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POPL 2021
Sun 17 - Fri 22 January 2021 Online
Fri 22 Jan 2021 15:45 - 15:55 at POPL-A - Probabilistic Programming

Deep learning is moving towards increasingly sophisticated optimization objectives that employ higher-order functions, such as integration, continuous optimization, and root-finding. Since differentiable programming frameworks such as PyTorch and TensorFlow do not have first-class representations of these functions, developers must reason about the semantics of such objectives and manually translate them to differentiable code.

We present a differentiable programming language, λS, that is the first to deliver a semantics for higher-order functions, higher-order derivatives, and Lipschitz but nondifferentiable functions. Together, these features enable λS to expose differentiable, higher-order functions for integration, optimization, and root-finding as first-class functions with automatically computed derivatives. λS’s semantics is computable, meaning that values can be computed to arbitrary precision, and we implement λS as an embedded language in Haskell.

We use λS to construct novel differentiable libraries for representing probability distributions, implicit surfaces, and generalized parametric surfaces — all as instances of higher-order datatypes — and present case studies that rely on computing the derivatives of these higher-order functions and datatypes. In addition to modeling existing differentiable algorithms, such as a differentiable ray tracer for implicit surfaces, without requiring any user-level differentiation code, we demonstrate new differentiable algorithms, such as the Hausdorff distance of generalized parametric surfaces.

Fri 22 Jan
Times are displayed in time zone: Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna change

15:45 - 16:45
Probabilistic ProgrammingPOPL at POPL-A
15:45
10m
Talk
λS: Computable Semantics for Differentiable Programming with Higher-Order Functions and Datatypes
POPL
Benjamin ShermanMassachusetts Institute of Technology, USA, Jesse MichelMassachusetts Institute of Technology, Michael CarbinMassachusetts Institute of Technology
Link to publication DOI
15:55
10m
Talk
Deciding Accuracy of Differential Privacy Schemes
POPL
Gilles BartheMPI-SP, Germany / IMDEA Software Institute, Spain, Rohit ChadhaUniversity of Missouri, Paul KrogmeierUniversity of Illinois at Urbana-Champaign, A. Prasad SistlaUniversity of Illinois at Chicago, Mahesh ViswanathanUniversity of Illinois at Urbana-Champaign
Link to publication DOI
16:05
10m
Talk
Probabilistic Programming Semantics for Name Generation
POPL
Marcin SabokMcGill University, Sam StatonUniversity of Oxford, Dario SteinUniversity of Oxford, Michael WolmanMcGill University
Link to publication DOI Pre-print
16:15
10m
Talk
Simplifying Multiple-Statement Reductions with the Polyhedral Model
POPL
Cambridge YangMIT CSAIL, Eric AtkinsonMIT CSAIL, Michael CarbinMassachusetts Institute of Technology
Link to publication DOI
16:25
10m
Talk
A Pre-Expectation Calculus for Probabilistic SensitivityDistinguished Paper
POPL
Alejandro AguirreIMDEA Software Institute and T.U. of Madrid (UPM), Gilles BartheMPI-SP, Germany / IMDEA Software Institute, Spain, Justin HsuUniversity of Wisconsin-Madison, USA, Benjamin Lucien KaminskiRWTH Aachen University, Germany, Joost-Pieter KatoenRWTH Aachen University, Christoph MathejaETH Zurich
Link to publication DOI
16:35
10m
Talk
Paradoxes of probabilistic programming
POPL
Jules JacobsRadboud University Nijmegen
Link to publication DOI Pre-print