About Me

Hi, I’m Eshaan! I am a final-year PhD student in the ECE department at Princeton University, jointly advised by Jason D. Lee and Yuxin Chen.

You can contact me at eshnich (at) princeton (dot) edu.

CV Google Scholar

I spent Summer 2024 as a research associate at the Flatiron Institute Center for Computational Mathematics, working with Alberto Bietti. I am supported by the DoD NDSEG Fellowship and the IBM PhD Fellowship. I previously received my B.S. degrees in Math and Computer Science (2020) and my M.Eng degree in EECS (2021) from MIT, where I was advised by Caroline Uhler.

Research Overview

The goal of my research is to develop mathematical theories of how deep neural networks learn from data. This follows three broad themes:

Feature Learning: How do shallow neural networks trained via SGD learn sophisticated representations from data?

• Provable Guarantees for Nonlinear Feature Learning in Three-Layer Neural Networks
  Eshaan Nichani, Alex Damian, Jason D. Lee.
  Neural Information Processing Systems (NeurIPS), 2023 (Spotlight).

• Emergence and scaling laws in SGD learning of shallow neural networks
  Yunwei Ren*, Eshaan Nichani*, Denny Wu, Jason D. Lee.
  Neural Information Processing Systems (NeurIPS), 2025.

Transformer Phenomena: How do transformers learn to acquire capabilities during pretraining?

• How Transformers Learn Causal Structure with Gradient Descent
  Eshaan Nichani, Alex Damian, Jason D. Lee.
  International Conference on Machine Learning (ICML), 2024.

• Learning Compositional Functions with Transformers from Easy-to-Hard Data
  Zixuan Wang*, Eshaan Nichani*, Alberto Bietti, Alex Damian, Daniel Hsu, Jason D. Lee, Denny Wu.
  Conference on Learning Theory (COLT), 2025.

Optimization Dynamics: Can we model deep learning optimization, and derive insights for training deep networks in practice?

• Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability
  Alex Damian*, Eshaan Nichani*, Jason D. Lee.
  International Conference on Learning Representations (ICLR), 2023.

• Fine-Tuning Language Models with Just Forward Passes
  Sadhika Malladi, Tianyu Gao, Eshaan Nichani, Alex Damian, Jason D. Lee, Danqi Chen, and Sanjeev Arora.
  Neural Information Processing Systems (NeurIPS), 2023 (Oral).

Check out my publications page for more!