Search Talks

A scientific understanding of modern deep learning is still in its early stages. As a first step towards understanding the learning dynamics of neural networks, one can simplify the problem by studying limits that might have theoretical tractability and practical relevance. I’ll begin with a brief survey of our earlier body of work that has investigated the infinite width limit of deep networks, a topic of active study recently. With these results in hand, it nonetheless appears there is still a gap towards theoretically describing neural networks at finite width. I’ll argue that the choice of learning rate is one crucial factor in dynamics away from the infinite width limit and naturally classifies deep networks into two classes separated by a sharp transition. This is elucidated in a class of solvable simple models we present, which give quantitative predictions for the two classes. Quite remarkably, we test these predictions empirically in practical settings and find excellent agreement. 

Yasaman Bahri is a research scientist on the Google Brain team. Her current research program is to build a scientific understanding of deep learning using a combination of theoretical analysis and empirical investigation. Prior to Google, she was at the University of California, Berkeley, where she received her Ph.D. in physics in 2017, specializing in theoretical quantum condensed matter.

Classical work by Thurston in the theory of surfaces gives symplectic co-ordinate charts on Teichmüller space, associated to quadratic differentials. Motivated by wall crossing in 4d field theories Gaiotto, Moore and Neitzke defined a generalization of these; giving maps from the moduli of one dimensional local systems on a spectral curve to the moduli space of n-dimensional local systems on a non-compact Riemann surface. I will describe joint work with M. Ionita which extends this construction to arbitrary reductive algebraic groups G. Time permitting I will describe the interpretation of this construction in terms of the wild Riemann--Hilbert Correspondence in the closely related setting of Frobenius manifolds.

Beginning with the landmark gravitational wave detections by LIGO/Virgo, we have been gaining an unprecedented view of the dynamics of strongly curved spacetime originally predicted by Einstein. Enabling and motivated by these observations, there has been rapid development in the theoretical and computational tools we use to understand and interpret the nature of gravity and matter in this regime. This is essential to fulfilling the promise of gravitational wave astronomy to not only be a new window on the astrophysics of black hole and neutron star mergers, but also to be a unique probe of fundamental physics. I will illustrate this, highlighting the example of how black holes can be used to search for new particles. The same theoretical tools also allow us to push Einstein's theory to the extreme in search of the limits of its predictability, for example testing cosmic censorship, the idea that the breakdown in Einstein's equations associated with unhalted collapse is always hidden behind a black hole horizon. I will describe some recent work resolving a long-standing putative counterexample to this conjecture.