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Machine Learning

Training a Simple LSTM ​

In this tutorial we will go over using a recurrent neural network to classify clockwise and anticlockwise spirals. By the end of this tutorial you will be able to:

  1. Create custom Lux models.

  2. Become familiar with the Lux recurrent neural network API.

  3. Training using Optimisers.jl and Zygote.jl.

Package Imports ​

Note: If you wish to use AutoZygote() for automatic differentiation, add Zygote to your project dependencies and include using Zygote.

julia
using ADTypes, Lux, JLD2, MLUtils, Optimisers, Printf, Reactant, Random

Dataset ​

We will use MLUtils to generate 500 (noisy) clockwise and 500 (noisy) anticlockwise spirals. Using this data we will create a MLUtils.DataLoader. Our dataloader will give us sequences of size 2 × seq_len × batch_size and we need to predict a binary value whether the sequence is clockwise or anticlockwise.

julia
function create_dataset(; dataset_size=1000, sequence_length=50)
    # Create the spirals
    data = [MLUtils.Datasets.make_spiral(sequence_length) for _ in 1:dataset_size]
    # Get the labels
    labels = vcat(repeat([0.0f0], dataset_size ÷ 2), repeat([1.0f0], dataset_size ÷ 2))
    clockwise_spirals = [
        reshape(d[1][:, 1:sequence_length], :, sequence_length, 1) for
        d in data[1:(dataset_size ÷ 2)]
    ]
    anticlockwise_spirals = [
        reshape(d[1][:, (sequence_length + 1):end], :, sequence_length, 1) for
        d in data[((dataset_size ÷ 2) + 1):end]
    ]
    x_data = Float32.(cat(clockwise_spirals..., anticlockwise_spirals...; dims=3))
    return x_data, labels
end

function get_dataloaders(; dataset_size=1000, sequence_length=50)
    x_data, labels = create_dataset(; dataset_size, sequence_length)
    # Split the dataset
    (x_train, y_train), (x_val, y_val) = splitobs((x_data, labels); at=0.8, shuffle=true)
    # Create DataLoaders
    return (
        # Use DataLoader to automatically minibatch and shuffle the data
        DataLoader(
            collect.((x_train, y_train)); batchsize=128, shuffle=true, partial=false
        ),
        # Don't shuffle the validation data
        DataLoader(collect.((x_val, y_val)); batchsize=128, shuffle=false, partial=false),
    )
end

Creating a Classifier ​

We will be extending the Lux.AbstractLuxContainerLayer type for our custom model since it will contain a LSTM block and a classifier head.

We pass the field names lstm_cell and classifier to the type to ensure that the parameters and states are automatically populated and we don't have to define Lux.initialparameters and Lux.initialstates.

To understand more about container layers, please look at Container Layer.

julia
struct SpiralClassifier{L,C} <: AbstractLuxContainerLayer{(:lstm_cell, :classifier)}
    lstm_cell::L
    classifier::C
end

We won't define the model from scratch but rather use the Lux.LSTMCell and Lux.Dense.

julia
function SpiralClassifier(in_dims, hidden_dims, out_dims)
    return SpiralClassifier(
        LSTMCell(in_dims => hidden_dims), Dense(hidden_dims => out_dims, sigmoid)
    )
end

We can use default Lux blocks – Recurrence(LSTMCell(in_dims => hidden_dims) – instead of defining the following. But let's still do it for the sake of it.

Now we need to define the behavior of the Classifier when it is invoked.

julia
function (s::SpiralClassifier)(
    x::AbstractArray{T,3}, ps::NamedTuple, st::NamedTuple
) where {T}
    # First we will have to run the sequence through the LSTM Cell
    # The first call to LSTM Cell will create the initial hidden state
    # See that the parameters and states are automatically populated into a field called
    # `lstm_cell` We use `eachslice` to get the elements in the sequence without copying,
    # and `Iterators.peel` to split out the first element for LSTM initialization.
    x_init, x_rest = Iterators.peel(LuxOps.eachslice(x, Val(2)))
    (y, carry), st_lstm = s.lstm_cell(x_init, ps.lstm_cell, st.lstm_cell)
    # Now that we have the hidden state and memory in `carry` we will pass the input and
    # `carry` jointly
    for x in x_rest
        (y, carry), st_lstm = s.lstm_cell((x, carry), ps.lstm_cell, st_lstm)
    end
    # After running through the sequence we will pass the output through the classifier
    y, st_classifier = s.classifier(y, ps.classifier, st.classifier)
    # Finally remember to create the updated state
    st = merge(st, (classifier=st_classifier, lstm_cell=st_lstm))
    return vec(y), st
end

Using the @compact API ​

We can also define the model using the Lux.@compact API, which is a more concise way of defining models. This macro automatically handles the boilerplate code for you and as such we recommend this way of defining custom layers

julia
function SpiralClassifierCompact(in_dims, hidden_dims, out_dims)
    lstm_cell = LSTMCell(in_dims => hidden_dims)
    classifier = Dense(hidden_dims => out_dims, sigmoid)
    return @compact(; lstm_cell, classifier) do x::AbstractArray{T,3} where {T}
        x_init, x_rest = Iterators.peel(LuxOps.eachslice(x, Val(2)))
        y, carry = lstm_cell(x_init)
        for x in x_rest
            y, carry = lstm_cell((x, carry))
        end
        @return vec(classifier(y))
    end
end

