There is a previously identified equivalence between wide fully connected neural networks (FCNs) and Gaussian processes (GPs). This equivalence enables, for instance, test set predictions that would have resulted from a fully Bayesian, infinitely wid...

Document(s)

Title

Recent hardware developments have dramatically increased the scale of data parallelism available for neural network training. Among the simplest ways to harness next-generation hardware is to increase the batch size in standard mini-batch neural netw...

We study CFT data of 3-dimensional superconformal field theories (SCFTs) arising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via so-called 3d/3d correspondence, central charges of these SCFTs are related to a $SL(2)$ Chern-Simons (CS...

It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian inference ...

In this thesis, we study the structure of various arithmetic cohomology groups as Iwasawamodules, made out of two different $p$-adic variations. In the first part, for an abelian varietyover a number field and a $\mathbb{Z}_p$-extension, we study the...

A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we show that fo...

Electrical conductivity (EC) as measured by the Geonics® EM-38 has shown promise as a soil survey tool. EC is determined by a combination of soluble salts, clay content and mineralogy, water content, and temperature. While investigating use of the EM...