Project Grant 2450734
- This Project Grant award from the National Science Foundation (NSF) under the Computer and Information Science and Engineering (CFDA 47.070) program provides $100,000 to the University of Wisconsin System to conduct research on the mathematical foundations of advanced generative AI models. The project aims to characterize the mathematical principles that underpin the effectiveness of frontier AI models, such as large language models, and identify key mathematical quantities driving their...
- This $100,000 Project Grant awarded by the National Science Foundation (NSF) Engineering program (CFDA 47.041) supports research to elucidate the fundamental mechanisms underlying flow-based generative AI models, such as diffusion models, and extend their capabilities to handle complex data types. The research aims to: (1) understand why trained flow models often generalize better than theoretically expected, using tools from geometry, ODE, manifold learning, and deep learning theory; and (2)...
- This $175,000 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports the development of a unified generative prediction and inference framework using diffusion processes, normalizing flows, and transfer learning to model joint distributions of tabular and unstructured data. The key products and services delivered under this award include: Algorithms for domain adaptation, reliability metrics for trustworthy AI,...
- This $300,000 Project Grant was awarded on September 1, 2025 by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049). The grant will fund research at Carnegie Mellon University to develop mathematically sound approaches for sampling and generative modeling in high-dimensional problems, which is critical for advancing machine learning and artificial intelligence (AI) techniques. The research aims to create efficient sampling methods with rigorous...
- This $175,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will fund research to develop new statistical and computational methods to enhance the reliability of data analysis in modern, large-scale datasets, particularly in the era of AI. The key areas of focus include: (1) analyzing the robustness of manifold and deep learning algorithms for high-dimensional, noisy, and nonlinear data; (2) developing statistical theory...
- This Project Grant award of $350,000 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research to develop new mathematical frameworks and solution algorithms for large-scale stochastic models across a range of application areas. The project will investigate geometric principles and strategies for effectively incorporating randomness into model representations and algorithm design, with a focus on solving equilibrium problems in...
- This Project Grant award of $150,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program aims to enhance the development and understanding of machine learning and artificial intelligence through techniques from applied algebraic geometry, specifically in the context of polynomial neural networks. The research will analyze polynomial neural networks to provide global insights that can inform a priori design choices and improve the learning process for...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides funding of $296,023 to establish the mathematical foundations of two key models used in generative artificial intelligence (AI) methodologies. The primary goals are to: Examine the generative capabilities of score-based generative models in high dimensions and understand the predictive capabilities and limitations of transformer-based foundation models for...
- This federal Project Grant award of $180,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at Michigan State University to improve the robustness and trustworthiness of artificial intelligence (AI) models. The project aims to establish statistical frameworks for adversarial training in neural networks and develop scalable algorithms that leverage dynamic attack strategies and selective sampling to enhance the...
- This $218,771 Project Grant award from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program supports research to develop new theoretical tools to enhance flow-based generative artificial intelligence (AI) models. The research aims to elucidate how these models, including diffusion models, produce novel outputs and extend their capabilities to handle complex data types beyond the Euclidean setting, such as graphs and point clouds. The project,...
This federal Project Grant award of $100,000.00, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports research on advanced probabilistic models and their application to cutting-edge machine learning techniques. The research aims to bring mathematical rigor and develop new methods related to complex systems in areas such as image processing, reinforcement learning, and generative AI. Key focus areas include: 1) extracting robust features from image data using 2D-signatures based on rough paths and Hopf algebra structures; 2) constructing new image descriptors through expansions inspired by regularity structures and nonlinear PDEs; 3) formulating reinforcement learning problems as relaxed control problems driven by rough paths; and 4) studying generative modeling through reversed diffusions and score-based methods to improve theoretical guarantees and algorithmic implementations. This award, with a performance period from September 1, 2025 to August 31, 2026, is expected to contribute to more interpretable, robust, and effective AI systems with applications ranging from medical imaging to autonomous driving. The project also promotes interdisciplinary collaboration and offers mentorship opportunities for students and junior researchers.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $100.0k | 8/14/25 |