publications

My current research involves diffusion models for image and video generation using stochastic differential equations, deep learning, and high performance computing. Here are a few things I've worked on in the past.

2025

  1. kans.jpg
    Kolmogorov–Arnold Networks: Representation and Architecture
    Peter W. Hoffman, Farrell W. Eldrianm, and Petros Prastakos
    Working paper, 2025
    PDF
  2. kans2.jpg
    Theory-Inspired Architecture for Kolmogorov-Arnold Networks
    Peter W. Hoffman
    Working paper, 2025
    PDF

2023

  1. 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
    PDF
  2. nested.jpg
    Algorithmic Foundations of the Nested Sampling Algorithm
    Peter W. Hoffman
    Supervised by Prof. Peter Kempthorne, MIT Mathematics, 2023
    PDF
  3. expander.jpg
    Expander Graphs and their Construction
    Peter W. Hoffman
    MIT Math project, 2023
    PDF

2022

  1. polygon.jpg
    Polygon Dynamics Under Reflection Operations
    Peter W. Hoffman, Oscar P. Lores, and Cathy Yung
    MIT Math project, 2022
    PDF
  2. billiards.jpg
    Billiards Mathematics in the Unit Square and Equilateral Triangle
    Peter W. Hoffman, Oscar P. Lores, and Cathy Yung
    MIT Math project, 2022
    PDF

2021

  1. random.jpg
    Random Matrix Initialization Methods
    Peter W. Hoffman, Sage Simhon, Viktor Urvantsev, and 1 more author
    Supervised by Prof Gil Strang, MIT Mathematics, 2021
    PDF