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UID:pretalx-juliacon-2026-URPF3H@pretalx.com
DTSTART;TZID=CET:20260814T164500
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DESCRIPTION:Information about the sensitivity (the derivative) of a functio
 n is of great use in\, among many other things\, non-linear optimization a
 nd root-finding algorithms.\nIn particular\, second-order derivative infor
 mation (curvature) can be used to accelerate such solvers\, for example\, 
 the Newton method for optimization and [Halley's method](https://en.wikipe
 dia.org/wiki/Halley%27s_method) for root finding.\n*Automatic Differentiat
 ion* (AD)\, where these sensitivities are effectively available "for free"
  (in terms of developer time investment)\, is therefore attractive since i
 t can significantly reduce the time of an implementation. In addition\, th
 e performance cost of the AD may either be close to a hand-optimized imple
 mentation or not be significant compared to other parts of the full proble
 m\, making AD attractive even from a performance standpoint.\n\nIn Julia\,
  there are many packages for AD\, each with different trade-offs. They mig
 ht use forward mode AD or reverse mode AD\, they might be implemented usin
 g operator overloading or by using code inspection\, or they might focus o
 n a certain application like machine learning\, etc.\nHyperHessians.jl is 
 a Julia package for forward mode AD that specializes in taking second-orde
 r derivatives (Hessians). It does this by using [*HyperDual* numbers](http
 s://www.mdpi.com/2227-7390/13/24/3909)\, which is an extension of [Dual nu
 mbers](https://en.wikipedia.org/wiki/Dual_number). By adopting hyperdual n
 umbers\, we can show performance gains over traditional nested dual number
 s for second-order derivatives\, which is employed by\, e.g.\, ForwardDiff
 .jl. In addition\, HyperHessians.jl supports computing Hessian-vector prod
 ucts (Hvp) and quadratic forms (v'Hvp) at a much lower cost than computing
  the full Hessian\, which is not available with straightforward usage of F
 orwardDiff.\n\nIn this presentation\, I will go through some of the theory
  behind hyperdual numbers\, how this theory is implemented in the HyperHes
 sians.jl package\, some of the implementation considerations\, and present
  some benchmarks (both micro and real-world benchmarks) that show HyperHes
 sians.jl has value as yet another AD package in the Julia AD ecosystem.
DTSTAMP:20260428T145936Z
LOCATION:Room 2
SUMMARY:HyperHessians.jl -- Forward mode AD specialized for second order de
 rivatives - Kristoffer Carlsson
URL:https://pretalx.com/juliacon-2026/talk/URPF3H/
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