Simon Heilig

Simon Heilig

ELLIS PhD @ RUB

Publications

You can also find my articles on my Google Scholar profile.

Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks

Published in 2025 International Conference on Learning Representations (ICLR), 2025

This work tackles the challenge of long-range information propagation in graph neural networks. We proposed port-Hamiltonian Deep Graph Networks, a novel framework inspired by physics that models neural information flow using principles from Hamiltonian systems. By combining conservative and dissipative dynamics, we control how information spreads or fades across the graph. Despite its theoretical grounding, the method integrates easily into standard message-passing networks and shows strong empirical performance, especially in tasks that require effective long-range reasoning. Download paper here

Memory Efficient Kernel Approximation for Non-Stationary and Indefinite Kernels

Published in 2022 International Joint Conference on Neural Networks (IJCNN), 2022

This paper originated from my bachelor thesis and is all about large scale kernel methods. We explored the memory efficient approximation of kernel matrices that lead to invalid kernels. We proposed to correct the eigenspectrum with a shift computed via the Lanczos-Iteration. This correction leads to stable downstream tasks and despite having a large approximation error, competitive scores on the tasks. Download paper here