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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 0.49186
Validation:	Loss 0.44366	Accuracy 1.00000
Epoch [  2]: Loss 0.40700
Validation:	Loss 0.35775	Accuracy 1.00000
Epoch [  3]: Loss 0.31977
Validation:	Loss 0.26817	Accuracy 1.00000
Epoch [  4]: Loss 0.23175
Validation:	Loss 0.19112	Accuracy 1.00000
Epoch [  5]: Loss 0.16322
Validation:	Loss 0.13463	Accuracy 1.00000
Epoch [  6]: Loss 0.11699
Validation:	Loss 0.09471	Accuracy 1.00000
Epoch [  7]: Loss 0.08252
Validation:	Loss 0.06946	Accuracy 1.00000
Epoch [  8]: Loss 0.06104
Validation:	Loss 0.05038	Accuracy 1.00000
Epoch [  9]: Loss 0.04478
Validation:	Loss 0.03754	Accuracy 1.00000
Epoch [ 10]: Loss 0.03391
Validation:	Loss 0.02972	Accuracy 1.00000
Epoch [ 11]: Loss 0.02735
Validation:	Loss 0.02443	Accuracy 1.00000
Epoch [ 12]: Loss 0.02273
Validation:	Loss 0.02055	Accuracy 1.00000
Epoch [ 13]: Loss 0.01915
Validation:	Loss 0.01735	Accuracy 1.00000
Epoch [ 14]: Loss 0.01613
Validation:	Loss 0.01459	Accuracy 1.00000
Epoch [ 15]: Loss 0.01353
Validation:	Loss 0.01227	Accuracy 1.00000
Epoch [ 16]: Loss 0.01145
Validation:	Loss 0.01044	Accuracy 1.00000
Epoch [ 17]: Loss 0.00984
Validation:	Loss 0.00909	Accuracy 1.00000
Epoch [ 18]: Loss 0.00866
Validation:	Loss 0.00811	Accuracy 1.00000
Epoch [ 19]: Loss 0.00778
Validation:	Loss 0.00735	Accuracy 1.00000
Epoch [ 20]: Loss 0.00710
Validation:	Loss 0.00674	Accuracy 1.00000
Epoch [ 21]: Loss 0.00652
Validation:	Loss 0.00622	Accuracy 1.00000
Epoch [ 22]: Loss 0.00603
Validation:	Loss 0.00578	Accuracy 1.00000
Epoch [ 23]: Loss 0.00562
Validation:	Loss 0.00540	Accuracy 1.00000
Epoch [ 24]: Loss 0.00525
Validation:	Loss 0.00505	Accuracy 1.00000
Epoch [ 25]: Loss 0.00492
Validation:	Loss 0.00475	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 0.57609
Validation:	Loss 0.49708	Accuracy 1.00000
Epoch [  2]: Loss 0.46201
Validation:	Loss 0.40478	Accuracy 1.00000
Epoch [  3]: Loss 0.37232
Validation:	Loss 0.33042	Accuracy 1.00000
Epoch [  4]: Loss 0.29955
Validation:	Loss 0.26404	Accuracy 1.00000
Epoch [  5]: Loss 0.23541
Validation:	Loss 0.20433	Accuracy 1.00000
Epoch [  6]: Loss 0.18004
Validation:	Loss 0.15316	Accuracy 1.00000
Epoch [  7]: Loss 0.13447
Validation:	Loss 0.11283	Accuracy 1.00000
Epoch [  8]: Loss 0.09976
Validation:	Loss 0.08405	Accuracy 1.00000
Epoch [  9]: Loss 0.07567
Validation:	Loss 0.06496	Accuracy 1.00000
Epoch [ 10]: Loss 0.05958
Validation:	Loss 0.05220	Accuracy 1.00000
Epoch [ 11]: Loss 0.04842
Validation:	Loss 0.04303	Accuracy 1.00000
Epoch [ 12]: Loss 0.04030
Validation:	Loss 0.03616	Accuracy 1.00000
Epoch [ 13]: Loss 0.03418
Validation:	Loss 0.03098	Accuracy 1.00000
Epoch [ 14]: Loss 0.02964
Validation:	Loss 0.02712	Accuracy 1.00000
Epoch [ 15]: Loss 0.02615
Validation:	Loss 0.02416	Accuracy 1.00000
Epoch [ 16]: Loss 0.02345
Validation:	Loss 0.02179	Accuracy 1.00000
Epoch [ 17]: Loss 0.02126
Validation:	Loss 0.01980	Accuracy 1.00000
Epoch [ 18]: Loss 0.01933
Validation:	Loss 0.01803	Accuracy 1.00000
Epoch [ 19]: Loss 0.01763
Validation:	Loss 0.01634	Accuracy 1.00000
Epoch [ 20]: Loss 0.01595
Validation:	Loss 0.01464	Accuracy 1.00000
Epoch [ 21]: Loss 0.01430
Validation:	Loss 0.01303	Accuracy 1.00000
Epoch [ 22]: Loss 0.01283
Validation:	Loss 0.01166	Accuracy 1.00000
Epoch [ 23]: Loss 0.01157
Validation:	Loss 0.01047	Accuracy 1.00000
Epoch [ 24]: Loss 0.01040
Validation:	Loss 0.00942	Accuracy 1.00000
Epoch [ 25]: Loss 0.00942
Validation:	Loss 0.00851	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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