About Me

I’m a fourth year Ph.D. student in the Program in Applied and Computational Mathematics at Princeton University and I am fortunate to be advised by Prof. Jason Lee. I’m currently working on understanding implicit regularization and feature learning in deep learning and my research interests broadly lie in optimization and machine learning. My research is supported by a National Science Foundation Graduate Research Fellowship and a Jane Street Graduate Research Fellowship.

I did my undergrad at Duke University where I received a B.S. in Mathematics and was fortunate to work with Prof. Cynthia Rudin and Prof. Hau-Tieng Wu.

Publications

• How Transformers Learn Causal Structure with Gradient Descent
  Eshaan Nichani, Alex Damian, Jason D. Lee (preprint)
• Smoothing the Landscape Boosts the Signal for SGD: Optimal Sample Complexity for Learning Single Index Models
  Alex Damian, Eshaan Nichani, Jason D. Lee (NeurIPS 2023, Oral)
• Fine-Tuning Language Models with Just Forward Passes
  Sadhika Malladi, Tianyu Gao, Eshaan Nichani, Alex Damian, Jason D. Lee, Danqi Chen, Sanjeev Arora (NeurIPS 2023, Oral)
• Provable Guarantees for Nonlinear Feature Learning in Three-Layer Neural Networks
  Eshaan Nichani, Alex Damian, Jason D. Lee (NeurIPS 2023, Spotlight)
• Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability
  Alex Damian*, Eshaan Nichani*, Jason D. Lee (ICLR 2023)
• Neural Networks can Learn Representations with Gradient Descent
  Alex Damian, Jason D. Lee, Mahdi Soltanolkotabi (COLT 2022)
• Label Noise SGD Provably Prefers Flat Global Minimizers
  Alex Damian, Tengyu Ma, Jason D. Lee (NeurIPS 2021)
• PULSE: Self-supervised photo upsampling via latent space exploration of generative models
  Sachit Menon*, Alex Damian*, Shijia Hu, Nikhil Ravi, Cynthia Rudin (CVPR 2020)
• New techniques for preserving global structure and denoising with low information loss in single-image super-resolution
  Yijie Bei*, Alex Damian*, Shijia Hu*, Sachit Menon*, Nikhil Ravi*, Cynthia Rudin* (CVPR NTIRE Workshop 2018)
• Squeeze-Free Hamiltonian Paths in Grid Graphs
  Alex Damian, Robin Flatland (CCCG 2015)

Note: * denotes equal contributions to the paper.

Awards

• Jane Street Graduate Research Fellowship (2024)
• NSF Graduate Research Fellowship (2021)
• Julia Dale Award, Duke University (2020)
• Angier B. Duke Scholarship, Duke University (2016)