I’m a fourth year graduate student at Lab for Information and Decision Systems (LIDS) at MIT advised by Prof. Guy Bresler. I work on various problems in theoretical machine learning([1]), applied probability and statistics. My current work focuses on representation power of deep neural networks, random graphs with latent geometric structure and stochastic optimization algorithms. Previously I was an undergraduate student at IIT Madras.

Email: dheeraj[at]mit[dot]edu

[1] “आकाशात् पतितं तोयं यथा गच्छति सागरम्” 

Publications:

Manuscripts:

• • Sharp Representation Theorems for ReLU Networks with Precise Dependence on Depth. (2020)
    arXiv preprint, under review
    with Guy Bresler.
  • Least Squares Regression with Markovian Data: Fundamental Limits and Algorithms. (2020)
    arXiv preprint, under review
    with Guy Bresler, Prateek Jain, Praneeth Netrapalli, Xian Wu

Journal Publications: 

• Phase Transition for Detecting Latent Geometry in Random Graphs. (2020)
  Probability Theory and Related Fields
  arXiv preprint: arxiv:1910.14167
• Stein’s Method for Stationary Distributions of Markov Chains and Application to Ising Models. (2019)
  Annals of Applied Probability 
  arXiv preprint: arxiv:1712.05743, 
  with Guy Bresler
•  Continuous limit of discrete quantum walks. (2015)
  Physical Review A, arxiv:1501.06950
  with Todd A. Brun

Conference Publications:

• A Corrective View of Neural Networks: Representation, Memorization and Learning. (2020)
  COLT 2020
  arXiv preprint : arxiv:2002.00274
  with Guy Bresler.
• Making Last Iterate of Stochastic Gradient Descent Information Theoretically Optimal. (2019)
  COLT 2019
  with Praneeth Netrapalli and Prateek Jain
• SGD without Replacement: Sharper Rates for General Smooth Convex Functions. (2019)
  ICML 2019
  with Praneeth Netrapalli and Prateek Jain
• Optimal Single Sample Tests for Structured versus Unstructured Network Data. (2018)
  COLT 2018.
  arxiv preprint 
  with Guy Bresler