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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 0.49847
Validation:	Loss 0.37191	Accuracy 1.00000
Epoch [  2]: Loss 0.31066
Validation:	Loss 0.24295	Accuracy 1.00000
Epoch [  3]: Loss 0.21989
Validation:	Loss 0.18314	Accuracy 1.00000
Epoch [  4]: Loss 0.17249
Validation:	Loss 0.14558	Accuracy 1.00000
Epoch [  5]: Loss 0.13803
Validation:	Loss 0.11845	Accuracy 1.00000
Epoch [  6]: Loss 0.11243
Validation:	Loss 0.09601	Accuracy 1.00000
Epoch [  7]: Loss 0.09016
Validation:	Loss 0.07603	Accuracy 1.00000
Epoch [  8]: Loss 0.06971
Validation:	Loss 0.05619	Accuracy 1.00000
Epoch [  9]: Loss 0.04959
Validation:	Loss 0.03862	Accuracy 1.00000
Epoch [ 10]: Loss 0.03484
Validation:	Loss 0.02960	Accuracy 1.00000
Epoch [ 11]: Loss 0.02763
Validation:	Loss 0.02477	Accuracy 1.00000
Epoch [ 12]: Loss 0.02350
Validation:	Loss 0.02142	Accuracy 1.00000
Epoch [ 13]: Loss 0.02041
Validation:	Loss 0.01872	Accuracy 1.00000
Epoch [ 14]: Loss 0.01790
Validation:	Loss 0.01650	Accuracy 1.00000
Epoch [ 15]: Loss 0.01592
Validation:	Loss 0.01482	Accuracy 1.00000
Epoch [ 16]: Loss 0.01435
Validation:	Loss 0.01350	Accuracy 1.00000
Epoch [ 17]: Loss 0.01315
Validation:	Loss 0.01240	Accuracy 1.00000
Epoch [ 18]: Loss 0.01211
Validation:	Loss 0.01146	Accuracy 1.00000
Epoch [ 19]: Loss 0.01125
Validation:	Loss 0.01064	Accuracy 1.00000
Epoch [ 20]: Loss 0.01046
Validation:	Loss 0.00993	Accuracy 1.00000
Epoch [ 21]: Loss 0.00981
Validation:	Loss 0.00930	Accuracy 1.00000
Epoch [ 22]: Loss 0.00918
Validation:	Loss 0.00874	Accuracy 1.00000
Epoch [ 23]: Loss 0.00865
Validation:	Loss 0.00823	Accuracy 1.00000
Epoch [ 24]: Loss 0.00814
Validation:	Loss 0.00778	Accuracy 1.00000
Epoch [ 25]: Loss 0.00770
Validation:	Loss 0.00736	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 0.83670
Validation:	Loss 0.74083	Accuracy 0.51562
Epoch [  2]: Loss 0.68688
Validation:	Loss 0.60140	Accuracy 0.51562
Epoch [  3]: Loss 0.55429
Validation:	Loss 0.48177	Accuracy 1.00000
Epoch [  4]: Loss 0.45153
Validation:	Loss 0.39969	Accuracy 1.00000
Epoch [  5]: Loss 0.38463
Validation:	Loss 0.35237	Accuracy 1.00000
Epoch [  6]: Loss 0.34632
Validation:	Loss 0.31532	Accuracy 1.00000
Epoch [  7]: Loss 0.31024
Validation:	Loss 0.28181	Accuracy 1.00000
Epoch [  8]: Loss 0.27542
Validation:	Loss 0.24293	Accuracy 1.00000
Epoch [  9]: Loss 0.22810
Validation:	Loss 0.18752	Accuracy 1.00000
Epoch [ 10]: Loss 0.16558
Validation:	Loss 0.12450	Accuracy 1.00000
Epoch [ 11]: Loss 0.10887
Validation:	Loss 0.08466	Accuracy 1.00000
Epoch [ 12]: Loss 0.07648
Validation:	Loss 0.06374	Accuracy 1.00000
Epoch [ 13]: Loss 0.05823
Validation:	Loss 0.04921	Accuracy 1.00000
Epoch [ 14]: Loss 0.04532
Validation:	Loss 0.03966	Accuracy 1.00000
Epoch [ 15]: Loss 0.03754
Validation:	Loss 0.03441	Accuracy 1.00000
Epoch [ 16]: Loss 0.03308
Validation:	Loss 0.03065	Accuracy 1.00000
Epoch [ 17]: Loss 0.02968
Validation:	Loss 0.02755	Accuracy 1.00000
Epoch [ 18]: Loss 0.02677
Validation:	Loss 0.02495	Accuracy 1.00000
Epoch [ 19]: Loss 0.02426
Validation:	Loss 0.02272	Accuracy 1.00000
Epoch [ 20]: Loss 0.02225
Validation:	Loss 0.02083	Accuracy 1.00000
Epoch [ 21]: Loss 0.02043
Validation:	Loss 0.01919	Accuracy 1.00000
Epoch [ 22]: Loss 0.01878
Validation:	Loss 0.01774	Accuracy 1.00000
Epoch [ 23]: Loss 0.01743
Validation:	Loss 0.01647	Accuracy 1.00000
Epoch [ 24]: Loss 0.01619
Validation:	Loss 0.01533	Accuracy 1.00000
Epoch [ 25]: Loss 0.01519
Validation:	Loss 0.01431	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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