ekmett/ad

ad – Automatic Differentiation for Haskell

What it is

• A Haskell library that lets you compute exact derivatives of numeric functions directly in code. It implements both forward‑mode and reverse‑mode automatic differentiation (AD) behind a small, type‑safe API.

Why it matters

• In machine‑learning, optimisation, physics simulation, and many other fields you often need gradients, Jacobians, Hessians, etc. Writing these by hand is error‑prone; using finite differences is slow and inaccurate. ad gives you the speed of compiled code with the precision of symbolic differentiation, while staying pure Haskell.

Key features

• Forward‑mode and reverse‑mode AD with a common, easy‑to‑learn interface.
• Higher‑order derivatives (gradients, Jacobians, Hessians, arbitrary‑order tensors) available lazily and efficiently.
• Type‑level branding to prevent accidental mixing of “infinitesimal” AD values with ordinary numbers.
• Modular design – each mode lives in its own module (Numeric.AD.Mode.Forward, ...Reverse, ...Sparse, ...Tower, etc.) so you can pick the implementation that fits your problem size.
• Root‑finding helpers (Newton, Halley) built on top of the AD engine.
• Rank‑1 combinators for maximum flexibility when you need to manipulate AD values with higher‑order functions (at the cost of some type safety).

Typical usage

import Numeric.AD

-- First derivative of sin at 0
> diff sin 0
1.0

-- Value and derivative of exp . log at 2
> diff' (exp . log) 2
(2.0,1.0)

-- Gradient of a multivariate function
> grad (\[x,y,z] -> x * sin (x + log y)) [1,2,3]
[ sin (1 + log 2) + cos (1 + log 2) * 1
, recip 2 * cos (1 + log 2) * 1
, 0 ]

The library also supports streams of higher‑order derivatives (diffs, grads) and a Jet type for inspecting each “layer” of the derivative tower.

Who should use it

• Haskell developers building machine‑learning models, optimisation algorithms, or scientific simulations that need fast, exact gradients.
• Researchers who want to experiment with custom loss functions or differential equations without leaving the Haskell ecosystem.
• Anyone needing reliable root‑finding (Newton, Halley) that benefits from automatic derivatives.

Getting started

• Install from Hackage: cabal install ad or add ad to your project’s .cabal file.
• Import Numeric.AD (or a specific mode module) and start calling diff, grad, jacobian, hessian, etc.

Where to ask questions

• Open issues or pull requests on the GitHub repo: https://github.com/ekmett/ad
• Join the Haskell community on IRC (#haskell on irc.libera.chat) or the project's issue tracker.

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This summary is based solely on the repository’s README.