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)
    return @compact(;
        lstm_cell=LSTMCell(in_dims => hidden_dims),
        classifier=Dense(hidden_dims => out_dims, sigmoid)
    ) 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 = 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 ? AutoReactant() : 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 0.46247
Validation:	Loss 0.37022	Accuracy 1.00000
Epoch [  2]: Loss 0.36059
Validation:	Loss 0.31003	Accuracy 1.00000
Epoch [  3]: Loss 0.30653
Validation:	Loss 0.26356	Accuracy 1.00000
Epoch [  4]: Loss 0.26543
Validation:	Loss 0.22726	Accuracy 1.00000
Epoch [  5]: Loss 0.22794
Validation:	Loss 0.19664	Accuracy 1.00000
Epoch [  6]: Loss 0.19866
Validation:	Loss 0.16823	Accuracy 1.00000
Epoch [  7]: Loss 0.17038
Validation:	Loss 0.13958	Accuracy 1.00000
Epoch [  8]: Loss 0.13710
Validation:	Loss 0.10823	Accuracy 1.00000
Epoch [  9]: Loss 0.10103
Validation:	Loss 0.07335	Accuracy 1.00000
Epoch [ 10]: Loss 0.06450
Validation:	Loss 0.04279	Accuracy 1.00000
Epoch [ 11]: Loss 0.03611
Validation:	Loss 0.02515	Accuracy 1.00000
Epoch [ 12]: Loss 0.02183
Validation:	Loss 0.01665	Accuracy 1.00000
Epoch [ 13]: Loss 0.01493
Validation:	Loss 0.01238	Accuracy 1.00000
Epoch [ 14]: Loss 0.01129
Validation:	Loss 0.00994	Accuracy 1.00000
Epoch [ 15]: Loss 0.00920
Validation:	Loss 0.00843	Accuracy 1.00000
Epoch [ 16]: Loss 0.00786
Validation:	Loss 0.00741	Accuracy 1.00000
Epoch [ 17]: Loss 0.00694
Validation:	Loss 0.00666	Accuracy 1.00000
Epoch [ 18]: Loss 0.00628
Validation:	Loss 0.00609	Accuracy 1.00000
Epoch [ 19]: Loss 0.00575
Validation:	Loss 0.00561	Accuracy 1.00000
Epoch [ 20]: Loss 0.00532
Validation:	Loss 0.00521	Accuracy 1.00000
Epoch [ 21]: Loss 0.00495
Validation:	Loss 0.00487	Accuracy 1.00000
Epoch [ 22]: Loss 0.00463
Validation:	Loss 0.00456	Accuracy 1.00000
Epoch [ 23]: Loss 0.00435
Validation:	Loss 0.00429	Accuracy 1.00000
Epoch [ 24]: Loss 0.00410
Validation:	Loss 0.00405	Accuracy 1.00000
Epoch [ 25]: Loss 0.00386
Validation:	Loss 0.00383	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 ~/work/Lux.jl/Lux.jl/lib/LuxCore/src/LuxCore.jl:18
Epoch [  1]: Loss 0.63055
Validation:	Loss 0.48314	Accuracy 1.00000
Epoch [  2]: Loss 0.44890
Validation:	Loss 0.37623	Accuracy 1.00000
Epoch [  3]: Loss 0.37478
Validation:	Loss 0.31747	Accuracy 1.00000
Epoch [  4]: Loss 0.31729
Validation:	Loss 0.26656	Accuracy 1.00000
Epoch [  5]: Loss 0.26392
Validation:	Loss 0.21990	Accuracy 1.00000
Epoch [  6]: Loss 0.21426
Validation:	Loss 0.17879	Accuracy 1.00000
Epoch [  7]: Loss 0.17340
Validation:	Loss 0.14572	Accuracy 1.00000
Epoch [  8]: Loss 0.14092
Validation:	Loss 0.11887	Accuracy 1.00000
Epoch [  9]: Loss 0.11502
Validation:	Loss 0.09679	Accuracy 1.00000
Epoch [ 10]: Loss 0.09326
Validation:	Loss 0.07887	Accuracy 1.00000
Epoch [ 11]: Loss 0.07629
Validation:	Loss 0.06486	Accuracy 1.00000
Epoch [ 12]: Loss 0.06177
Validation:	Loss 0.04980	Accuracy 1.00000
Epoch [ 13]: Loss 0.04521
Validation:	Loss 0.04006	Accuracy 1.00000
Epoch [ 14]: Loss 0.03767
Validation:	Loss 0.03239	Accuracy 1.00000
Epoch [ 15]: Loss 0.03098
Validation:	Loss 0.02791	Accuracy 1.00000
Epoch [ 16]: Loss 0.02679
Validation:	Loss 0.02389	Accuracy 1.00000
Epoch [ 17]: Loss 0.02330
Validation:	Loss 0.02105	Accuracy 1.00000
Epoch [ 18]: Loss 0.02070
Validation:	Loss 0.01860	Accuracy 1.00000
Epoch [ 19]: Loss 0.01861
Validation:	Loss 0.01671	Accuracy 1.00000
Epoch [ 20]: Loss 0.01688
Validation:	Loss 0.01509	Accuracy 1.00000
Epoch [ 21]: Loss 0.01535
Validation:	Loss 0.01375	Accuracy 1.00000
Epoch [ 22]: Loss 0.01411
Validation:	Loss 0.01258	Accuracy 1.00000
Epoch [ 23]: Loss 0.01302
Validation:	Loss 0.01155	Accuracy 1.00000
Epoch [ 24]: Loss 0.01206
Validation:	Loss 0.01065	Accuracy 1.00000
Epoch [ 25]: Loss 0.01117
Validation:	Loss 0.00985	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 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 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-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 4 default, 1 interactive, 4 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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