English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Reverse-mode differentiation is used for optimization, but it introducesreferences, which break the purity of the underlying programs, making themnotoriously harder to optimize. We present a reverse-mode differentiation on apurely functional language with array operations. It is the first one todeliver a provably efficient, purely functional, and denotationally correctreverse-mode differentiation. We show that our transformation is semanticallycorrect and verifies the cheap gradient principle. Inspired by PROPs andcompilation to categories, we introduce a novel intermediate representationthat we call 'unary form'. Our reverse-mode transformation is factored as acompilation scheme through this intermediate representation. We obtain provablyefficient gradients by performing general partial evaluation optimizationsafter our reverse-mode transformation, as opposed to manually derived ones. Forsimple first-order programs, the obtained output programs resemblestatic-single-assignment (SSA) code. We emphasize the modularity of ourapproach and show how our language can easily be enriched with more optimizedprimitives, as required for some speed-ups in practice.

Denotationally Correct, Purely Functional, Efficient Reverse-mode Automatic Differentiation