𝜆ₛ: computable semantics for differentiable programming with higher-order functions and datatypes
Name
3434284.pdf
Description
Published version
Size
424.81 KB
Format
Adobe PDF
Checksum (MD5)
08334194879f90911d9c301e1e151b0a
Author(s)
Sherman, Benjamin
Michel, Jesse
Carbin, Michael
Date Issued
2021
Journal
Proceedings of the ACM on Programming Languages
Publisher
Association for Computing Machinery (ACM)
Version
Final published version
Abstract
© 2021 Owner/Author. 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 enableλS 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution NoDerivatives 4.0 International License.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3434284
