# Compute gradients in neuralODE with Zygote

**URL:** <https://discourse.julialang.org/t/compute-gradients-in-neuralode-with-zygote/103106>\
**Category:** Machine Learning\
**Created:** [August 23, 2023, 10:10am UTC](https://discourse.julialang.org/t/compute-gradients-in-neuralode-with-zygote/103106 "2023-08-23T10:10:30Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![tommy\_J](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tommy_j/32/51703_2.png) [@tommy\_J](https://discourse.julialang.org/u/tommy_J)\
**Post date:** [August 23, 2023, 10:10am UTC](https://discourse.julialang.org/t/compute-gradients-in-neuralode-with-zygote/103106/1 "2023-08-23T10:10:31Z")

</div>

Hello everyone,

I would like to know how to check the gradients for a single batch in [this example](https://docs.sciml.ai/Optimization/stable/tutorials/minibatch/#Data-Iterators-and-Minibatching).

After the computation of `l1` I did:

```julia
batch1 = train_loader.data[1]

time1 = train_loader.data[2]

loss, back = Zygote.pullback((θ, p, batch, time_batch) -> loss_adjoint(θ, batch, time_batch), pp, batch1, time1)

```

But this is giving me an error saying:  
`ERROR: MethodError: no method matching (::var"#10#11")(::Vector{Float32}, ::Matrix{Float32}, ::StepRangeLen{Float32, Float64, Float64, Int64})`

How can I correctly get the gradients in this case?  
Also, how can I get the gradients with respect to the inputs to the network `u`?

Best Regards

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [August 23, 2023, 10:56am UTC](https://discourse.julialang.org/t/compute-gradients-in-neuralode-with-zygote/103106/2 "2023-08-23T10:56:39Z")

</div>

What verisons?

---

<div class="post-metadata">

**Author:** ![tommy\_J](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tommy_j/32/51703_2.png) [@tommy\_J](https://discourse.julialang.org/u/tommy_J)\
**Post date:** [August 23, 2023, 11:21am UTC](https://discourse.julialang.org/t/compute-gradients-in-neuralode-with-zygote/103106/3 "2023-08-23T11:21:23Z")

</div>

`Julia 1.9.2`  
`Zygote v0.6.63`  
`Flux v0.14.2`

I think I solved it with:

```julia
loss, back = Zygote.pullback((θ, batch, time_batch) -> loss_adjoint(θ, batch, time_batch), pp, batch1, time1)

```

This returns the `loss` as a tuple from `sum(abs2, batch .- pred), pred`

When I compute the gradients with:  
`back(loss)`

What am I getting? The gradients w.r.t to the loss [network] and the gradients w.r.t to the batch?  
Where does the latter come into play?

Edit:

Also,

If I check the gradients on batch and without batch, I end up with slightly different values.

```julia
using Random
Random.seed!(123);

batch1 = train_loader.data[1]
time1 = train_loader.data[2]
prob2 = ODEProblem{false}(dudt_, u0, tspan, pp, saveat=time1)

function predict_adjoint2(fullp)
    Array(solve(prob2, Tsit5(), p = fullp))
end

function loss_adjoint2(fullp)
    pred = predict_adjoint2(fullp)
    sum(abs2, batch1 .- pred)
end

loss, back = Zygote.pullback((θ, batch, time_batch) -> loss_adjoint(θ, batch,
time_batch), pp, batch1, time1)

loss2, back2 = Zygote.pullback((θ) -> loss_adjoint2(θ), pp)

a = back(loss)
b = back2(loss2)

```

```julia
julia> a[1]
25-element Vector{Float32}:
    0.0
   -2.933251f8
    0.0
 -183.55194
    0.0
    0.0
    0.0
    0.0
    0.0
   -3.9543002f6
    0.0
   -8.834232
    0.0
    0.0
    0.0
    0.0
    1.7576794f10
   -1.752914f10
    1.7576794f10
   -1.7576794f10
    1.7576794f10
   -1.7576794f10
   -1.7576794f10
    1.7576794f10
   -1.7576784f10

```

```julia
julia> b[1]
25-element Vector{Float32}:
    0.0
   -2.9332538f8
    0.0
 -183.55225
    0.0
    0.0
    0.0
    0.0
    0.0
   -3.9543042f6
    0.0
   -8.834239
    0.0
    0.0
    0.0
    0.0
    1.7576827f10
   -1.7529172f10
    1.7576827f10
   -1.7576827f10
    1.7576827f10
   -1.7576827f10
   -1.7576827f10
    1.7576827f10
   -1.7576817f10

```

Shouldn’t they be exactly the same?

Best Regards

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [August 24, 2023, 7:50am UTC](https://discourse.julialang.org/t/compute-gradients-in-neuralode-with-zygote/103106/4 "2023-08-24T07:50:41Z")

</div>

> [@tommy\_J](#):
>
> What am I getting? The gradients w.r.t to the loss [network] and the gradients w.r.t to the batch?

The gradients with respect to each of the input arguments.

> [@tommy\_J](#):
>
> Shouldn’t they be exactly the same?

`loss_adjoint` is not defined in your code so it should error. But if it is just a different call to `loss_adjoint2` which passes in the same arguments, then likely the issue is that the version with the global `batch1`, because it’s global, removes a compiler optimization and thus slightly changes the floating point results. Remember, floating point is not associative and all of that jazz, and 32-bit floats only have 8 digits of accuracy, and so the difference that you’re seeing is the expected difference you’d have from `(x + y) + z` vs `x + (y + z)` for floating point numbers.