# Gradient of sum

**URL:** <https://discourse.julialang.org/t/gradient-of-sum/55389>\
**Category:** Machine Learning\
**Tags:** flux, zygote\
**Created:** [February 16, 2021, 11:09am UTC](https://discourse.julialang.org/t/gradient-of-sum/55389 "2021-02-16T11:09:00Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![e3c6](https://avatars.discourse-cdn.com/v4/letter/e/e79b87/32.png) [@e3c6](https://discourse.julialang.org/u/e3c6)\
**Post date:** [February 16, 2021, 11:09am UTC](https://discourse.julialang.org/t/gradient-of-sum/55389/1 "2021-02-16T11:09:00Z")

</div>

```julia
T = randn(10,10)
ps = Flux.params(T)
opt=ADAM()
for iter = 1:100
    gs = gradient(ps) do
        sum(T)
    end
    Flux.update!(opt, ps, gs)
end

```

throws an error:

```julia
ArgumentError: Cannot setindex! to 0.0009999999900000003 for an AbstractFill with value 1.0.

Stacktrace:
 [1] setindex! at /home/cossio/.julia/packages/FillArrays/tE9Xq/src/FillArrays.jl:41 [inlined]
 [2] _setindex! at ./abstractarray.jl:1176 [inlined]
 [3] setindex! at ./abstractarray.jl:1153 [inlined]
 [4] macro expansion at ./broadcast.jl:932 [inlined]
 [5] macro expansion at ./simdloop.jl:77 [inlined]
 [6] copyto! at ./broadcast.jl:931 [inlined]
 [7] copyto! at ./broadcast.jl:886 [inlined]
 [8] materialize! at ./broadcast.jl:848 [inlined]
 [9] materialize!(::FillArrays.Fill{Float64,2,Tuple{Base.OneTo{Int64},Base.OneTo{Int64}}}, ::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{2},Nothing,typeof(*),Tuple{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{2},Nothing,typeof(/),Tuple{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{2},Nothing,typeof(/),Tuple{Array{Float64,2},Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{0},Nothing,typeof(-),Tuple{Int64,Float64}}}},Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{2},Nothing,typeof(+),Tuple{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{2},Nothing,typeof(sqrt),Tuple{Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{2},Nothing,typeof(/),Tuple{Array{Float64,2},Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{0},Nothing,typeof(-),Tuple{Int64,Float64}}}}}},Float64}}}},Float64}}) at ./broadcast.jl:845
 [10] apply!(::ADAM, ::Array{Float64,2}, ::FillArrays.Fill{Float64,2,Tuple{Base.OneTo{Int64},Base.OneTo{Int64}}}) at /home/cossio/.julia/packages/Flux/05b38/src/optimise/optimisers.jl:177
 [11] update!(::ADAM, ::Array{Float64,2}, ::FillArrays.Fill{Float64,2,Tuple{Base.OneTo{Int64},Base.OneTo{Int64}}}) at /home/cossio/.julia/packages/Flux/05b38/src/optimise/train.jl:23
 [12] update!(::ADAM, ::Params, ::Zygote.Grads) at /home/cossio/.julia/packages/Flux/05b38/src/optimise/train.jl:29
 [13] top-level scope at In[89]:8
 [14] include_string(::Function, ::Module, ::String, ::String) at ./loading.jl:1091

```

What is going on here?

---

<div class="post-metadata">

**Author:** ![e3c6](https://avatars.discourse-cdn.com/v4/letter/e/e79b87/32.png) [@e3c6](https://discourse.julialang.org/u/e3c6)\
**Post date:** [February 16, 2021, 11:34am UTC](https://discourse.julialang.org/t/gradient-of-sum/55389/2 "2021-02-16T11:34:45Z")

</div>

[https://github.com/FluxML/Flux.jl/issues/1510](https://github.com/FluxML/Flux.jl/issues/1510)

---

<div class="post-metadata">

**Author:** ![simeonschaub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/simeonschaub/32/216566_2.png) [@simeonschaub](https://discourse.julialang.org/u/simeonschaub)\
**Post date:** [February 16, 2021, 11:56am UTC](https://discourse.julialang.org/t/gradient-of-sum/55389/3 "2021-02-16T11:56:40Z")

</div>

The issue here is that `Flux.apply!` assumes gradients to be mutable, but Zygote returned a `FillArrays.Fill` here, since that can be a lot more efficient in some cases. The easiest solution would be to pass `Array.(gs)` to `Flux.update!` instead of `gs`.

---

<div class="post-metadata">

**Author:** ![e3c6](https://avatars.discourse-cdn.com/v4/letter/e/e79b87/32.png) [@e3c6](https://discourse.julialang.org/u/e3c6)\
**Post date:** [February 16, 2021, 11:58am UTC](https://discourse.julialang.org/t/gradient-of-sum/55389/4 "2021-02-16T11:58:36Z")

</div>

It would be nice to solve this within `Flux` instead of at the user’s code. Maybe `Flux.apply!(...)` should dispatch on the type of `gs`, and exploit the mutability of `gs` when appropriate.

---

<div class="post-metadata">

**Author:** ![simeonschaub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/simeonschaub/32/216566_2.png) [@simeonschaub](https://discourse.julialang.org/u/simeonschaub)\
**Post date:** [February 16, 2021, 12:06pm UTC](https://discourse.julialang.org/t/gradient-of-sum/55389/5 "2021-02-16T12:06:39Z")

</div>

It’s not quite as straightforward, since the current optimizer API relies heavily on `IdDicts`, so it might cause wrong results for stateful optimizers with immutable types. The proper fix here is a new optimizer API and then use the explicit instead of the implicit differentiation API of Zygote. See also [https://github.com/FluxML/Flux.jl/pull/1481](https://github.com/FluxML/Flux.jl/pull/1481), but there might be more to be done for this to work seamlessly.