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Data Science and Statistics Seminar

Speaker: Devanshu Agrawal

Affiliation: University of Tennessee Knoxville

Title: Towards a Complete Family of *G*-invariant Deep Neural Network Architectures

Abstract: When trying to fit a deep neural network (DNN) to a target function that is known to be *G*-invariant with respect to a symmetry group *G*, it is desirable to enforce *G*-invariance on the DNN as prior knowledge. However, there can be many different ways to do this, thus raising the problem of "*G*-invariant neural architecture design": What is the optimal *G*-invariant architecture for a given problem? This begs the more basic question: What does the search space of all possible *G*-invariant architectures look like? In this talk, I will discuss some of our work towards answering this ultimate question. First, I will describe the application that first prompted us to pose this question, wherein we develop a *G*-equivariant autoencoder to detect phase transitions in simulated systems of classical statistical physics. Second, I will provide a complete theoretical description of *G*-invariant architecture space in the limited case of shallow neural networks, a major upshot of which is the discovery of a novel family of *G*-invariant shallow architectures. Third and finally, as an extension of the shallow case, I will introduce a novel family of densely connected *G*-invariant *deep* neural network architectures, and I will discuss its implementation, implications for neural architecture search, and demonstrated utility in applications such as 3D object classification.

Thursday, September 28, 2023 at 4:30pm to 5:30pm

Ayres Hall, Room 111
1403 Circle Drive, Knoxville, TN 37996

Event Type

Lectures & Presentations

Topic

Science, Engineering

Audience

Current Students, Faculty & Staff, General Public

Department
Mathematics
Contact Name

Vasileios Maroulas

Contact Email

vasileios.maroulas@utk.edu

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