NumGM — Numerically Efficient Learning of Generative Models and Beyond
Mathematically grounded and computationally efficient methods for generative artificial intelligence
Generative artificial intelligence has enabled major advances across science and technology, but training and deploying large models requires substantial computing power, memory and energy. NumGM addresses this challenge at the mathematical and numerical level. Its aim is to improve the models and algorithms underlying generative AI, rather than relying only on larger architectures and datasets.
By combining probability, geometry, PDE-based modelling and numerical optimization, NumGM seeks methods that are computationally efficient, mathematically interpretable and robust.
Scientific programme
- Geometry-aware generative models: geometrically consistent loss regularization for score-based diffusion models, latent distributions beyond the standard Gaussian choice, generative dynamics based on PDEs other than diffusion, and distillation methods with rigorous convergence rates.
- Accelerated numerical optimization: Nesterov- and Anderson-type acceleration, including applications to transformer architectures, together with second-order methods for non-smooth objectives and geometric manifolds.
The programme aims to improve stability and reduce the cost of both training and inference. Its results are expected to contribute not only to generative modelling but also to numerical optimization and computational science more broadly.
Project facts
| Programme | DFG Research Grants Programme |
| Official acronym | NumGM |
| DFG project number | 580928721 |
| DFG reference | STE 571/23-1 |
| Internal reference | AOBJ 722293 |
| Period | From 2026; approved duration 36 months |
| SAiS lead | Benjamin Gess |
SAiS lead
Collaborators
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Official sources
Related publications
No qualifying publication is currently assigned to this project.