects of geometric deep learning. The question whether more data and compute are sufficient to improve neural networks is highly debated at the moment in all areas of deep learning. In this project, you will work on a theoretical framework which will help to better understand these questions in the context of geometric deep learning and add rigorous arguments to a debate driven by empirical results.

Application Deadline is 21 May 2025.

Our work on Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks is now on the arXiv! In this paper, we combine lattice gauge equivariant networks with a novel training mechanism to learn topological invariants (Chern numbers) of topological insulators. This paper combines several beautiful topics in machine learning, physics and mathematics.

First author is our master’s student Longde Huang. Congratulations to his first publication! From our group, Hampus Linander, Daniel Persson and Jan Gerken were also involved. Thanks to our phyiscs-collaborators Oleksandr Balabanov (then at Stockholm University) and Mats Granath (University of Gothenburg) for their expertise and a fun collaboration!

Elias Nyholm is one of the organisers of the LoG Meetup Sweden in Uppsala this year. This two-day workshop is the official local meetup of the online LoG Conference and will consist of keynote talks, contributed talks and a poster session.

The group had a strong presence at the WASP Winter Conference in Norrköping this year, including poster presentations by Elias, Philipp and Oscar.

Inauguration lecture for Daniel Persson’s promotion to full professor of mathematics.

Interview with Daniel Persson on the occasion of his upcoming promotion to full professor of mathematics.

Public lecture by Daniel Persson for high school students at Hulebäcksgymnasiet.

Paper by Daniel Persson together with Emma Andersdotter and Fredrik Ohlsson at Umeå University.

This week Elias Nyholm is attending the CaLISTA workshop on Geometry-Informed Machine Learning in Paris, where he will present a poster on General Equivariant Transformers.

Daniel Persson organized a workshop at Hässelby slott in Stockholm, aimed at gathering all supervisors within the WASP math-AI track. Jan Gerken gave a talk on Geometric deep learning and neural tangent kernels.

Philipp Misof is currently at the Princeton University and meeting other PhD students and lecturers focusing on theoretical aspects of ML. Today he will present his poster on “Equivariant Neural Tangent Kernels” at the poster session.

Our group members Max Guillen and Jan Gerken participated in the IAIFI 2024 Summer Workshop about physics and AI at MIT and presented work on the RG flow of the NTK dynamics at finite-width from Feynman diagrams as well as Symmetries and the Neural Tangent Kernel.

William Nyrén and Ibrahim Taha defended their master thesis on “Predicting UV-Vis absorption spectra by using graph neural network models”. Congratulations!

Several members of our group, Oscar Carlsson, Jan Gerken, Hampus Linander and Christoffer Petersson traveled to Seattle to participate in CVPR 2024. We had an inspiring conference, met many new and old colleagues and presented our work on HEAL-SWIN: A Vision Transformer on The Sphere.

Thanks to all the speakers and participants of this interesting workshop at the Umeå University which was coorganized by our colleague Jan Gerken. We had a broad range of talks and discussions focusing on geometric aspects of deep learning.

The paper “Emergent Equivariance in Deep Ensembles” from our group was accepted for an oral presentation at ICML 2024. Congratulations Jan Gerken and Pan Kessel!

The preprint “Equivariant Neural Tangent Kernels” from our group appeared on the arXiv today. We compute neural tangent kernels (NTKs) for group convolutional networks for the first time and show that equivariant NTKs outperform their non-equivariant counterparts on a medical image dataset.