Khanna earns NSF CAREER Award

08-27-2026

Rajiv Khanna, Purdue Computer Science assistant professor (photo by Brian Powell Photography for Purdue University)

Purdue University Department of Computer Science Assistant Professor Rajiv Khanna has received a National Science Foundation (NSF) CAREER Award to develop new mathematical and algorithmic approaches for understanding how the structure of data influences the way machine learning systems learn.

Khanna’s five-year award is titled “Algorithmic Advances in Structure-aware Learning.” The project will support graduate student researchers, Khanna’s summer research effort, and materials and supplies for educational activities associated with the project.

Artificial intelligence systems increasingly learn from enormous amounts of data, but the relationship between the structure of that data and the behavior of learning algorithms remains poorly understood. Khanna’s research seeks to uncover the mathematical principles underlying that relationship.

“My research develops mathematical tools to uncover that hidden structure,” Khanna said. “By understanding how different training examples influence a model, we can design AI systems that train more reliably, learn from less data, and selectively remove information when it is no longer appropriate to retain.”

The project will investigate how data-induced geometry interacts with optimization algorithms, with the goal of establishing this interaction as a practical design principle for machine learning. The research will produce mathematical theory, practical algorithms, experimental benchmarks, open-source tools and instructional materials.

Khanna’s broader research interests include optimization, learning theory, interpretability and privacy. Across these areas, his work focuses on understanding why machine learning algorithms behave the way they do and identifying the underlying mechanisms that govern their behavior.

This project builds on several years of Khanna’s foundational research and brings together ideas previously studied separately. Over the five-year project, his team will develop new mathematical theory, design algorithms based on those principles and evaluate the resulting methods on increasingly complex AI systems.

“Machine learning has advanced incredibly quickly, but many of its most important successes still lack satisfying scientific explanations,” Khanna said. “I enjoy the challenge of finding simple mathematical principles behind behaviors that initially appear complicated. Watching those ideas grow—from theory, to algorithms, to students building on them—is one of the most rewarding parts of being a researcher.”

The work comes at a pivotal point for the field of artificial intelligence. The rapid development of increasingly large models, vast datasets and powerful computing systems has produced remarkable capabilities, while many of the scientific principles behind those successes remain unclear.

“The exciting opportunity now is to uncover the scientific principles that explain those successes and use them to guide the next generation of algorithms,” Khanna said. “Just as physics and biology advanced by discovering unifying principles, I believe machine learning is approaching a stage where deeper mathematical understanding will become increasingly important.”

Purdue provides an environment well suited to this type of research, combining expertise in the mathematical foundations of AI with significant computational resources and opportunities for collaboration across disciplines. Khanna’s collaborations span theoretical machine learning and application domains including computational chemistry, scientific computing and generative AI, allowing mathematical ideas to be evaluated in practical settings.

Khanna is also affiliated with Purdue’s Center for Education and Research in Information Assurance and Security (CERIAS).

Ultimately, Khanna hopes the project will help move machine learning beyond trial-and-error algorithm design toward methods that are more predictable, efficient and trustworthy.

“Research is often portrayed as a series of breakthroughs, but in reality it is a process of asking better questions,” Khanna said. “I hope this project not only advances our understanding of machine learning, but also encourages students to pursue ambitious, curiosity-driven research that seeks lasting scientific principles rather than short-term improvements.”

 

About the Department of Computer Science at Purdue University

Founded in 1962, the Department of Computer Science was created to be an innovative base of knowledge in the emerging field of computing as the first degree-awarding program in the United States. The department continues to advance the computer science industry through research. U.S. News & World Report ranks the department No. 16 and No. 15 overall in undergraduate and graduate computer science, respectively. Graduates of the program are able to solve complex and challenging problems in many fields. Our consistent success in an ever-changing landscape is reflected in the record undergraduate enrollment, increased faculty hiring, innovative research projects, and the creation of new academic programs. Learn more at cs.purdue.edu.