In 1984, J. Rosický gave an abstract presentation of the structure associated to tangent
bundle functors in differential and algebraic geometry. By slightly generalizing this notion …

Deep learning, despite its remarkable achievements, is still a young field. Like the early
stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad …

Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories,
have been widely applied in denotational semantics as a way to measure to which extent …

We present semantic correctness proofs of automatic differentiation (AD). We consider a
forward-mode AD method on a higher order language with algebraic data types, and we …

Cartesian differential categories were introduced to provide an abstract axiomatization of
categories of differentiable functions. The fundamental example is the category whose …

With the increased interest in machine learning, and deep learning in particular, the use of
automatic differentiation has become more wide-spread in computation. There have been …

Change structures, introduced by Cai et al., have recently been proposed as a semantic
framework for incremental computation. We generalise change actions, an alternative to …

In this paper, we introduce differential exponential maps in Cartesian differential categories,
which generalizes the exponential function e^ x ex from classical differential calculus. A …

We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular
kind of enriched category. The base for the enrichment is the category of commutative …

The Fa\a di Bruno construction, introduced by Cockett and Seely, constructs a comonad
$\mathsf {Fa {\grave {a}}} $ whose coalgebras are precisely Cartesian differential categories …