Topic: Numerical stability

The training school develops three foundations for AI in scientific computing. Daniel Bartl introduces statistical learning through high-dimensional probability, explaining how the geometry and complexity of function classes govern generalization. Stanislav Budzinskiy covers floating-point errors, deterministic and stochastic rounding, matrix multiplication, mixed precision and conditioning in neural-network training and inference. Maximilian Herde introduces neural operators and foundation models for partial differential equations, studying pretraining, scaling and transfer to new physical pr

This RICAM workshop examines the numerical foundations of reliable deep-learning computation. Low-precision and mixed-precision arithmetic, quantization and parallel GPU computation enable larger models and deployment on constrained devices, while introducing questions about error, stability and performance. Researchers from theoretical and applied communities will compare methods for stable training and efficient inference and identify directions for further work. The programme brings together expertise in numerical analysis, machine learning and hardware-aware computation. The in-person wor

Matrix multiplication underpins scientific computing and artificial intelligence, yet practical numerical libraries and hardware accelerators commonly retain the classical cubic-time algorithm despite decades of subcubic theoretical advances. This talk reviews the effort to make faster multiplication algorithms useful in practice. It examines why arithmetic complexity alone does not determine performance: some algorithms require enormous matrices or incur large hidden constants, while communication costs, numerical stability and the match between software and hardware create additional obstacl