Dr. Devanshu Agrawal
UT Knoxville
Post-doc Researcher
Friday, March 31, 2023
2:15-3:15pm Tickle 500
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.
Bio: Devanshu Agrawal is a postdoctoral researcher in the Industrial and Systems Engineering Department at University of Tennessee, Knoxville (UTK) and is a recipient of an NSF mathematical sciences postdoctoral research fellowship. Devanshu received his PhD in data science and engineering from the Bredesen Center at UTK while conducting his doctoral work at Oak Ridge National Lab. He also holds an MS degree in mathematics and a BS degree in mathematics and physics from East Tennessee State University. Devanshu is broadly interested in various topics at the intersection of deep learning and mathematics, but his current work focuses on G-invariant deep learning with implications for neural architecture search and applications to statistical physics.