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.

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.

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.

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.

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.

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

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.

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

function main(model_type)
    dev = reactant_device()
    cdev = cpu_device()

    # Get the dataloaders
    train_loader, val_loader = dev(get_dataloaders())

    # Create the model
    model = model_type(2, 8, 1)
    ps, st = dev(Lux.setup(Random.default_rng(), model))

    train_state = Training.TrainState(model, ps, st, Adam(0.01f0))
    model_compiled = if dev isa ReactantDevice
        Reactant.with_config(;
            dot_general_precision=PrecisionConfig.HIGH,
            convolution_precision=PrecisionConfig.HIGH,
        ) do
            @compile model(first(train_loader)[1], ps, Lux.testmode(st))
        end
    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 cpu_device()((train_state.parameters, train_state.states))
end

ps_trained, st_trained = main(SpiralClassifier)

┌ Warning: `replicate` doesn't work for `TaskLocalRNG`. Returning the same `TaskLocalRNG`.
└ @ LuxCore /var/lib/buildkite-agent/builds/gpuci-15/julialang/lux-dot-jl/lib/LuxCore/src/LuxCore.jl:18
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1758301112.445723 1172032 service.cc:158] XLA service 0xb3d7860 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices:
I0000 00:00:1758301112.445820 1172032 service.cc:166]   StreamExecutor device (0): Quadro RTX 5000, Compute Capability 7.5
I0000 00:00:1758301112.446669 1172032 se_gpu_pjrt_client.cc:1338] Using BFC allocator.
I0000 00:00:1758301112.446735 1172032 gpu_helpers.cc:136] XLA backend allocating 12526534656 bytes on device 0 for BFCAllocator.
I0000 00:00:1758301112.446787 1172032 gpu_helpers.cc:177] XLA backend will use up to 4175511552 bytes on device 0 for CollectiveBFCAllocator.
I0000 00:00:1758301112.456036 1172032 cuda_dnn.cc:463] Loaded cuDNN version 91200
Epoch [  1]: Loss 0.68730
Validation:	Loss 0.62905	Accuracy 0.56250
Epoch [  2]: Loss 0.60175
Validation:	Loss 0.54224	Accuracy 1.00000
Epoch [  3]: Loss 0.51158
Validation:	Loss 0.44042	Accuracy 1.00000
Epoch [  4]: Loss 0.40892
Validation:	Loss 0.33205	Accuracy 1.00000
Epoch [  5]: Loss 0.30078
Validation:	Loss 0.24234	Accuracy 1.00000
Epoch [  6]: Loss 0.22024
Validation:	Loss 0.17760	Accuracy 1.00000
Epoch [  7]: Loss 0.16320
Validation:	Loss 0.13305	Accuracy 1.00000
Epoch [  8]: Loss 0.12186
Validation:	Loss 0.09922	Accuracy 1.00000
Epoch [  9]: Loss 0.08955
Validation:	Loss 0.07283	Accuracy 1.00000
Epoch [ 10]: Loss 0.06477
Validation:	Loss 0.05212	Accuracy 1.00000
Epoch [ 11]: Loss 0.04706
Validation:	Loss 0.03981	Accuracy 1.00000
Epoch [ 12]: Loss 0.03655
Validation:	Loss 0.03179	Accuracy 1.00000
Epoch [ 13]: Loss 0.02966
Validation:	Loss 0.02639	Accuracy 1.00000
Epoch [ 14]: Loss 0.02493
Validation:	Loss 0.02248	Accuracy 1.00000
Epoch [ 15]: Loss 0.02131
Validation:	Loss 0.01929	Accuracy 1.00000
Epoch [ 16]: Loss 0.01845
Validation:	Loss 0.01676	Accuracy 1.00000
Epoch [ 17]: Loss 0.01612
Validation:	Loss 0.01478	Accuracy 1.00000
Epoch [ 18]: Loss 0.01430
Validation:	Loss 0.01310	Accuracy 1.00000
Epoch [ 19]: Loss 0.01274
Validation:	Loss 0.01167	Accuracy 1.00000
Epoch [ 20]: Loss 0.01142
Validation:	Loss 0.01041	Accuracy 1.00000
Epoch [ 21]: Loss 0.01018
Validation:	Loss 0.00929	Accuracy 1.00000
Epoch [ 22]: Loss 0.00917
Validation:	Loss 0.00829	Accuracy 1.00000
Epoch [ 23]: Loss 0.00820
Validation:	Loss 0.00745	Accuracy 1.00000
Epoch [ 24]: Loss 0.00743
Validation:	Loss 0.00677	Accuracy 1.00000
Epoch [ 25]: Loss 0.00680
Validation:	Loss 0.00624	Accuracy 1.00000

