Hans Riess

Bio

Hans Riess received a B.S. in pure mathematics from Duke University. In 2022, he received a Ph.D. in Electrical and Systems Engineering from the University of Pennsylvania where, with Robert Ghrist, he developed a novel approach of extracting global insights into complex systems using algebraic lattices and sheaves. Hans employs algebraic and topological methods to pioneer advancements in machine learning, autonomy, and optimization. He is currently a postdoctoral associate in the Autonomous Systems Lab directed by Michael M. Zavlanos at Duke University where he leads efforts in the development and analysis of networked autonomous systems.

Spatiotemporal GNNs

Graph representation learning is challenging for time-varying or graph signals. The path signature uniquely represents a local path via iterated integrals, leading to a tensor in the extended tensor algebra. Integrating graph neural networks (GNNs) with path signatures leads to models that incorporate both spatial and temporal dependencies. We are exploring applications in UAVs and earth monitoring systems.

Sheaf Laplacians

Sheaves and their assignments capture local-to-global patterns in complex systems. Laplacians on sheaves lead to harmonic flow which solves consistency problems (e.g. synchronization and consensus). Sheaves indexing data of different types correspond to different Laplacians. We are exploring sheaf Laplacians in the context of multi-modal logic, discrete event systems, and preference dynamics.

Publications

Preprints

Riess, H., Veveakis, M., Zavlanos, M. (2024). Path signatures and graph neural networks for slow earthquake analysis: netter together?.
Parada-Mayorga, A., Riess, H., Ribeiro, A., & Ghrist, R. (2020). Quiver signal processing (QSP).

Journal Publications

Battiloro, C., Wang, Z., Riess, H., Di Lorenzo, P., Ribeiro, A. (2023). Tangent bundle convolutional learning: from manifolds to cellular sheaves and back, in IEEE Transactions on Signal Processing.
Ghrist, R., & Riess, H. (2022). Cellular sheaves of lattices and the Tarski Laplacian, in Homology, Homotopy and Applications, 24(1), 325-345.
Catanzaro, M. J., Curry, J. M., Fasy, B. T., Lazovskis, J., Malen, G., Riess, H., Wang, B., & Zabka, M. (2020). Moduli spaces of morse functions for persistence, in Journal of Applied and Computational Topology, 4(3), 353-385.

Conference Proceedings

Konti, X., Riess, H., Giannopoulos, M., Shen, Y., Pencina, M., Economou-Zavlanos, N., Zavlanos, M. (2024). Distributionally robust clustered federated learning: a case study in healthcare, to appear in 63rd IEEE Conference on Control and Decision Systems (CDC), Milan.
Riess, H., Henselman-Petrusek, G., Munger, M., Ghrist, R., Bell, Z., & Zavlanos, M. (2023). Network preference dynamics using lattice theory, in 2024 American Control Conference, Toronto.
Hayhoe, M., Riess, H., Preciado, V., & Ribeiro, A. (2023). Transferable hypergraph neural networks via spectral similarity, in Second Learning on Graphs Conference, virtual.
Riess, H., Munger, M., & Zavlanos, M. (2023). Max-Plus synchronization in decentralized trading systems, in 2023 IEEE 62nd Conference on Decision and Control (CDC), Singapore.
Battiloro, C., Wang, Z., Riess, H., Di Lorenzo, P., & Ribeiro, A. (2022). Tangent bundle filters and neural networks: from manifolds to cellular sheaves and back, in 2023 Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP).
Riess, H., Ghrist, R. (2022). Diffusion of information on networked lattices by gossip, in IEEE 61st Conference on Decision and Control (CDC), Cancun, Mexico, 5946-5952.
Riess, H., Kantaros, Y., Pappas, G., & Ghrist, R. (2021). A Temporal logic-based hierarchical network connectivity controller, in 2021 Proceedings of the Conference on Control and its Applications, virtual.

Workshop

Riess, H., & Hansen, J. (2020). Multidimensional persistence module classification via lattice-theoretic convolutions. In NeurIPS Workshop on Topological Data Analysis and Beyond.

Thesis

Riess, H. (2022). Lattice theory in multi-agent systems. Doctor of Philosophy, University of Pennsylvania.