Nick Richardson will present his General Exam "Fiber Sampling: Differentiable Monte Carlo for Geometric Objectives" on May 11, 2022 at 2pm via Zoom and CS 402 Zoom link: [ https://us02web.zoom.us/j/84741197027?pwd=STBHTFd0WnpBeVIrTjF0d2dhbkZSUT09 | https://us02web.zoom.us/j/84741197027?pwd=STBHTFd0WnpBeVIrTjF0d2dhbkZSUT09 ] The members of his committee are as follows: Ryan Adams (adviser), Adji Bousso Dieng, and Szymon Rusinkiewicz Abstract: Integrals with parametric, discontinuous integrands are ubiquitous, and arise via the discrete latent structure resident in applications like shape optimization, phys- ical simulation, and graphics. Treating these tasks as inverse problems with an associated generative process requires optimizing model parameters which inter- act via these discontinuities. The advent of powerful automatic differentiation libraries teases the use of generic gradient-based optimization to perform inference in these models, but this requires computing derivatives of integrals with paramet- ric discontinuities. A systematic methodology to wield conventional automatic differentiation frameworks in these discrete contexts is wanting. In this work, we engage with the difficulty of computing these derivatives by noting a dual between the geometric/analytic properties of these functions and the probabilistic view of integration, namely Monte Carlo estimation. We introduce a differentiable variant of the simple Monte Carlo estimator which facilitates the general computation of these challenging derivatives, utilizing conventional automatic differentiation frameworks. We justify the estimator analytically, and demonstrate the generality of the method as applied to differentiable rendering, implicit shape optimization, PDE solving, and volumetric reconstruction. Reading List: https://drive.google.com/drive/u/1/folders/1VT6kaFKBOnprydP0a_ACaH45IFKcz-ad Everyone is invited to attend the talk, and those faculty wishing to remain for the oral exam following are welcome to do so.