We can also train the compact model with the exact same code!

ps_trained2, st_trained2 = main(SpiralClassifierCompact)

┌ Warning: `replicate` doesn't work for `TaskLocalRNG`. Returning the same `TaskLocalRNG`.
└ @ LuxCore /var/lib/buildkite-agent/builds/gpuci-15/julialang/lux-dot-jl/lib/LuxCore/src/LuxCore.jl:18
Epoch [  1]: Loss 0.65773
Validation:	Loss 0.59896	Accuracy 0.48438
Epoch [  2]: Loss 0.54844
Validation:	Loss 0.50481	Accuracy 0.48438
Epoch [  3]: Loss 0.46562
Validation:	Loss 0.44668	Accuracy 0.48438
Epoch [  4]: Loss 0.41867
Validation:	Loss 0.40673	Accuracy 0.48438
Epoch [  5]: Loss 0.38028
Validation:	Loss 0.37494	Accuracy 1.00000
Epoch [  6]: Loss 0.34868
Validation:	Loss 0.34632	Accuracy 1.00000
Epoch [  7]: Loss 0.32582
Validation:	Loss 0.31730	Accuracy 1.00000
Epoch [  8]: Loss 0.29679
Validation:	Loss 0.28482	Accuracy 1.00000
Epoch [  9]: Loss 0.26280
Validation:	Loss 0.24613	Accuracy 1.00000
Epoch [ 10]: Loss 0.22103
Validation:	Loss 0.20139	Accuracy 1.00000
Epoch [ 11]: Loss 0.17753
Validation:	Loss 0.15859	Accuracy 1.00000
Epoch [ 12]: Loss 0.13786
Validation:	Loss 0.12561	Accuracy 1.00000
Epoch [ 13]: Loss 0.11194
Validation:	Loss 0.10407	Accuracy 1.00000
Epoch [ 14]: Loss 0.09491
Validation:	Loss 0.08956	Accuracy 1.00000
Epoch [ 15]: Loss 0.08239
Validation:	Loss 0.07924	Accuracy 1.00000
Epoch [ 16]: Loss 0.07345
Validation:	Loss 0.07117	Accuracy 1.00000
Epoch [ 17]: Loss 0.06716
Validation:	Loss 0.06446	Accuracy 1.00000
Epoch [ 18]: Loss 0.06039
Validation:	Loss 0.05869	Accuracy 1.00000
Epoch [ 19]: Loss 0.05467
Validation:	Loss 0.05356	Accuracy 1.00000
Epoch [ 20]: Loss 0.05022
Validation:	Loss 0.04879	Accuracy 1.00000
Epoch [ 21]: Loss 0.04581
Validation:	Loss 0.04416	Accuracy 1.00000
Epoch [ 22]: Loss 0.04077
Validation:	Loss 0.03933	Accuracy 1.00000
Epoch [ 23]: Loss 0.03632
Validation:	Loss 0.03393	Accuracy 1.00000
Epoch [ 24]: Loss 0.03056
Validation:	Loss 0.02759	Accuracy 1.00000
Epoch [ 25]: Loss 0.02393
Validation:	Loss 0.02099	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.

@save "trained_model.jld2" ps_trained st_trained

Let's try loading the model

@load "trained_model.jld2" ps_trained st_trained

2-element Vector{Symbol}:
 :ps_trained
 :st_trained

Appendix

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 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 48 × AMD EPYC 7402 24-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver2)
Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
Environment:
  JULIA_CPU_THREADS = 2
  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
  JULIA_PKG_SERVER = 
  JULIA_NUM_THREADS = 48
  JULIA_CUDA_HARD_MEMORY_LIMIT = 100%
  JULIA_PKG_PRECOMPILE_AUTO = 0
  JULIA_DEBUG = Literate

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