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Talk Title: Covariant Neural Networks for Physics Applications

Watch Alexander’s Research Lightning Talk

Talk Abstract: Most traditional neural network architectures do not respect any intrinsic structure of the input data, and instead are expect to “learn” it. CNNs are the first widespread example of a symmetry, in this case the translational symmetry of images, being used to advise much more efficient and transparent network architectures. More recently, CNNs were generalized to other non-commutative symmetry groups such as SO(3). However, in physics application one is more likely to encounter input data that belong to linear representations of Lie Groups, as opposed to being functions (or “images”) on a symmetric space of the group.

To deal with such problems, I will present a general feed-forward architecture that takes vectors as inputs, works entirely in the Fourier space of the symmetry group, and is fully covariant. This approach allows one to achieve equal performance with drastically fewer learnable parameters, Moreover, the models become much more physically meaningful and more likely to be interpretable. My application of choice is in particle physics, where the main symmetry is the 6-dimensional Lorentz group. I will demonstrate the success of covariant architectures compared to more conventional approaches.

Bio: I am a PhD student at the University of Chicago working on theoretical hydrodynamics problems in relation to the quantum Hall effect. In addition, I am working on developing new group-covariant machine learning tools for physics applications, such as Lorentz-covariant neural networks for particle physics. My background is in mathematical physics, in which I hold a master’s degree from the Saint-Petersburg University in Russia. My interests lie on the intersection of theoretical and mathematical physics and new inter-disciplinary applications of such ideas.