# How to actually take hessian in Zygote

**URL:** <https://discourse.julialang.org/t/how-to-actually-take-hessian-in-zygote/109531>\
**Category:** Numerics\
**Tags:** zygote\
**Created:** [January 31, 2024, 9:13pm UTC](https://discourse.julialang.org/t/how-to-actually-take-hessian-in-zygote/109531 "2024-01-31T21:13:49Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![KapilKhanal](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kapilkhanal/32/43976_2.png) [@KapilKhanal](https://discourse.julialang.org/u/KapilKhanal)\
**Post date:** [January 31, 2024, 9:13pm UTC](https://discourse.julialang.org/t/how-to-actually-take-hessian-in-zygote/109531/1 "2024-01-31T21:13:49Z")

</div>

for a simple function like this, why can’t

```julia
hessian(((a, b),) -> a[1]*b[2] + a[2]*b[1], [[2,1], [3,4]]) 

```

It throws `BoundsError: attempt to access ForwardDiff.Dual{Nothing, Any, 2} at index [2]`  
biut for `hessian(((a, b,c,d),) -> a*b + c*d, [2,1, 3,4])` it works. So for large array inputs, they should be unpacked and repacked ? that seems like a lot of work. Is there any other better solutions?

---

<div class="post-metadata">

**Author:** ![gdalle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gdalle/32/224680_2.png) [@gdalle](https://discourse.julialang.org/u/gdalle)\
**Post date:** [February 1, 2024, 9:01am UTC](https://discourse.julialang.org/t/how-to-actually-take-hessian-in-zygote/109531/2 "2024-02-01T09:01:42Z")

</div>

From the [documentation of `hessian`](https://fluxml.ai/Zygote.jl/stable/utils/#Zygote.hessian), it seems it only acceps a single argument which must be an array or a number. Any other behavior, even if it appears to work like your second example, is undocumented and therefore not guaranteed.

One possible solution would be to use ComponentArrays.jl to encapsulate several inputs into one. However, this code throws another bug that I don’t understand:

```julia
using ComponentArrays, Zygote
x = ComponentVector(a = [2, 1], b = [3, 4])
f(x) = x.a[1] * x.b[2] + x.a[2] * x.b[1]

```

The Jacobian works but the Hessian fails:

```julia-repl
julia> jacobian(f, x)
([4 3 1 2],)

julia> hessian(f, x)
ERROR: type Array has no field a
Stacktrace:
  [1] adjoint
    @ ~/.julia/packages/Zygote/jxHJc/src/lib/lib.jl:229 [inlined]
  [2] _pullback
    @ ~/.julia/packages/ZygoteRules/M4xmc/src/adjoint.jl:67 [inlined]
  [3] f
    @ ~/Downloads/quadgk.jl:4 [inlined]
  [4] _pullback(ctx::Zygote.Context{false}, f::typeof(f), args::Vector{ForwardDiff.Dual{Nothing, Int64, 4}})
    @ Zygote ~/.julia/packages/Zygote/jxHJc/src/compiler/interface2.jl:0
  [5] pullback(f::Function, cx::Zygote.Context{false}, args::Vector{ForwardDiff.Dual{Nothing, Int64, 4}})

```

Probably because ForwardDiff.jl discards the `ComponentVector`