Geometric Deep Learning and Stochastics
I develop and study universal deep learning models that leverage the infinite-dimensional curved geometries arising in stochastic analysis and mathematical finance.
Approximation theory, analysis on metric spaces, geometric topology, mathematical finance, optimal transport.
Geometric deep learning, approximation theory of deep neural networks, meta-learning.
- A. Acciaio, A. Kratsios, and G. Pammer: Designing Universal Causal Deep Learning Models: The Geometric (Hyper) Transformer, Mathematical Finance, 2023.
- A. Kratsios, V. Debarnot, I. Dokmanić: Small Transformers Compute Universal Metric Embeddings, JMLR - Journal of Machine Learning Research, 2023.
- A. Kratsios, L. Papon: Universal Approximation Theorems for Differentiable Geometric Deep Learning, JMLR - Journal of Machine Learning Research, 2022.
- Guarantees that Hyperbolic NNs can Actually Represent Trees: Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures.
- A General Universal Approximation Theroy: An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning.