Abstract: Integral equations, such as the rendering equation or the Walk-on-Spheres integrator, are the natural language for many problems in graphics and physics. As these integrals are often high-dimensional and recursive, we typically evaluate them using Monte Carlo integration. The best Monte Carlo estimator, however, is scene-dependent and frequently merges many separate optimization strategies together in a complex architecture–there is no “one-size fits all” solution. Furthermore, navigating this design space–by iteratively implementing and testing different estimators for a problem–is difficult and error-prone, requiring a combination of mathematical derivations and low-level numerics programming.

This talk presents Martingale, a new DSL for programming estimators. Martingale is based on three key ideas. First, the integral that the user wishes to estimate is represented explicitly in code. Second, integral transformations (i.e., meaning-preserving rewrites of integrals) are reified as compositional metaprograms, which can be abstracted and reused across problems. Third, even complex estimators can be derived by first rewriting an integral, and then applying standard importance sampling techniques. Together, these ideas enable a new method for building correct-by-construction estimators that are easy to inspect and modify, and allow us to package high-level estimation strategies into reusable library components.

Speaker Bio: Kevin Mu is a fourth year graduate student at the University of Washington, advised by Zachary Tatlock. He studies programming languages for integration and differentiation, with applications to computer graphics and scientific computing.

Sponsor: The Carnegie Mellon Graphics Seminar is generously supported by Roblox.