# Challenges with Zygote Differentiation in Multivariate Mixture Models as input noise of an implicit machine learning method

**URL:** <https://discourse.julialang.org/t/challenges-with-zygote-differentiation-in-multivariate-mixture-models-as-input-noise-of-an-implicit-machine-learning-method/112560>\
**Category:** Machine Learning\
**Tags:** machine-learning, zygote\
**Created:** [April 5, 2024, 7:48am UTC](https://discourse.julialang.org/t/challenges-with-zygote-differentiation-in-multivariate-mixture-models-as-input-noise-of-an-implicit-machine-learning-method/112560 "2024-04-05T07:48:27Z")\
**Posts on this page:** 1\
**Showing post:** 8

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**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:** [April 5, 2024, 9:27am UTC](https://discourse.julialang.org/t/challenges-with-zygote-differentiation-in-multivariate-mixture-models-as-input-noise-of-an-implicit-machine-learning-method/112560/8 "2024-04-05T09:27:43Z")

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Okay, so typically it’s easier to help you if you isolate a Minimum Working Example (MWE) first. Apparently this is the crux of your issue:

```julia
julia> using Zygote, Distributions

julia> f(μ) = rand(MvNormal(μ, I))
f (generic function with 1 method)

julia> g(μ) = rand(MixtureModel([MvNormal(μ, I), MvNormal(μ, I)]))
g (generic function with 1 method)

julia> f([1])
1-element Vector{Float64}:
 0.9848461195702295

julia> g([1])
1-element Vector{Float64}:
 1.216579611318481

julia> Zygote.jacobian(f, [1])
([0.0;;],)

julia> Zygote.jacobian(g, [1])
ERROR: Mutating arrays is not supported -- called setindex!(Vector{Float64}, ...)
This error occurs when you ask Zygote to differentiate operations that change
the elements of arrays in place (e.g. setting values with x .= ...)

Possible fixes:
- avoid mutating operations (preferred)
- or read the documentation and solutions for this error
  https://fluxml.ai/Zygote.jl/latest/limitations

```

First of all, this shows us that differentiating through random number generation is not well-defined behavior (see the zero jacobian), so I think it’s worth exploring why you feel the need to do that. There might be better alternatives like the reparametrization trick.

But setting that aside for a moment, it seems that sampling from the mixture model leads to mutating operations, while sampling from the distribution alone doesn’t. I’m honestly not sure why.

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_[View the full topic](https://discourse.julialang.org/t/challenges-with-zygote-differentiation-in-multivariate-mixture-models-as-input-noise-of-an-implicit-machine-learning-method/112560)._