Yale Physics Summer Research 2021 - Krish Desai

June 3, 2021

My most recent research has been with Ben Nachman at LBNL and Jesse Thaler at MIT. It is titled “Symmetry Discovery with Deep Learning” and here is a brief statement about it:

Symmetries are a fundamental property of functions applied to datasets.  A key function for any dataset is the probability density and the corresponding symmetries are often referred to as the symmetries of the dataset itself.  We provide a rigorous statistical notion of symmetry for a dataset, which involves reference datasets that we call inertial in analogy to inertial frames in classical mechanics.  Then, we construct a novel approach to automatically discover symmetries from a dataset using a deep learning method based on an adversarial neural network.  We show how this model performs on simple examples and provide a corresponding analytic description of the loss landscape.  Symmetry discovery may lead to new insights and can reduce the effective dimensionality of a dataset to increase its effective statistics.