Defining Accuracy, Loss and Optimiser ​

Now let's define the binary cross-entropy loss. Typically it is recommended to use logitbinarycrossentropy since it is more numerically stable, but for the sake of simplicity we will use binarycrossentropy.

julia
const lossfn = BinaryCrossEntropyLoss()

function compute_loss(model, ps, st, (x, y))
    ŷ, st_ = model(x, ps, st)
    loss = lossfn(ŷ, y)
    return loss, st_, (; y_pred=ŷ)
end

matches(y_pred, y_true) = sum((y_pred .> 0.5f0) .== y_true)
accuracy(y_pred, y_true) = matches(y_pred, y_true) / length(y_pred)

Training the Model ​

julia
function main(model_type)
    dev = reactant_device()
    cdev = cpu_device()

    # Get the dataloaders
    train_loader, val_loader = get_dataloaders() |> dev

    # Create the model
    model = model_type(2, 8, 1)
    ps, st = Lux.setup(Random.default_rng(), model) |> dev

    train_state = Training.TrainState(model, ps, st, Adam(0.01f0))
    model_compiled = if dev isa ReactantDevice
        @compile model(first(train_loader)[1], ps, Lux.testmode(st))
    else
        model
    end
    ad = dev isa ReactantDevice ? AutoEnzyme() : AutoZygote()

    for epoch in 1:25
        # Train the model
        total_loss = 0.0f0
        total_samples = 0
        for (x, y) in train_loader
            (_, loss, _, train_state) = Training.single_train_step!(
                ad, lossfn, (x, y), train_state
            )
            total_loss += loss * length(y)
            total_samples += length(y)
        end
        @printf("Epoch [%3d]: Loss %4.5f\n", epoch, total_loss / total_samples)

        # Validate the model
        total_acc = 0.0f0
        total_loss = 0.0f0
        total_samples = 0

        st_ = Lux.testmode(train_state.states)
        for (x, y) in val_loader
            ŷ, st_ = model_compiled(x, train_state.parameters, st_)
            ŷ, y = cdev(ŷ), cdev(y)
            total_acc += accuracy(ŷ, y) * length(y)
            total_loss += lossfn(ŷ, y) * length(y)
            total_samples += length(y)
        end

        @printf(
            "Validation:\tLoss %4.5f\tAccuracy %4.5f\n",
            total_loss / total_samples,
            total_acc / total_samples
        )
    end

    return (train_state.parameters, train_state.states) |> cdev
end

ps_trained, st_trained = main(SpiralClassifier)
┌ Warning: `replicate` doesn't work for `TaskLocalRNG`. Returning the same `TaskLocalRNG`.
└ @ LuxCore ~/work/Lux.jl/Lux.jl/lib/LuxCore/src/LuxCore.jl:18
Epoch [  1]: Loss 0.57961
Validation:	Loss 0.47402	Accuracy 0.89062
Epoch [  2]: Loss 0.44470
Validation:	Loss 0.39015	Accuracy 1.00000
Epoch [  3]: Loss 0.36560
Validation:	Loss 0.32219	Accuracy 1.00000
Epoch [  4]: Loss 0.30164
Validation:	Loss 0.26073	Accuracy 1.00000
Epoch [  5]: Loss 0.24237
Validation:	Loss 0.20406	Accuracy 1.00000
Epoch [  6]: Loss 0.18766
Validation:	Loss 0.15460	Accuracy 1.00000
Epoch [  7]: Loss 0.13929
Validation:	Loss 0.11342	Accuracy 1.00000
Epoch [  8]: Loss 0.10249
Validation:	Loss 0.08443	Accuracy 1.00000
Epoch [  9]: Loss 0.07695
Validation:	Loss 0.06492	Accuracy 1.00000
Epoch [ 10]: Loss 0.05973
Validation:	Loss 0.05031	Accuracy 1.00000
Epoch [ 11]: Loss 0.04569
Validation:	Loss 0.03730	Accuracy 1.00000
Epoch [ 12]: Loss 0.03268
Validation:	Loss 0.02593	Accuracy 1.00000
Epoch [ 13]: Loss 0.02314
Validation:	Loss 0.01933	Accuracy 1.00000
Epoch [ 14]: Loss 0.01756
Validation:	Loss 0.01479	Accuracy 1.00000
Epoch [ 15]: Loss 0.01350
Validation:	Loss 0.01187	Accuracy 1.00000
Epoch [ 16]: Loss 0.01111
Validation:	Loss 0.01004	Accuracy 1.00000
Epoch [ 17]: Loss 0.00949
Validation:	Loss 0.00878	Accuracy 1.00000
Epoch [ 18]: Loss 0.00841
Validation:	Loss 0.00793	Accuracy 1.00000
Epoch [ 19]: Loss 0.00766
Validation:	Loss 0.00729	Accuracy 1.00000
Epoch [ 20]: Loss 0.00707
Validation:	Loss 0.00676	Accuracy 1.00000
Epoch [ 21]: Loss 0.00658
Validation:	Loss 0.00632	Accuracy 1.00000
Epoch [ 22]: Loss 0.00616
Validation:	Loss 0.00593	Accuracy 1.00000
Epoch [ 23]: Loss 0.00579
Validation:	Loss 0.00559	Accuracy 1.00000
Epoch [ 24]: Loss 0.00547
Validation:	Loss 0.00528	Accuracy 1.00000
Epoch [ 25]: Loss 0.00517
Validation:	Loss 0.00500	Accuracy 1.00000

