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-7/julialang/lux-dot-jl/lib/LuxCore/src/LuxCore.jl:18
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1757913472.245851 2595121 service.cc:163] XLA service 0x4c241000 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices:
I0000 00:00:1757913472.245928 2595121 service.cc:171]   StreamExecutor device (0): NVIDIA A100-PCIE-40GB MIG 1g.5gb, Compute Capability 8.0
I0000 00:00:1757913472.246891 2595121 se_gpu_pjrt_client.cc:1338] Using BFC allocator.
I0000 00:00:1757913472.246969 2595121 gpu_helpers.cc:136] XLA backend allocating 3825205248 bytes on device 0 for BFCAllocator.
I0000 00:00:1757913472.247045 2595121 gpu_helpers.cc:177] XLA backend will use up to 1275068416 bytes on device 0 for CollectiveBFCAllocator.
I0000 00:00:1757913472.259358 2595121 cuda_dnn.cc:463] Loaded cuDNN version 91200
Epoch [  1]: Loss 0.80516
Validation:	Loss 0.64988	Accuracy 0.52344
Epoch [  2]: Loss 0.57096
Validation:	Loss 0.49920	Accuracy 1.00000
Epoch [  3]: Loss 0.46926
Validation:	Loss 0.43792	Accuracy 1.00000
Epoch [  4]: Loss 0.41021
Validation:	Loss 0.38683	Accuracy 1.00000
Epoch [  5]: Loss 0.36168
Validation:	Loss 0.33917	Accuracy 1.00000
Epoch [  6]: Loss 0.31661
Validation:	Loss 0.30016	Accuracy 1.00000
Epoch [  7]: Loss 0.27970
Validation:	Loss 0.26388	Accuracy 1.00000
Epoch [  8]: Loss 0.24520
Validation:	Loss 0.22701	Accuracy 1.00000
Epoch [  9]: Loss 0.20671
Validation:	Loss 0.18923	Accuracy 1.00000
Epoch [ 10]: Loss 0.16906
Validation:	Loss 0.14787	Accuracy 1.00000
Epoch [ 11]: Loss 0.12796
Validation:	Loss 0.10734	Accuracy 1.00000
Epoch [ 12]: Loss 0.09470
Validation:	Loss 0.08237	Accuracy 1.00000
Epoch [ 13]: Loss 0.07522
Validation:	Loss 0.06762	Accuracy 1.00000
Epoch [ 14]: Loss 0.06262
Validation:	Loss 0.05722	Accuracy 1.00000
Epoch [ 15]: Loss 0.05357
Validation:	Loss 0.04971	Accuracy 1.00000
Epoch [ 16]: Loss 0.04691
Validation:	Loss 0.04388	Accuracy 1.00000
Epoch [ 17]: Loss 0.04158
Validation:	Loss 0.03900	Accuracy 1.00000
Epoch [ 18]: Loss 0.03697
Validation:	Loss 0.03473	Accuracy 1.00000
Epoch [ 19]: Loss 0.03303
Validation:	Loss 0.03103	Accuracy 1.00000
Epoch [ 20]: Loss 0.02957
Validation:	Loss 0.02793	Accuracy 1.00000
Epoch [ 21]: Loss 0.02674
Validation:	Loss 0.02536	Accuracy 1.00000
Epoch [ 22]: Loss 0.02435
Validation:	Loss 0.02316	Accuracy 1.00000
Epoch [ 23]: Loss 0.02230
Validation:	Loss 0.02128	Accuracy 1.00000
Epoch [ 24]: Loss 0.02054
Validation:	Loss 0.01965	Accuracy 1.00000
Epoch [ 25]: Loss 0.01900
Validation:	Loss 0.01825	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-7/julialang/lux-dot-jl/lib/LuxCore/src/LuxCore.jl:18
Epoch [  1]: Loss 0.56233
Validation:	Loss 0.53499	Accuracy 0.46094
Epoch [  2]: Loss 0.48659
Validation:	Loss 0.48022	Accuracy 0.46094
Epoch [  3]: Loss 0.43482
Validation:	Loss 0.42802	Accuracy 1.00000
Epoch [  4]: Loss 0.38674
Validation:	Loss 0.37540	Accuracy 1.00000
Epoch [  5]: Loss 0.33431
Validation:	Loss 0.32171	Accuracy 1.00000
Epoch [  6]: Loss 0.28397
Validation:	Loss 0.27240	Accuracy 1.00000
Epoch [  7]: Loss 0.24136
Validation:	Loss 0.23341	Accuracy 1.00000
Epoch [  8]: Loss 0.20637
Validation:	Loss 0.20344	Accuracy 1.00000
Epoch [  9]: Loss 0.18280
Validation:	Loss 0.17919	Accuracy 1.00000
Epoch [ 10]: Loss 0.16163
Validation:	Loss 0.15870	Accuracy 1.00000
Epoch [ 11]: Loss 0.14297
Validation:	Loss 0.14052	Accuracy 1.00000
Epoch [ 12]: Loss 0.12539
Validation:	Loss 0.12329	Accuracy 1.00000
Epoch [ 13]: Loss 0.10785
Validation:	Loss 0.10505	Accuracy 1.00000
Epoch [ 14]: Loss 0.09051
Validation:	Loss 0.08307	Accuracy 1.00000
Epoch [ 15]: Loss 0.06976
Validation:	Loss 0.05998	Accuracy 1.00000
Epoch [ 16]: Loss 0.04953
Validation:	Loss 0.04190	Accuracy 1.00000
Epoch [ 17]: Loss 0.03490
Validation:	Loss 0.02940	Accuracy 1.00000
Epoch [ 18]: Loss 0.02512
Validation:	Loss 0.02139	Accuracy 1.00000
Epoch [ 19]: Loss 0.01845
Validation:	Loss 0.01567	Accuracy 1.00000
Epoch [ 20]: Loss 0.01364
Validation:	Loss 0.01141	Accuracy 1.00000
Epoch [ 21]: Loss 0.00993
Validation:	Loss 0.00862	Accuracy 1.00000
Epoch [ 22]: Loss 0.00782
Validation:	Loss 0.00721	Accuracy 1.00000
Epoch [ 23]: Loss 0.00668
Validation:	Loss 0.00634	Accuracy 1.00000
Epoch [ 24]: Loss 0.00594
Validation:	Loss 0.00572	Accuracy 1.00000
Epoch [ 25]: Loss 0.00539
Validation:	Loss 0.00523	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 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 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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