Geometric Deep Learning
- Developed the first neural model which can proveably approximate any function while implementing exact constraint satisfaction with B. Zamanlooy, I. Dokmanic, T. Liu.
- Developed a simple framework for building universal approximators between any differentiable manifold with L. Papon and E. Bilokopytov.
- Introduced the universal the first known class of UAP (Universal Approximation Property)-Invariant feature maps with C. Hyndman.
- Identified the first known homotopic obstructions to non-Euclidean universal approximation with L. Papon.
Foundations of Data Science
- Developed the first probability-measure valued universal approximator and showed that it can approximate any regular conditional distribution.
- Introduced the first regret-optimal descent algorithms via control and variational approach to meta-optimization with P. Casgrain.
- Developed the first deep neural model capable of uniformly approximating any piecewise continuous function with finitely many pieces with B. Zamanlooy.
- Introduced the first penalty for arbitrage-free learning with C. Hyndman.
- Introduce the fastest matrix completion algorithm for rapid low-rank + sparse decomposition of asset's covariance matrices with J. Teichmann, C. Herrera, F. Krach, and Google Research's P. Ruyssen.