We can also train the compact model with the exact same code!

julia
ps_trained2, st_trained2 = main(SpiralClassifierCompact)
┌ Warning: `replicate` doesn't work for `TaskLocalRNG`. Returning the same `TaskLocalRNG`.
└ @ LuxCore ~/work/Lux.jl/Lux.jl/lib/LuxCore/src/LuxCore.jl:18
Epoch [  1]: Loss 0.71066
Validation:	Loss 0.67123	Accuracy 0.53125
Epoch [  2]: Loss 0.65536
Validation:	Loss 0.60271	Accuracy 0.53125
Epoch [  3]: Loss 0.57324
Validation:	Loss 0.49963	Accuracy 1.00000
Epoch [  4]: Loss 0.46617
Validation:	Loss 0.38726	Accuracy 1.00000
Epoch [  5]: Loss 0.36129
Validation:	Loss 0.29529	Accuracy 1.00000
Epoch [  6]: Loss 0.27896
Validation:	Loss 0.22857	Accuracy 1.00000
Epoch [  7]: Loss 0.21753
Validation:	Loss 0.17092	Accuracy 1.00000
Epoch [  8]: Loss 0.15732
Validation:	Loss 0.11990	Accuracy 1.00000
Epoch [  9]: Loss 0.10764
Validation:	Loss 0.08035	Accuracy 1.00000
Epoch [ 10]: Loss 0.06991
Validation:	Loss 0.05142	Accuracy 1.00000
Epoch [ 11]: Loss 0.04545
Validation:	Loss 0.03547	Accuracy 1.00000
Epoch [ 12]: Loss 0.03270
Validation:	Loss 0.02705	Accuracy 1.00000
Epoch [ 13]: Loss 0.02551
Validation:	Loss 0.02185	Accuracy 1.00000
Epoch [ 14]: Loss 0.02070
Validation:	Loss 0.01817	Accuracy 1.00000
Epoch [ 15]: Loss 0.01734
Validation:	Loss 0.01539	Accuracy 1.00000
Epoch [ 16]: Loss 0.01476
Validation:	Loss 0.01331	Accuracy 1.00000
Epoch [ 17]: Loss 0.01284
Validation:	Loss 0.01166	Accuracy 1.00000
Epoch [ 18]: Loss 0.01129
Validation:	Loss 0.01038	Accuracy 1.00000
Epoch [ 19]: Loss 0.01010
Validation:	Loss 0.00935	Accuracy 1.00000
Epoch [ 20]: Loss 0.00910
Validation:	Loss 0.00851	Accuracy 1.00000
Epoch [ 21]: Loss 0.00828
Validation:	Loss 0.00779	Accuracy 1.00000
Epoch [ 22]: Loss 0.00761
Validation:	Loss 0.00718	Accuracy 1.00000
Epoch [ 23]: Loss 0.00703
Validation:	Loss 0.00664	Accuracy 1.00000
Epoch [ 24]: Loss 0.00650
Validation:	Loss 0.00617	Accuracy 1.00000
Epoch [ 25]: Loss 0.00604
Validation:	Loss 0.00575	Accuracy 1.00000

Saving the Model ​

We can save the model using JLD2 (and any other serialization library of your choice) Note that we transfer the model to CPU before saving. Additionally, we recommend that you don't save the model struct and only save the parameters and states.

julia
@save "trained_model.jld2" ps_trained st_trained

Let's try loading the model

julia
@load "trained_model.jld2" ps_trained st_trained
2-element Vector{Symbol}:
 :ps_trained
 :st_trained

Appendix ​

julia
using InteractiveUtils
InteractiveUtils.versioninfo()

if @isdefined(MLDataDevices)
    if @isdefined(CUDA) && MLDataDevices.functional(CUDADevice)
        println()
        CUDA.versioninfo()
    end

    if @isdefined(AMDGPU) && MLDataDevices.functional(AMDGPUDevice)
        println()
        AMDGPU.versioninfo()
    end
end
Julia Version 1.11.8
Commit cf1da5e20e3 (2025-11-06 17:49 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 4 default, 0 interactive, 2 GC (on 4 virtual cores)
Environment:
  JULIA_DEBUG = Literate
  LD_LIBRARY_PATH = 
  JULIA_NUM_THREADS = 4
  JULIA_CPU_HARD_MEMORY_LIMIT = 100%
  JULIA_PKG_PRECOMPILE_AUTO = 0

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