[Pl-seminar] 1/28 Seminar: Damiano Mazza: "Automatic Differentiation in PCF"

[Nathaniel Yazdani]

NUPRL Seminar Presents

Damiano Mazza
CNRS, Université Sorbonne Paris Nord

10:00AM to 11:30AM
Tuesday, January 28th, 2020
Room 366 WVH (www.ccs.neu.edu/home/wand/directions.html)

Automatic Differentiation in PCF

Abstract

Automatic differentiation (AD) is the science of efficiently computing
the derivative (or gradient, or Jacobian) of functions specified by
computer programs. It is a fundamental tool in several fields, most
notably machine learning, where it is the key for training deep neural
networks. Albeit AD techniques natively focus on a restricted class of
programs, namely first-order straight-line programs, the rise of
so-called differentiable programming in recent years has urged for the
need of applying AD to complex programs, endowed with control flow
operators and higher-order combinators, such as map and fold. In this
talk, I will discuss the extension of AD algorithms to PCF, a(n idealized)
purely functional programming language. We will first consider the
simply-typed lambda-calculus, showing in particular how linear
negation is related to reverse-mode AD (a.k.a., backpropagation), and
then see how the extra features of PCF, namely full recursion and
conditionals, may be dealt with, stressing the difficulties posed by the
latter.

Joint work with Aloïs Brunel (Deepomatic) and Michele Pagani (IRIF,
Université de Paris).

Bio

Damiano Mazza is chargé de recherche (researcher) at CNRS, working at
the CS lab of Université Sorbonne Paris Nord, a position he has held
since 2008. He obtained his Ph.D. in 2006 at the Institut de
Mathématiques de Luminy, in Marseille. Before that, he studied CS
Engineering in Rome, Italy, which is where he is from. His research
interest are at the interface between logic in computer science, the
theory of programming languages and complexity theory, with a bias
towards the viewpoint provided by linear logic and category theory.