Inference Time Algorithms for SciML and GenAI
Bellman defect correction provides a “predict first, then correct” framework for designing principled algorithms for scientific computing, diffusion sampling, scientific discovery, and LLM reasoning.
Operator norm geometry, width scaling, and learning rate transfer.
A matrix operator norm perspective on neural network optimization, connecting Adam, Lion, and Muon to learning rate scaling as networks grow in width.
A research agenda for turning scale into mathematical and computational reliability.
View slidesScaling laws, defect correction, and resource aware scientific learning.
View slidesFrom physics informed learning to operator approximation and inference time correction.
Simulation calibrated correction for learned scientific models.
Slides VideoA tutorial on models, algorithms, and theory for scientific learning.
View slidesMinimax rates and multilevel training for infinite dimensional operators.
View slidesGeneralization, scaling laws, and minimax optimality for elliptic equations.
View slidesRepresentations and algorithms connecting neural networks with numerical analysis.
View slidesDifferential equations as a language for deep architectures and scientific discovery.
Slides VideoRandomized linear algebra, experiment design, and robust optimization.
What inverse power analysis really explains about randomized eigensolvers.
View slidesCovariate balancing through a connection with phase retrieval and spectral geometry.
View slidesNeural collapse and worst group generalization through optimization geometry.
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