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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 0.78204
Validation:	Loss 0.69532	Accuracy 0.42188
Epoch [  2]: Loss 0.59822
Validation:	Loss 0.51748	Accuracy 1.00000
Epoch [  3]: Loss 0.45883
Validation:	Loss 0.38609	Accuracy 1.00000
Epoch [  4]: Loss 0.35797
Validation:	Loss 0.31100	Accuracy 1.00000
Epoch [  5]: Loss 0.30220
Validation:	Loss 0.26855	Accuracy 1.00000
Epoch [  6]: Loss 0.26252
Validation:	Loss 0.23255	Accuracy 1.00000
Epoch [  7]: Loss 0.22490
Validation:	Loss 0.19837	Accuracy 1.00000
Epoch [  8]: Loss 0.18849
Validation:	Loss 0.16559	Accuracy 1.00000
Epoch [  9]: Loss 0.15526
Validation:	Loss 0.13492	Accuracy 1.00000
Epoch [ 10]: Loss 0.12455
Validation:	Loss 0.10692	Accuracy 1.00000
Epoch [ 11]: Loss 0.09761
Validation:	Loss 0.08220	Accuracy 1.00000
Epoch [ 12]: Loss 0.07419
Validation:	Loss 0.06098	Accuracy 1.00000
Epoch [ 13]: Loss 0.05424
Validation:	Loss 0.04487	Accuracy 1.00000
Epoch [ 14]: Loss 0.04037
Validation:	Loss 0.03496	Accuracy 1.00000
Epoch [ 15]: Loss 0.03213
Validation:	Loss 0.02889	Accuracy 1.00000
Epoch [ 16]: Loss 0.02684
Validation:	Loss 0.02456	Accuracy 1.00000
Epoch [ 17]: Loss 0.02289
Validation:	Loss 0.02138	Accuracy 1.00000
Epoch [ 18]: Loss 0.02015
Validation:	Loss 0.01928	Accuracy 1.00000
Epoch [ 19]: Loss 0.01830
Validation:	Loss 0.01768	Accuracy 1.00000
Epoch [ 20]: Loss 0.01685
Validation:	Loss 0.01637	Accuracy 1.00000
Epoch [ 21]: Loss 0.01566
Validation:	Loss 0.01527	Accuracy 1.00000
Epoch [ 22]: Loss 0.01463
Validation:	Loss 0.01431	Accuracy 1.00000
Epoch [ 23]: Loss 0.01372
Validation:	Loss 0.01347	Accuracy 1.00000
Epoch [ 24]: Loss 0.01293
Validation:	Loss 0.01271	Accuracy 1.00000
Epoch [ 25]: Loss 0.01221
Validation:	Loss 0.01203	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 0.49986
Validation:	Loss 0.46301	Accuracy 1.00000
Epoch [  2]: Loss 0.39759
Validation:	Loss 0.38119	Accuracy 1.00000
Epoch [  3]: Loss 0.32218
Validation:	Loss 0.32276	Accuracy 1.00000
Epoch [  4]: Loss 0.26669
Validation:	Loss 0.27410	Accuracy 1.00000
Epoch [  5]: Loss 0.22613
Validation:	Loss 0.22847	Accuracy 1.00000
Epoch [  6]: Loss 0.18567
Validation:	Loss 0.18457	Accuracy 1.00000
Epoch [  7]: Loss 0.14464
Validation:	Loss 0.14147	Accuracy 1.00000
Epoch [  8]: Loss 0.11030
Validation:	Loss 0.10427	Accuracy 1.00000
Epoch [  9]: Loss 0.08028
Validation:	Loss 0.07503	Accuracy 1.00000
Epoch [ 10]: Loss 0.05757
Validation:	Loss 0.05221	Accuracy 1.00000
Epoch [ 11]: Loss 0.03974
Validation:	Loss 0.03494	Accuracy 1.00000
Epoch [ 12]: Loss 0.02648
Validation:	Loss 0.02405	Accuracy 1.00000
Epoch [ 13]: Loss 0.01921
Validation:	Loss 0.01808	Accuracy 1.00000
Epoch [ 14]: Loss 0.01507
Validation:	Loss 0.01443	Accuracy 1.00000
Epoch [ 15]: Loss 0.01218
Validation:	Loss 0.01156	Accuracy 1.00000
Epoch [ 16]: Loss 0.00966
Validation:	Loss 0.00914	Accuracy 1.00000
Epoch [ 17]: Loss 0.00767
Validation:	Loss 0.00723	Accuracy 1.00000
Epoch [ 18]: Loss 0.00618
Validation:	Loss 0.00588	Accuracy 1.00000
Epoch [ 19]: Loss 0.00517
Validation:	Loss 0.00495	Accuracy 1.00000
Epoch [ 20]: Loss 0.00442
Validation:	Loss 0.00424	Accuracy 1.00000
Epoch [ 21]: Loss 0.00380
Validation:	Loss 0.00366	Accuracy 1.00000
Epoch [ 22]: Loss 0.00332
Validation:	Loss 0.00319	Accuracy 1.00000
Epoch [ 23]: Loss 0.00294
Validation:	Loss 0.00284	Accuracy 1.00000
Epoch [ 24]: Loss 0.00265
Validation:	Loss 0.00259	Accuracy 1.00000
Epoch [ 25]: Loss 0.00243
Validation:	Loss 0.00239	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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