Machine Learning Theory and Mathematics in the Era of Infinite GPUs
A research agenda for turning scale into mathematical and computational reliability.
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03 · Talks
Ideas in public.
Selected talks and tutorials on scaling, scientific machine learning, numerical algorithms, optimization, and the mathematics of deep learning.
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Current research program
Talks that give the fastest route into the group’s present research agenda.
Dimension Dependence of Neural Optimizers
Operator norm geometry, width scaling, and learning rate transfer.
View slidesHow to Scale Scientific Machine Learning at Training and Inference Time
Scaling laws, defect correction, and resource aware scientific learning.
View slidesScientific machine learning
Learning with physical structure
From physics informed learning to operator approximation and inference time correction.
Physics Informed Inference Time Scaling via Hybrid Scientific Computing and Machine Learning
Simulation calibrated correction for learned scientific models.
Slides VideoRecent Advances in Physics Informed Machine Learning
A tutorial on models, algorithms, and theory for scientific learning.
View slidesStatistically Optimal Operator Learning
Minimax rates and multilevel training for infinite dimensional operators.
View slidesStatistical Analysis of Machine Learning for PDEs
Generalization, scaling laws, and minimax optimality for elliptic equations.
View slidesDeep Learning for Numerical PDEs
Representations and algorithms connecting neural networks with numerical analysis.
View slidesNeural ODE and PDE Net
Differential equations as a language for deep architectures and scientific discovery.
Slides VideoAlgorithms and robustness
Computation beyond the model
Randomized linear algebra, experiment design, and robust optimization.
Sketch and Precondition for Low Rank Approximation
What inverse power analysis really explains about randomized eigensolvers.
View slidesSynthetic Design via Spectral Methods
Covariate balancing through a connection with phase retrieval and spectral geometry.
View slidesImplicit Regularization for Algorithm Design
Neural collapse and worst group generalization through optimization geometry.
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