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:

  • A Corrective View of Neural Networks: Representation, Memorization and Learning. (2020)
    arXiv preprint, accepted at COLT 2020
    with Guy Bresler.
    Description: We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the error in approximation produced by the first group and corrects it, the third group approximates the error produced by the first and second groups together and so on. This technique yields several new representation and learning results for neural networks.
  • Phase Transition for Detecting Latent Geometry in Random Graphs. (2019)
    arXiv preprint, under review
    with Matthew Brennan and Guy Bresler.
    Description: We consider sparse Random Intersection Graphs and Random Geometric Graphs and give sharp (and sharper) conditions on their dimensionality which ensure their convergence to Erdos Renyi random graphs in terms of total variation distance.

Journal Publications: 

  • 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
    Description: We give a method to bound the Wasserstein distance of binary random vectors by comparing their associated Glauber dynamics. The method is applied to show that two randomly picked sites in an Ising model over a d-regular expander graph behave very similar to two randomly picked sites over a Curie-Weiss model at the same temperature in the low temperature phase.
  •  Continuous limit of discrete quantum walks. (2015)
    Physical Review A, arxiv:1501.06950
    with Todd A. Brun
    Description: We give a general method to obtain continuous time analogues of discrete time quantum walks under certain assumptions by mapping it to a different space. We illustrate our method by showing that the grid-walk variant of Grover’s algorithm performs just as well in  continuous time as it does in the discrete time.

Conference Publications: