2 citations · 3 across the 14 of their papers we have counts for
5 papers · 1 filter
RNADyn: A Benchmark for Generating and Understanding RNA Dynamics
Yiming Huang, Lennart Bastian, Hanqun Cao +2
Ribonucleic acid (RNA) functions through conformational changes that are not fully captured by static structures. However, large-scale standardized RNA dynamics data remain limited…
Collapsed Effective Operators for Higher-order Structures
Maximilian Krahn, Lennart Bastian, Vikas Garg +2
Higher-order structures are powerful relational modeling tools, yet existing spectral operators decompose the topology into separate ranks, leaving practitioners to fuse the inform…
Topological Neural Operators
Lennart Bastian, Samuel Leventhal, Mustafa Hajij +1
We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or e…
Stability, Complexity and Data-Dependent Worst-Case Generalization Bounds
Mario Tuci, Lennart Bastian, Benjamin Dupuis +3
Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geome…
Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework
Mustafa Hajij, Lennart Bastian, Sarah Osentoski +9
We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on…