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 00:00:1761832279.528135 1770187 service.cc:158] XLA service 0x3dedde00 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices:
I0000 00:00:1761832279.528191 1770187 service.cc:166]   StreamExecutor device (0): NVIDIA A100-PCIE-40GB MIG 1g.5gb, Compute Capability 8.0
I0000 00:00:1761832279.529168 1770187 se_gpu_pjrt_client.cc:770] Using BFC allocator.
I0000 00:00:1761832279.529213 1770187 gpu_helpers.cc:136] XLA backend allocating 3825205248 bytes on device 0 for BFCAllocator.
I0000 00:00:1761832279.529256 1770187 gpu_helpers.cc:177] XLA backend will use up to 1275068416 bytes on device 0 for CollectiveBFCAllocator.
I0000 00:00:1761832279.539648 1770187 cuda_dnn.cc:463] Loaded cuDNN version 91400
Epoch [  1]: Loss 0.91827
Validation:	Loss 0.81789	Accuracy 0.00000
Epoch [  2]: Loss 0.76624
Validation:	Loss 0.68915	Accuracy 0.57031
Epoch [  3]: Loss 0.66400
Validation:	Loss 0.60288	Accuracy 0.57031
Epoch [  4]: Loss 0.59221
Validation:	Loss 0.53883	Accuracy 1.00000
Epoch [  5]: Loss 0.52566
Validation:	Loss 0.45933	Accuracy 1.00000
Epoch [  6]: Loss 0.44136
Validation:	Loss 0.36855	Accuracy 1.00000
Epoch [  7]: Loss 0.35628
Validation:	Loss 0.28217	Accuracy 1.00000
Epoch [  8]: Loss 0.27262
Validation:	Loss 0.21063	Accuracy 1.00000
Epoch [  9]: Loss 0.20703
Validation:	Loss 0.15889	Accuracy 1.00000
Epoch [ 10]: Loss 0.15829
Validation:	Loss 0.12274	Accuracy 1.00000
Epoch [ 11]: Loss 0.12319
Validation:	Loss 0.09704	Accuracy 1.00000
Epoch [ 12]: Loss 0.09818
Validation:	Loss 0.07849	Accuracy 1.00000
Epoch [ 13]: Loss 0.07995
Validation:	Loss 0.06508	Accuracy 1.00000
Epoch [ 14]: Loss 0.06610
Validation:	Loss 0.05520	Accuracy 1.00000
Epoch [ 15]: Loss 0.05665
Validation:	Loss 0.04750	Accuracy 1.00000
Epoch [ 16]: Loss 0.04864
Validation:	Loss 0.04123	Accuracy 1.00000
Epoch [ 17]: Loss 0.04211
Validation:	Loss 0.03586	Accuracy 1.00000
Epoch [ 18]: Loss 0.03648
Validation:	Loss 0.03091	Accuracy 1.00000
Epoch [ 19]: Loss 0.03076
Validation:	Loss 0.02624	Accuracy 1.00000
Epoch [ 20]: Loss 0.02613
Validation:	Loss 0.02307	Accuracy 1.00000
Epoch [ 21]: Loss 0.02322
Validation:	Loss 0.02085	Accuracy 1.00000
Epoch [ 22]: Loss 0.02104
Validation:	Loss 0.01895	Accuracy 1.00000
Epoch [ 23]: Loss 0.01905
Validation:	Loss 0.01731	Accuracy 1.00000
Epoch [ 24]: Loss 0.01739
Validation:	Loss 0.01589	Accuracy 1.00000
Epoch [ 25]: Loss 0.01594
Validation:	Loss 0.01465	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 0.72208
Validation:	Loss 0.59976	Accuracy 0.54688
Epoch [  2]: Loss 0.58334
Validation:	Loss 0.51740	Accuracy 0.54688
Epoch [  3]: Loss 0.51568
Validation:	Loss 0.46638	Accuracy 0.85938
Epoch [  4]: Loss 0.46452
Validation:	Loss 0.42209	Accuracy 1.00000
Epoch [  5]: Loss 0.42428
Validation:	Loss 0.37702	Accuracy 1.00000
Epoch [  6]: Loss 0.37346
Validation:	Loss 0.32911	Accuracy 1.00000
Epoch [  7]: Loss 0.32384
Validation:	Loss 0.28516	Accuracy 1.00000
Epoch [  8]: Loss 0.28159
Validation:	Loss 0.24646	Accuracy 1.00000
Epoch [  9]: Loss 0.24123
Validation:	Loss 0.21235	Accuracy 1.00000
Epoch [ 10]: Loss 0.20713
Validation:	Loss 0.18244	Accuracy 1.00000
Epoch [ 11]: Loss 0.17695
Validation:	Loss 0.15624	Accuracy 1.00000
Epoch [ 12]: Loss 0.15055
Validation:	Loss 0.13321	Accuracy 1.00000
Epoch [ 13]: Loss 0.12712
Validation:	Loss 0.11280	Accuracy 1.00000
Epoch [ 14]: Loss 0.10655
Validation:	Loss 0.09430	Accuracy 1.00000
Epoch [ 15]: Loss 0.08749
Validation:	Loss 0.07776	Accuracy 1.00000
Epoch [ 16]: Loss 0.07178
Validation:	Loss 0.06523	Accuracy 1.00000
Epoch [ 17]: Loss 0.06073
Validation:	Loss 0.05674	Accuracy 1.00000
Epoch [ 18]: Loss 0.05305
Validation:	Loss 0.05030	Accuracy 1.00000
Epoch [ 19]: Loss 0.04728
Validation:	Loss 0.04515	Accuracy 1.00000
Epoch [ 20]: Loss 0.04248
Validation:	Loss 0.04094	Accuracy 1.00000
Epoch [ 21]: Loss 0.03853
Validation:	Loss 0.03742	Accuracy 1.00000
Epoch [ 22]: Loss 0.03533
Validation:	Loss 0.03443	Accuracy 1.00000
Epoch [ 23]: Loss 0.03258
Validation:	Loss 0.03183	Accuracy 1.00000
Epoch [ 24]: Loss 0.03014
Validation:	Loss 0.02955	Accuracy 1.00000
Epoch [ 25]: Loss 0.02801
Validation:	Loss 0.02750	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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