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-3/julialang/lux-dot-jl/lib/LuxCore/src/LuxCore.jl:18
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1760673750.372638  233271 service.cc:158] XLA service 0x2f415cc0 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices:
I0000 00:00:1760673750.372747  233271 service.cc:166]   StreamExecutor device (0): NVIDIA A100-PCIE-40GB MIG 1g.5gb, Compute Capability 8.0
I0000 00:00:1760673750.373817  233271 se_gpu_pjrt_client.cc:1339] Using BFC allocator.
I0000 00:00:1760673750.373909  233271 gpu_helpers.cc:136] XLA backend allocating 3825205248 bytes on device 0 for BFCAllocator.
I0000 00:00:1760673750.373977  233271 gpu_helpers.cc:177] XLA backend will use up to 1275068416 bytes on device 0 for CollectiveBFCAllocator.
I0000 00:00:1760673750.397344  233271 cuda_dnn.cc:463] Loaded cuDNN version 91200
Epoch [  1]: Loss 0.55500
Validation:	Loss 0.49278	Accuracy 1.00000
Epoch [  2]: Loss 0.45001
Validation:	Loss 0.39263	Accuracy 1.00000
Epoch [  3]: Loss 0.35885
Validation:	Loss 0.31489	Accuracy 1.00000
Epoch [  4]: Loss 0.28881
Validation:	Loss 0.25442	Accuracy 1.00000
Epoch [  5]: Loss 0.23292
Validation:	Loss 0.20642	Accuracy 1.00000
Epoch [  6]: Loss 0.18920
Validation:	Loss 0.16688	Accuracy 1.00000
Epoch [  7]: Loss 0.15214
Validation:	Loss 0.13381	Accuracy 1.00000
Epoch [  8]: Loss 0.12171
Validation:	Loss 0.10624	Accuracy 1.00000
Epoch [  9]: Loss 0.09659
Validation:	Loss 0.08423	Accuracy 1.00000
Epoch [ 10]: Loss 0.07636
Validation:	Loss 0.06725	Accuracy 1.00000
Epoch [ 11]: Loss 0.06143
Validation:	Loss 0.05400	Accuracy 1.00000
Epoch [ 12]: Loss 0.04909
Validation:	Loss 0.04305	Accuracy 1.00000
Epoch [ 13]: Loss 0.03879
Validation:	Loss 0.03331	Accuracy 1.00000
Epoch [ 14]: Loss 0.02974
Validation:	Loss 0.02565	Accuracy 1.00000
Epoch [ 15]: Loss 0.02346
Validation:	Loss 0.02088	Accuracy 1.00000
Epoch [ 16]: Loss 0.01935
Validation:	Loss 0.01750	Accuracy 1.00000
Epoch [ 17]: Loss 0.01632
Validation:	Loss 0.01476	Accuracy 1.00000
Epoch [ 18]: Loss 0.01387
Validation:	Loss 0.01277	Accuracy 1.00000
Epoch [ 19]: Loss 0.01215
Validation:	Loss 0.01122	Accuracy 1.00000
Epoch [ 20]: Loss 0.01072
Validation:	Loss 0.00996	Accuracy 1.00000
Epoch [ 21]: Loss 0.00958
Validation:	Loss 0.00897	Accuracy 1.00000
Epoch [ 22]: Loss 0.00867
Validation:	Loss 0.00818	Accuracy 1.00000
Epoch [ 23]: Loss 0.00796
Validation:	Loss 0.00754	Accuracy 1.00000
Epoch [ 24]: Loss 0.00733
Validation:	Loss 0.00699	Accuracy 1.00000
Epoch [ 25]: Loss 0.00676
Validation:	Loss 0.00652	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-3/julialang/lux-dot-jl/lib/LuxCore/src/LuxCore.jl:18
Epoch [  1]: Loss 0.58049
Validation:	Loss 0.47145	Accuracy 1.00000
Epoch [  2]: Loss 0.41388
Validation:	Loss 0.35308	Accuracy 1.00000
Epoch [  3]: Loss 0.31272
Validation:	Loss 0.26217	Accuracy 1.00000
Epoch [  4]: Loss 0.22645
Validation:	Loss 0.18497	Accuracy 1.00000
Epoch [  5]: Loss 0.15904
Validation:	Loss 0.13088	Accuracy 1.00000
Epoch [  6]: Loss 0.11542
Validation:	Loss 0.09825	Accuracy 1.00000
Epoch [  7]: Loss 0.08802
Validation:	Loss 0.07742	Accuracy 1.00000
Epoch [  8]: Loss 0.07064
Validation:	Loss 0.06312	Accuracy 1.00000
Epoch [  9]: Loss 0.05788
Validation:	Loss 0.05274	Accuracy 1.00000
Epoch [ 10]: Loss 0.04896
Validation:	Loss 0.04493	Accuracy 1.00000
Epoch [ 11]: Loss 0.04200
Validation:	Loss 0.03892	Accuracy 1.00000
Epoch [ 12]: Loss 0.03667
Validation:	Loss 0.03420	Accuracy 1.00000
Epoch [ 13]: Loss 0.03243
Validation:	Loss 0.03043	Accuracy 1.00000
Epoch [ 14]: Loss 0.02905
Validation:	Loss 0.02736	Accuracy 1.00000
Epoch [ 15]: Loss 0.02615
Validation:	Loss 0.02481	Accuracy 1.00000
Epoch [ 16]: Loss 0.02373
Validation:	Loss 0.02266	Accuracy 1.00000
Epoch [ 17]: Loss 0.02179
Validation:	Loss 0.02082	Accuracy 1.00000
Epoch [ 18]: Loss 0.01991
Validation:	Loss 0.01923	Accuracy 1.00000
Epoch [ 19]: Loss 0.01855
Validation:	Loss 0.01784	Accuracy 1.00000
Epoch [ 20]: Loss 0.01725
Validation:	Loss 0.01661	Accuracy 1.00000
Epoch [ 21]: Loss 0.01607
Validation:	Loss 0.01552	Accuracy 1.00000
Epoch [ 22]: Loss 0.01500
Validation:	Loss 0.01455	Accuracy 1.00000
Epoch [ 23]: Loss 0.01410
Validation:	Loss 0.01367	Accuracy 1.00000
Epoch [ 24]: Loss 0.01322
Validation:	Loss 0.01287	Accuracy 1.00000
Epoch [ 25]: Loss 0.01247
Validation:	Loss 0.01215	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

---

This page was generated using Literate.jl.