About Me

I’m a fifth year Ph.D. student in Applied and Computational Mathematics at Princeton University and I am fortunate to be advised by Prof. Jason Lee. I'm intersted in deep learning theory, especially optimization and representation 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

• Understanding Optimization in Deep Learning with Central Flows
  Jeremy M. Cohen*, Alex Damian*, Ameet Talwalkar, J. Zico Kolter, Jason D. Lee (preprint)
• Computational-Statistical Gaps in Gaussian Single-Index Models
  Alex Damian, Loucas Pillaud-Vivien, Jason D. Lee, Joan Bruna (COLT 2024)
• How Transformers Learn Causal Structure with Gradient Descent
  Eshaan Nichani, Alex Damian, Jason D. Lee (ICML 2024)
• Smoothing the Landscape Boosts the Signal for SGD: Optimal Sample Complexity for Learning Single Index Models
  Alex Damian, Eshaan Nichani, Rong Ge, 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 (2021-2024)
• Julia Dale Award, Duke University (2020)
• Putnam Honorable Mention (2019)
• Angier B. Duke Scholarship, Duke University (2016)