Maksim Zhdanov

PhD student at AMLab

m.zhdanov@uva.nl

Hi! I am a PhD candidate at AMLab supervised by Max Welling, Jan-Willem van de Meent and Alfons Hoekstra. I am trying to learn PDEs from data using deep learning. Before joining the University of Amsterdam, I was a research assistant at Helmholtz AI, where I worked on applications of machine learning for material science. I also spent some time working on graph neural networks and generative modelling with applications in neuroscience. Long ago, I developed statistical models of clinical treatment at TU Dresden.

Overall, my research interests revolve around physics-inspired deep learning and geometric deep learning. I am also interested in AI4Science and the applications of machine learning to physics.

In my free time, I enjoy reading, playing basketball and testing gravity when skateboarding.

news

Feb 2024	Together with David Ruhe, Maurice Weiler and others, we have developed Clifford-steerable CNNs - a new class of isometry-equivariant CNNs that are able to operate on pseudo-Euclidean spaces, such as Euclidean space and Minkowski spacetime. Really strong results on PDEs, new relativistic benchmark and lots of very cool math. The paper is available here.
Sep 2023	Our paper “Implicit Convolutional Kernels for Steerable CNNs” has been accepted to NeurIPS 2023! We developed a simple and efficient way to parameterize group equivariant convolutional kernels using implicit neural representation, which greatly simplifies the design of steerable CNNs. Check out the blog post for details.
Apr 2023	Absolutely thrilled to announce that I will join the University of Amsterdam and start my PhD this spring, working with Max Welling, Jan-Willem van de Meent and Alfons Hoekstra!

latest posts

Oct 2023	Implicit Kernels for Steerable CNNs

selected publications

Clifford-Steerable Convolutional Neural Networks

Maksim Zhdanov, David Ruhe, Maurice Weiler, and 3 more authors

Abs arXiv PDF Code

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of \(E(p, q)\)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces. They cover, for instance, \(E(3)\)-equivariance and Poincaré-equivariance on Minkowski spacetime. Our approach is based on an implicit parametrization of \(O(p,q)\)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.
Implicit Neural Convolutional Kernels for Steerable CNNs

Maksim Zhdanov, Nico Hoffmann, and Gabriele Cesa

NeurIPS 2023

Abs arXiv PDF Blog Code

Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and other transformations belonging to an origin-preserving group G, such as reflections and rotations. They rely on standard convolutions with G-steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group G, the implementation of a kernel basis does not generalize to other symmetry transformations, which complicates the development of group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize G-steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group G for which a G-equivariant MLP can be built. We apply our method to point cloud (ModelNet-40) and molecular data (QM9) and demonstrate a significant improvement in performance compared to standard Steerable CNNs.
Investigating Brain Connectivity with Graph Neural Networks and GNNExplainer

Maksim Zhdanov, Saskia Steinmann, and Nico Hoffmann

ICPR 2022

Abs arXiv PDF Code

Functional connectivity plays an essential role in modern neuroscience. The modality sheds light on the brain’s functional and structural aspects, including mechanisms behind multiple pathologies. One such pathology is schizophrenia which is often followed by auditory verbal hallucinations. The latter is commonly studied by observing functional connectivity during speech processing. In this work, we have made a step toward an in-depth examination of functional connectivity during a dichotic listening task via deep learning for three groups of people: schizophrenia patients with and without auditory verbal hallucinations and healthy controls. We propose a graph neural network-based framework within which we represent EEG data as signals in the graph domain. The framework allows one to 1) predict a brain mental disorder based on EEG recording, 2) differentiate the listening state from the resting state for each group and 3) recognize characteristic task-depending connectivity. Experimental results show that the proposed model can differentiate between the above groups with state-of-the-art performance. Besides, it provides a researcher with meaningful information regarding each group’s functional connectivity, which we validated on the current domain knowledge.