Peter Hoffman

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MIT LIDS, Building 45

Cambridge, MA 02139, US

I’m a 2nd-year PhD student at MIT LIDS working on generative artificial intelligence with Professor Pablo Parrilo and Professor Gabriele Farina. I am mainly interested in problems at the intersection of deep learning, probability, and optimization, particularly those related to diffusion and flow models.

I am also involved with teaching around MIT and otherwise. In the past, I’ve helped design and teach 6.S095, a student-run lecture series at MIT covering advanced problem-solving techniques in probability, random variables, and stochastic processes. I also frequently post notes on a variety of topics, which you can find here.

Previously, I completed my undergraduate degree in Mathematics, also at MIT, where I worked with Professor Pablo Parrilo on optimization algorithms with applications in game theory. During my undergraduate years, I spent time as a quantitative researcher at Point72 and Citibank.

If I’m not writing math or code, you can probably find me painting. Feel free to reach out at hoffmanp@mit.edu.  

Selected publications and projects

  1. diffconsist.jpg
    Consistent Diffusion for Gaussian Blur and General Linear Processes with Additive Gaussian Noise
    Kiril Bangachev, Victor Butoi, Peter W. Hoffman, and 1 more author
    Project, 2025
  2. kans.jpg
    Kolmogorov–Arnold Networks: Representation and Architecture
    Peter W. Hoffman, Farrell E. Wu, and Petros Prastakos
    Working paper, 2025
  3. kans2.jpg
    Theory-Inspired Architecture for Kolmogorov-Arnold Networks
    Peter W. Hoffman
    Blog post, 2025
  4. ip.jpg
    An Integer Program Approach to Generating Proper Colorings of Non-Planar Graphs
    Peter W. Hoffman, Amy Hu, Shivani Konduru, and 1 more author
    MIT Math Project, 2023
  5. nested.jpg
    Algorithmic Foundations of the Nested Sampling Algorithm
    Peter W. Hoffman
    Supervised by Prof. Peter Kempthorne, MIT Mathematics, 2023
  6. expander.jpg
    Expander Graphs and their Construction
    Peter W. Hoffman
    2023
  7. random.jpg
    Random Matrix Initialization Methods
    Peter W. Hoffman, Sage Simhon, Viktor Urvantsev, and 1 more author
    MIT Math Project, 2021