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I'm a third-year Ph.D. student in the Department of Statistics at Harvard University, where I'm grateful to be advised by Prof. Yue M. Lu in applied mathematics, and by Prof. Pragya Sur and Prof. Subhabrata Sen in statistics. My research focuses on the mathematical foundations of AI. In my work, I employ tools from classical and high-dimensional probability, and random matrix theory, to provide a rigorous understanding of phenomena in machine learning.

Aside from my principal work, I also develop robust algorithms in convex optimization, with applications across fields such as physics.

Prior to coming to Harvard, I studied probability as an undergrad at McGill University, in my hometown of Montréal, where I worked under the supervision of Prof. Vojkan Jakšić in the field of entropic information theory.

My doctoral research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through a Canada Graduate Research Scholarship.

Research interests

  • High-dimensional problems in probability and statistics
  • Theoretical machine learning
  • Mathematical optimization

Recent Publications

Barnfield, N., Kim, J., Nichani, E., Lee, J. D., & Lu, Y. M. (2026). Sharp Capacity Thresholds in Linear Associative Memory: From Top-1 Retrieval to Tail-Average Learning. ​arXiv:2605.05189.
Barnfield, N., Kim, J., Nichani, E., Lee, J. D., & Lu, Y. M. (2026). Sharp Capacity Thresholds in Linear Associative Memory: From Top-1 Retrieval to Tail-Average Learning. ​arXiv:2605.05189.
Barnfield, N., Burke, J. V., Friedlander, M. P., & Hoheisel, T. (2026). A Scale-Shape Dual Newton Method for Entropic Least Squares. ​arXiv:2604.27154.
Barnfield, N., Burke, J. V., Friedlander, M. P., & Hoheisel, T. (2026). A Scale-Shape Dual Newton Method for Entropic Least Squares. ​arXiv:2604.27154.
Barnfield, N., Sen, S., & Sur, P. (2026). Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning. ​arXiv:2602.04872.
Barnfield, N., Sen, S., & Sur, P. (2026). Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning. ​arXiv:2602.04872.
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