Year: 2019
Type: article
Abstract: Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the mathematical notion of derivative is not always entirely clear---discrepancies can arise, sometimes inadvertently. In order to study automatic differentiation in such programming contexts, we define a small but expressive programming language that includes a construct for reverse-mode differentiation. We give operational and denotational semantics for this language. The operational semantics employs popular implementation techniques, while the denotational semantics employs notions of differentiation familiar from real analysis. We establish that these semantics coincide.
DOI: 10.1145/3371106
Authors: Martín Abadi, Gordon D. Plotkin
Institution: Google (United States)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2988918532