DeepAI AI Chat
Log In Sign Up

Logical Relations for Partial Features and Automatic Differentiation Correctness

by   Fernando Lucatelli Nunes, et al.

We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a very straightforward proof of correctness of practical forward- and reverse-mode dual numbers style automatic differentiation (AD) on ML-family languages. The key idea is to combine it with a suitable open logical relations technique for reasoning about differentiable partial functions (a suitable lifting of the partiality monad to logical relations), which we introduce.


page 1

page 2

page 3

page 4


Automatic Differentiation for ML-family languages: correctness via logical relations

We give a simple, direct and reusable logical relations technique for la...

On the Versatility of Open Logical Relations: Continuity, Automatic Differentiation, and a Containment Theorem

Logical relations are one of the most powerful techniques in the theory ...

CHAD for Expressive Total Languages

We show how to apply forward and reverse mode Combinatory Homomorphic Au...

Denotational Correctness of Foward-Mode Automatic Differentiation for Iteration and Recursion

We present semantic correctness proofs of forward-mode Automatic Differe...

Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing

We present semantic correctness proofs of Automatic Differentiation (AD)...

On the Correctness of Automatic Differentiation for Neural Networks with Machine-Representable Parameters

Recent work has shown that automatic differentiation over the reals is a...

An Introduction to Logical Relations

Logical relations (LR) have been around for many years, and today they a...