Principles of Programming Seminar
— 4:00pm
Location:
In Person
-
Newell-Simon 3305
Speaker:
JESSE MICHEL
,
Ph.D. Student, Programming Systems Group, Department of Electrical Engineering & Computer Science, Massachusetts Institute of Technology
https://web.mit.edu/jmmichel/www/
Distributions for Compositionally Differentiating Parametric
Many computations in physical simulation, computer graphics, and probabilistic inference require differentiating discontinuous processes arising from contact, occlusion, or changes at a point in time. Unfortunately, popular differentiable programming languages, such as PyTorch and JAX, do not correctly handle discontinuities during differentiation, leading to invalid results for programs with parametric discontinuities, i.e., conditional statements containing at least one real-valued parameter and variable of integration.
This talk describes Potto, a first-order programming language that computes provably sound derivatives in the presence of parametric discontinuities. Potto is formalized in terms of novel a denotational semantics for program derivatives that is grounded in distribution theory, a generalization of measure theory that computes sound derivatives in settings where naive differentiation fails. As compared to the previous state-of-the-art baseline system, Potto supports separate program compilation, leading to 88.1x–441.2x speed up in compile time and 2.5x–.9x speed up in runtime respectively, on two increasingly large image stylization benchmarks. We further showcase Potto by implementing a prototype differentiable renderer with separately compiled shaders.
—
Jesse Michel is a fourth year PhD student in the Programming Systems Group at MIT advised by Michael Carbin. He is visiting CMU this semester to work with Feras Saad on automatic differentiation of probabilistic programs. He completed his undergraduate in pure math and computer science at MIT and his Master's in Engineering at MIT on speeding up arbitrary-precision arithmetic using automatic differentiation. He is the recipient of the Ashar Aziz Presidential Fellowship.
Faculty Host: Feras Saad
Event Website:
https://www.cs.cmu.edu/~pop/seminar/2024-04-18-Michel/