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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)
    return @compact(;
        lstm_cell=LSTMCell(in_dims => hidden_dims),
        classifier=Dense(hidden_dims => out_dims, sigmoid)
    ) 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 ? AutoReactant() : 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 0.78034
Validation:	Loss 0.68817	Accuracy 0.46094
Epoch [  2]: Loss 0.62268
Validation:	Loss 0.54428	Accuracy 1.00000
Epoch [  3]: Loss 0.50677
Validation:	Loss 0.44062	Accuracy 1.00000
Epoch [  4]: Loss 0.41961
Validation:	Loss 0.36382	Accuracy 1.00000
Epoch [  5]: Loss 0.34898
Validation:	Loss 0.30093	Accuracy 1.00000
Epoch [  6]: Loss 0.28888
Validation:	Loss 0.24770	Accuracy 1.00000
Epoch [  7]: Loss 0.23713
Validation:	Loss 0.20187	Accuracy 1.00000
Epoch [  8]: Loss 0.19217
Validation:	Loss 0.16171	Accuracy 1.00000
Epoch [  9]: Loss 0.15384
Validation:	Loss 0.12675	Accuracy 1.00000
Epoch [ 10]: Loss 0.11788
Validation:	Loss 0.09437	Accuracy 1.00000
Epoch [ 11]: Loss 0.08457
Validation:	Loss 0.06400	Accuracy 1.00000
Epoch [ 12]: Loss 0.05764
Validation:	Loss 0.04773	Accuracy 1.00000
Epoch [ 13]: Loss 0.04464
Validation:	Loss 0.03883	Accuracy 1.00000
Epoch [ 14]: Loss 0.03644
Validation:	Loss 0.03179	Accuracy 1.00000
Epoch [ 15]: Loss 0.03031
Validation:	Loss 0.02693	Accuracy 1.00000
Epoch [ 16]: Loss 0.02593
Validation:	Loss 0.02334	Accuracy 1.00000
Epoch [ 17]: Loss 0.02266
Validation:	Loss 0.02059	Accuracy 1.00000
Epoch [ 18]: Loss 0.02017
Validation:	Loss 0.01851	Accuracy 1.00000
Epoch [ 19]: Loss 0.01820
Validation:	Loss 0.01683	Accuracy 1.00000
Epoch [ 20]: Loss 0.01671
Validation:	Loss 0.01545	Accuracy 1.00000
Epoch [ 21]: Loss 0.01535
Validation:	Loss 0.01429	Accuracy 1.00000
Epoch [ 22]: Loss 0.01429
Validation:	Loss 0.01330	Accuracy 1.00000
Epoch [ 23]: Loss 0.01333
Validation:	Loss 0.01243	Accuracy 1.00000
Epoch [ 24]: Loss 0.01251
Validation:	Loss 0.01167	Accuracy 1.00000
Epoch [ 25]: Loss 0.01172
Validation:	Loss 0.01099	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 0.88368
Validation:	Loss 0.80062	Accuracy 0.49219
Epoch [  2]: Loss 0.75231
Validation:	Loss 0.69298	Accuracy 0.49219
Epoch [  3]: Loss 0.66322
Validation:	Loss 0.62488	Accuracy 1.00000
Epoch [  4]: Loss 0.60159
Validation:	Loss 0.56781	Accuracy 1.00000
Epoch [  5]: Loss 0.54311
Validation:	Loss 0.50504	Accuracy 1.00000
Epoch [  6]: Loss 0.47647
Validation:	Loss 0.42917	Accuracy 1.00000
Epoch [  7]: Loss 0.39416
Validation:	Loss 0.34169	Accuracy 1.00000
Epoch [  8]: Loss 0.30808
Validation:	Loss 0.25693	Accuracy 1.00000
Epoch [  9]: Loss 0.22243
Validation:	Loss 0.17625	Accuracy 1.00000
Epoch [ 10]: Loss 0.15390
Validation:	Loss 0.12629	Accuracy 1.00000
Epoch [ 11]: Loss 0.10857
Validation:	Loss 0.08640	Accuracy 1.00000
Epoch [ 12]: Loss 0.07379
Validation:	Loss 0.05929	Accuracy 1.00000
Epoch [ 13]: Loss 0.05164
Validation:	Loss 0.04409	Accuracy 1.00000
Epoch [ 14]: Loss 0.04001
Validation:	Loss 0.03529	Accuracy 1.00000
Epoch [ 15]: Loss 0.03249
Validation:	Loss 0.02931	Accuracy 1.00000
Epoch [ 16]: Loss 0.02731
Validation:	Loss 0.02520	Accuracy 1.00000
Epoch [ 17]: Loss 0.02370
Validation:	Loss 0.02215	Accuracy 1.00000
Epoch [ 18]: Loss 0.02097
Validation:	Loss 0.01973	Accuracy 1.00000
Epoch [ 19]: Loss 0.01882
Validation:	Loss 0.01774	Accuracy 1.00000
Epoch [ 20]: Loss 0.01694
Validation:	Loss 0.01604	Accuracy 1.00000
Epoch [ 21]: Loss 0.01534
Validation:	Loss 0.01457	Accuracy 1.00000
Epoch [ 22]: Loss 0.01400
Validation:	Loss 0.01329	Accuracy 1.00000
Epoch [ 23]: Loss 0.01276
Validation:	Loss 0.01218	Accuracy 1.00000
Epoch [ 24]: Loss 0.01175
Validation:	Loss 0.01123	Accuracy 1.00000
Epoch [ 25]: Loss 0.01082
Validation:	Loss 0.01042	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 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 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-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 4 default, 1 interactive, 4 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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