# Stochastic analysis and rough paths methods in machine learning

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Purdue University (IN) · $100,000

## Abstract

The PIs research is concerned with advanced probabilistic models which have potential real-world applications in cutting-edge machine learning techniques. It aims to bring mathematical rigor and come up with new methods related to complex systems in image processing, reinforcement learning, and generative AI. Invoking recent breakthroughs in stochastic analysis as well as developing new tools, the project intends to make progress in the following directions: it introduces new ways to extract meaningful features from images, possibly enhances decision-making systems through reinforcement learning in random environments, and improves the theoretical understanding of generative models such as diffusion-based algorithms. These developments have the potential to contribute to more interpretable, robust, and effective AI systems, with applications ranging from medical imaging to autonomous driving. Beyond technical contributions, the work promotes interdisciplinary collaboration and offers strong mentorship opportunities for students and junior researchers.

 
On a technical level, the project explores four main directions: (1) the development of 2D-signatures based on rough paths and Hopf algebra structures to extract robust features from image data; (2) the construction of new image descriptors via expansions inspired by regularity structures and nonlinear PDEs; (3) the formulation of reinforcement learning problems as relaxed control problems driven by rough paths, with entro

## Key facts

- **NSF award ID:** 2450734
- **Awardee organization:** Purdue University (IN)
- **SAM.gov UEI:** YRXVL4JYCEF5
- **PI:** Samy Tindel
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Machine Learning Theory
- **Estimated total:** $100,000
- **Funds obligated:** $100,000
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2026

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2450734

## Citation

> US National Science Foundation, Award 2450734, Stochastic analysis and rough paths methods in machine learning. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2450734. Licensed CC0.

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