[Colloquium] Horace Pan Dissertation Defense/Jun 1, 2022

[Megan Woodward]

This is an announcement of Horace Pan's Dissertation Defense.
===============================================
Candidate: Horace Pan

Date: Wednesday, June 01, 2022

Time: 11 am CST

Remote Location:  https://uchicago.zoom.us/j/96060037177?pwd=VW44TUxablhsSk55b2dSdlEzbE45Zz09 Meeting ID: 960 6003 7177 Passcode: 876833


Title: Leveraging Structure and Symmetry in Machine Learning

Abstract: In this thesis we describe two separate works: higher order permutation equivariant layers for neural networks and Fourier bases for reinforcement learning over combinatorial puzzles.

Recent work on permutation equivariant neural networks has mostly focused on the first order case (sets) and the second order case (graphs). We describe the machinery for generalizing permutation equivariance to arbitrary k-ary interactions and provide a systematic approach for efficiently computing these kth-order permutation equivariant layer and enumerating all the intermediate operations involved. We evaluate our proposed permutation equivariant architectures using higher order equivariant layers on a variety of set learning tasks and find that our models are competitive with existing baseline methods while using much fewer parameters.

Traditionally, permutation puzzles such as the Rubik's Cube were often solved by heuristic search like A*-search and value based reinforcement learning methods. Both heuristic search and Q-learning approaches to solving these puzzles can be reduced to learning a heuristic/value function to decide what puzzle move to make at each step. We propose learning a value function using the irreducible representations basis (which we will also call the Fourier basis) of the puzzle’s underlying group. Classical Fourier analysis on real valued functions tells us we can approximate smooth functions with low frequency basis functions. Similarly, smooth functions on finite groups can be represented by the analogous low frequency Fourier basis functions. We demonstrate that we can learn effective value functions in the Fourier basis for solving various permutation puzzles using fewer parameters and fewer samples than deep value networks.

Advisors: Risi Kondor

Committee Members: Risi Kondor, Yuxin Chen, and Eric Jonas


 http://www.people.cs.uchicago.edu/~hopan/horacepan_thesis_draft.pdf

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.cs.uchicago.edu/pipermail/colloquium/attachments/20220519/87da2e23/attachment-0001.html>