#  Home 

 



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](https://lu.seas.harvard.edu) in applied mathematics, and by [Prof. Pragya Sur](https://sites.harvard.edu/prs499/) and [Prof. Subhabrata Sen](https://sites.harvard.edu/sus977/) 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](https://jaksic.xyz) in the field of entropic information theory.

My doctoral research is supported by the [Natural Sciences and Engineering Research Council of Canada (NSERC)](https://nserc-crsng.canada.ca/en) through a Canada Graduate Research Scholarship.

## Research interests

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



 

 

##  Recent Publications 

 



  Download 3 citations  download- [BibTeX](/bibcite/export?pager_style=no_pager&number_of_items=3&sort_field=bibcite_year--desc&taxonomy_filters=&&&format=bibtex)
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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](https://arxiv.org/abs/2605.05189). *​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](https://arxiv.org/abs/2605.05189). *​arXiv:2605.05189*.



 

 

 

 

Barnfield, N., Burke, J. V., Friedlander, M. P., & Hoheisel, T. (2026). [A Scale-Shape Dual Newton Method for Entropic Least Squares](https://arxiv.org/abs/2604.27154). *​arXiv:2604.27154*.



 

 

Barnfield, N., Burke, J. V., Friedlander, M. P., & Hoheisel, T. (2026). [A Scale-Shape Dual Newton Method for Entropic Least Squares](https://arxiv.org/abs/2604.27154). *​arXiv:2604.27154*.



 

 

 

 

Barnfield, N., Sen, S., & Sur, P. (2026). [Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning](https://arxiv.org/abs/2602.04872). *​arXiv:2602.04872*.



 

 

Barnfield, N., Sen, S., & Sur, P. (2026). [Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning](https://arxiv.org/abs/2602.04872). *​arXiv:2602.04872*.



 

 

 

 

 



 

 

 

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