# Zygote: Differentiate over Zygote operation?

**URL:** <https://discourse.julialang.org/t/zygote-differentiate-over-zygote-operation/70853>\
**Category:** Numerics\
**Tags:** differentiation, zygote, ad\
**Created:** [November 3, 2021, 8:42am UTC](https://discourse.julialang.org/t/zygote-differentiate-over-zygote-operation/70853 "2021-11-03T08:42:35Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![ThummeTo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thummeto/32/26105_2.png) [@ThummeTo](https://discourse.julialang.org/u/ThummeTo)\
**Post date:** [November 3, 2021, 8:42am UTC](https://discourse.julialang.org/t/zygote-differentiate-over-zygote-operation/70853/1 "2021-11-03T08:42:35Z")

</div>

Hello everyone,

I wondered, if it is possible to differentiate with Zygote over another Zygote-Operation (I attached a minimal example).

```julia
using Zygote

function myFunction(a)
    Zygote.jacobian(sin, a)[1]
end

Zygote.jacobian(myFunction, 0.5)

```

At this point, I know that there are other ways to build hessians, this is just a simple code example. In fact I want to build derivatives that are more complicated. Code example generates the error message:

> ERROR: LoadError: UndefVarError: xs not defined  
> Stacktrace:  
> [1] (::Zygote.var"#442#443")(#unused#::Nothing)  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\lib\array.jl:79  
> [2] (::Zygote.var"#2359#back#444"{Zygote.var"#442#443"})(Δ::Nothing)  
> @ Zygote ….julia\packages\ZygoteRules\AIbCs\src\adjoint.jl:67  
> [3] Pullback  
> @ ….julia\packages\Zygote\TaBlo\src\lib\grad.jl:184 [inlined]  
> [4] (::typeof(∂(\_gradcopy!)))(Δ::Nothing)  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0  
> [5] Pullback  
> @ ….julia\packages\Zygote\TaBlo\src\lib\grad.jl:165 [inlined]  
> [6] (::typeof(∂(withjacobian)))(Δ::NamedTuple{(:val, :grad), Tuple{Nothing, Tuple{Vector{Float64}}}})  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0  
> [7] (::Zygote.var"#209#210"{Tuple{Tuple{Nothing}, Tuple{Nothing}}, typeof(∂(withjacobian))})(Δ::NamedTuple{(:val, :grad), Tuple{Nothing, Tuple{Vector{Float64}}}})  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\lib\lib.jl:203  
> [8] #1754#back  
> @ ….julia\packages\ZygoteRules\AIbCs\src\adjoint.jl:67 [inlined]  
> [9] Pullback  
> @ ….julia\packages\Zygote\TaBlo\src\lib\grad.jl:140 [inlined]  
> [10] (::typeof(∂(jacobian)))(Δ::Tuple{Vector{Float64}})  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\compiler\interface2.jl:0  
> [11] Pullback  
> @ …\Julia\zygoteRecursion.jl:7 [inlined]  
> [12] #209  
> @ ….julia\packages\Zygote\TaBlo\src\lib\lib.jl:203 [inlined]  
> [13] #1754#back  
> @ ….julia\packages\ZygoteRules\AIbCs\src\adjoint.jl:67 [inlined]  
> [14] Pullback  
> @ .\operators.jl:938 [inlined]  
> [15] (::Zygote.var"#46#47"{typeof(∂(ComposedFunction{typeof(Zygote.\_jvec), typeof(myFunction)}(Zygote.\_jvec, myFunction)))})(Δ::Vector{Float64})  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\compiler\interface.jl:41  
> [16] withjacobian(f::Function, args::Float64)  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\lib\grad.jl:162  
> [17] jacobian(f::Function, args::Float64)  
> @ Zygote ….julia\packages\Zygote\TaBlo\src\lib\grad.jl:140  
> [18] top-level scope  
> @ …\Julia\zygoteRecursion.jl:13  
> in expression starting at …\Julia\zygoteRecursion.jl:13

[Julia v1.6, Zygote v0.6.17]

So is there a way to differentiate over other Zygote-differentiation-calls?

Thanks in advance!

---

<div class="post-metadata">

**Author:** ![raphaelchinchilla](https://avatars.discourse-cdn.com/v4/letter/r/bbce88/32.png) [@raphaelchinchilla](https://discourse.julialang.org/u/raphaelchinchilla)\
**Post date:** [November 15, 2021, 8:43pm UTC](https://discourse.julialang.org/t/zygote-differentiate-over-zygote-operation/70853/2 "2021-11-15T20:43:51Z")

</div>

I get a different error trace than you get. However, if I redefine myFunction(a) as

```julia
function myFunction(a)
    Zygote.gradient(sin, a)[1]
end

```

The whole thing works. Maybe this is a bug / missing definition of Zygote?

---

<div class="post-metadata">

**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [November 15, 2021, 10:51pm UTC](https://discourse.julialang.org/t/zygote-differentiate-over-zygote-operation/70853/3 "2021-11-15T22:51:37Z")

</div>

Yes, “bug / missing definition” is about right.

Zygote’s `jacobian` works by making the output array `dx` (one for each argument) and then writing slices into it, [here](https://github.com/FluxML/Zygote.jl/blob/7f2b16987dc4eab236aabd889444cabdcc6f9caf/src/lib/grad.jl#L183), which won’t work within a derivative. It would not be very hard to avoid that, either by gathering all the slices and combining them using a differentiable function, or by adding another rule for the this part of the operation. Someone would just have to get around to doing it.

This is the story in general for 2nd derivatives. The machinery does in principle work, but particular rules or functions don’t co-operate, and would need to be fixed.

There are very few tests involving second derivatives. An easier way to contribute than upgrading things would be to invent many test cases of things which do now work, and use various different functions, and add those to the package’s tests so that they are not accidentally broken in the process of fixing other things.

---

<div class="post-metadata">

**Author:** ![ThummeTo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thummeto/32/26105_2.png) [@ThummeTo](https://discourse.julialang.org/u/ThummeTo)\
**Post date:** [November 16, 2021, 8:23am UTC](https://discourse.julialang.org/t/zygote-differentiate-over-zygote-operation/70853/4 "2021-11-16T08:23:50Z")

</div>

Didn’t try that one at first, but you are right, Gradients are working!

---

<div class="post-metadata">

**Author:** ![ThummeTo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thummeto/32/26105_2.png) [@ThummeTo](https://discourse.julialang.org/u/ThummeTo)\
**Post date:** [November 16, 2021, 9:03am UTC](https://discourse.julialang.org/t/zygote-differentiate-over-zygote-operation/70853/5 "2021-11-16T09:03:37Z")

</div>

Thank you for the reply. I just tried to get this working with the minimal example from above (in this case there is only one argument, so the jacobian is a tuple containing a single vector containing a single value)… but without success. Could you provide a working example? That would be helpful 🙂 Thanks in advance!