In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and prove its correctness by means of a logical relations argument.

Thu 20 Jan

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10:20 - 12:00
Foundation and Verification of Machine-Learning SystemsPOPL at Salon I
Chair(s): Gilbert Louis Bernstein University of California at Berkeley
10:20
25m
Research paper
A Dual Number Abstraction for Static Analysis of Clarke JacobiansInPerson
POPL
Jacob Laurel University of Illinois at Urbana-Champaign, Rem Yang University of Illinois at Urbana-Champaign, Gagandeep Singh University of Illinois at Urbana-Champaign; VMware, Sasa Misailovic University of Illinois at Urbana-Champaign
DOI Media Attached
10:45
25m
Research paper
Provably Correct, Asymptotically Efficient, Higher-Order Reverse-Mode Automatic DifferentiationRemote
POPL
Faustyna Krawiec University of Cambridge, Simon Peyton Jones Microsoft Research, Neel Krishnaswami University of Cambridge, Tom Ellis Microsoft Research, Richard A. Eisenberg Tweag, Andrew Fitzgibbon Graphcore
DOI Media Attached
11:10
25m
Research paper
Interval Universal Approximation for Neural NetworksInPerson
POPL
Zi Wang University of Wisconsin-Madison, Aws Albarghouthi University of Wisconsin-Madison, Gautam Prakriya Chinese University of Hong Kong, Somesh Jha University of Wisconsin
DOI Media Attached
11:35
25m
Research paper
PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull ApproximationsInPerson
POPL
Mark Niklas Müller ETH Zurich, Gleb Makarchuk ETH Zurich, Gagandeep Singh University of Illinois at Urbana-Champaign; VMware, Markus Püschel ETH Zurich, Martin Vechev ETH Zurich
DOI Media Attached