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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 0.64275
Validation:	Loss 0.53105	Accuracy 1.00000
Epoch [  2]: Loss 0.49565
Validation:	Loss 0.44159	Accuracy 1.00000
Epoch [  3]: Loss 0.41812
Validation:	Loss 0.37267	Accuracy 1.00000
Epoch [  4]: Loss 0.34997
Validation:	Loss 0.30750	Accuracy 1.00000
Epoch [  5]: Loss 0.28670
Validation:	Loss 0.24610	Accuracy 1.00000
Epoch [  6]: Loss 0.22590
Validation:	Loss 0.19309	Accuracy 1.00000
Epoch [  7]: Loss 0.17702
Validation:	Loss 0.15184	Accuracy 1.00000
Epoch [  8]: Loss 0.14052
Validation:	Loss 0.12292	Accuracy 1.00000
Epoch [  9]: Loss 0.11501
Validation:	Loss 0.10253	Accuracy 1.00000
Epoch [ 10]: Loss 0.09670
Validation:	Loss 0.08621	Accuracy 1.00000
Epoch [ 11]: Loss 0.08142
Validation:	Loss 0.07268	Accuracy 1.00000
Epoch [ 12]: Loss 0.06876
Validation:	Loss 0.06095	Accuracy 1.00000
Epoch [ 13]: Loss 0.05751
Validation:	Loss 0.05108	Accuracy 1.00000
Epoch [ 14]: Loss 0.04885
Validation:	Loss 0.04364	Accuracy 1.00000
Epoch [ 15]: Loss 0.04205
Validation:	Loss 0.03822	Accuracy 1.00000
Epoch [ 16]: Loss 0.03735
Validation:	Loss 0.03401	Accuracy 1.00000
Epoch [ 17]: Loss 0.03322
Validation:	Loss 0.03063	Accuracy 1.00000
Epoch [ 18]: Loss 0.03002
Validation:	Loss 0.02784	Accuracy 1.00000
Epoch [ 19]: Loss 0.02750
Validation:	Loss 0.02549	Accuracy 1.00000
Epoch [ 20]: Loss 0.02529
Validation:	Loss 0.02345	Accuracy 1.00000
Epoch [ 21]: Loss 0.02332
Validation:	Loss 0.02168	Accuracy 1.00000
Epoch [ 22]: Loss 0.02173
Validation:	Loss 0.02011	Accuracy 1.00000
Epoch [ 23]: Loss 0.02004
Validation:	Loss 0.01870	Accuracy 1.00000
Epoch [ 24]: Loss 0.01866
Validation:	Loss 0.01743	Accuracy 1.00000
Epoch [ 25]: Loss 0.01731
Validation:	Loss 0.01627	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 0.46825
Validation:	Loss 0.41625	Accuracy 1.00000
Epoch [  2]: Loss 0.39574
Validation:	Loss 0.34268	Accuracy 1.00000
Epoch [  3]: Loss 0.32513
Validation:	Loss 0.27711	Accuracy 1.00000
Epoch [  4]: Loss 0.26287
Validation:	Loss 0.22015	Accuracy 1.00000
Epoch [  5]: Loss 0.20938
Validation:	Loss 0.17555	Accuracy 1.00000
Epoch [  6]: Loss 0.16576
Validation:	Loss 0.13593	Accuracy 1.00000
Epoch [  7]: Loss 0.12614
Validation:	Loss 0.09868	Accuracy 1.00000
Epoch [  8]: Loss 0.08896
Validation:	Loss 0.06814	Accuracy 1.00000
Epoch [  9]: Loss 0.06107
Validation:	Loss 0.04859	Accuracy 1.00000
Epoch [ 10]: Loss 0.04532
Validation:	Loss 0.03955	Accuracy 1.00000
Epoch [ 11]: Loss 0.03762
Validation:	Loss 0.03344	Accuracy 1.00000
Epoch [ 12]: Loss 0.03173
Validation:	Loss 0.02832	Accuracy 1.00000
Epoch [ 13]: Loss 0.02691
Validation:	Loss 0.02415	Accuracy 1.00000
Epoch [ 14]: Loss 0.02298
Validation:	Loss 0.02080	Accuracy 1.00000
Epoch [ 15]: Loss 0.01985
Validation:	Loss 0.01816	Accuracy 1.00000
Epoch [ 16]: Loss 0.01738
Validation:	Loss 0.01605	Accuracy 1.00000
Epoch [ 17]: Loss 0.01541
Validation:	Loss 0.01433	Accuracy 1.00000
Epoch [ 18]: Loss 0.01379
Validation:	Loss 0.01287	Accuracy 1.00000
Epoch [ 19]: Loss 0.01237
Validation:	Loss 0.01153	Accuracy 1.00000
Epoch [ 20]: Loss 0.01104
Validation:	Loss 0.01013	Accuracy 1.00000
Epoch [ 21]: Loss 0.00956
Validation:	Loss 0.00849	Accuracy 1.00000
Epoch [ 22]: Loss 0.00801
Validation:	Loss 0.00708	Accuracy 1.00000
Epoch [ 23]: Loss 0.00688
Validation:	Loss 0.00624	Accuracy 1.00000
Epoch [ 24]: Loss 0.00611
Validation:	Loss 0.00562	Accuracy 1.00000
Epoch [ 25]: Loss 0.00553
Validation:	Loss 0.00507	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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