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Machine Learning

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.

julia
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.

julia
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.

julia
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.

julia
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.

julia
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

julia
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.

julia
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 ​

julia
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 ? 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 (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 0.49636
Validation:	Loss 0.41364	Accuracy 1.00000
Epoch [  2]: Loss 0.34957
Validation:	Loss 0.28538	Accuracy 1.00000
Epoch [  3]: Loss 0.24355
Validation:	Loss 0.20424	Accuracy 1.00000
Epoch [  4]: Loss 0.17615
Validation:	Loss 0.15283	Accuracy 1.00000
Epoch [  5]: Loss 0.13166
Validation:	Loss 0.11539	Accuracy 1.00000
Epoch [  6]: Loss 0.10000
Validation:	Loss 0.08683	Accuracy 1.00000
Epoch [  7]: Loss 0.07517
Validation:	Loss 0.06394	Accuracy 1.00000
Epoch [  8]: Loss 0.05502
Validation:	Loss 0.04693	Accuracy 1.00000
Epoch [  9]: Loss 0.04064
Validation:	Loss 0.03470	Accuracy 1.00000
Epoch [ 10]: Loss 0.03042
Validation:	Loss 0.02712	Accuracy 1.00000
Epoch [ 11]: Loss 0.02456
Validation:	Loss 0.02229	Accuracy 1.00000
Epoch [ 12]: Loss 0.02047
Validation:	Loss 0.01902	Accuracy 1.00000
Epoch [ 13]: Loss 0.01767
Validation:	Loss 0.01664	Accuracy 1.00000
Epoch [ 14]: Loss 0.01545
Validation:	Loss 0.01476	Accuracy 1.00000
Epoch [ 15]: Loss 0.01384
Validation:	Loss 0.01329	Accuracy 1.00000
Epoch [ 16]: Loss 0.01246
Validation:	Loss 0.01211	Accuracy 1.00000
Epoch [ 17]: Loss 0.01150
Validation:	Loss 0.01112	Accuracy 1.00000
Epoch [ 18]: Loss 0.01050
Validation:	Loss 0.01028	Accuracy 1.00000
Epoch [ 19]: Loss 0.00975
Validation:	Loss 0.00956	Accuracy 1.00000
Epoch [ 20]: Loss 0.00913
Validation:	Loss 0.00893	Accuracy 1.00000
Epoch [ 21]: Loss 0.00849
Validation:	Loss 0.00837	Accuracy 1.00000
Epoch [ 22]: Loss 0.00796
Validation:	Loss 0.00787	Accuracy 1.00000
Epoch [ 23]: Loss 0.00754
Validation:	Loss 0.00743	Accuracy 1.00000
Epoch [ 24]: Loss 0.00709
Validation:	Loss 0.00702	Accuracy 1.00000
Epoch [ 25]: Loss 0.00671
Validation:	Loss 0.00665	Accuracy 1.00000

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

julia
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 0.53041
Validation:	Loss 0.45583	Accuracy 0.55469
Epoch [  2]: Loss 0.48019
Validation:	Loss 0.41484	Accuracy 0.55469
Epoch [  3]: Loss 0.43721
Validation:	Loss 0.37564	Accuracy 0.55469
Epoch [  4]: Loss 0.39487
Validation:	Loss 0.33824	Accuracy 1.00000
Epoch [  5]: Loss 0.35836
Validation:	Loss 0.30188	Accuracy 1.00000
Epoch [  6]: Loss 0.32071
Validation:	Loss 0.26288	Accuracy 1.00000
Epoch [  7]: Loss 0.27459
Validation:	Loss 0.22041	Accuracy 1.00000
Epoch [  8]: Loss 0.22544
Validation:	Loss 0.17659	Accuracy 1.00000
Epoch [  9]: Loss 0.17677
Validation:	Loss 0.13635	Accuracy 1.00000
Epoch [ 10]: Loss 0.13645
Validation:	Loss 0.10527	Accuracy 1.00000
Epoch [ 11]: Loss 0.10600
Validation:	Loss 0.08316	Accuracy 1.00000
Epoch [ 12]: Loss 0.08344
Validation:	Loss 0.06591	Accuracy 1.00000
Epoch [ 13]: Loss 0.06697
Validation:	Loss 0.05101	Accuracy 1.00000
Epoch [ 14]: Loss 0.05075
Validation:	Loss 0.03859	Accuracy 1.00000
Epoch [ 15]: Loss 0.03837
Validation:	Loss 0.03015	Accuracy 1.00000
Epoch [ 16]: Loss 0.03081
Validation:	Loss 0.02459	Accuracy 1.00000
Epoch [ 17]: Loss 0.02531
Validation:	Loss 0.02082	Accuracy 1.00000
Epoch [ 18]: Loss 0.02145
Validation:	Loss 0.01804	Accuracy 1.00000
Epoch [ 19]: Loss 0.01891
Validation:	Loss 0.01579	Accuracy 1.00000
Epoch [ 20]: Loss 0.01650
Validation:	Loss 0.01375	Accuracy 1.00000
Epoch [ 21]: Loss 0.01425
Validation:	Loss 0.01179	Accuracy 1.00000
Epoch [ 22]: Loss 0.01211
Validation:	Loss 0.01005	Accuracy 1.00000
Epoch [ 23]: Loss 0.01022
Validation:	Loss 0.00857	Accuracy 1.00000
Epoch [ 24]: Loss 0.00869
Validation:	Loss 0.00739	Accuracy 1.00000
Epoch [ 25]: Loss 0.00753
Validation:	Loss 0.00644	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.

julia
@save "trained_model.jld2" ps_trained st_trained

Let's try loading the model

julia
@load "trained_model.jld2" ps_trained st_trained
2-element Vector{Symbol}:
 :ps_trained
 :st_trained

Appendix ​

julia
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 1.11.8
Commit cf1da5e20e3 (2025-11-06 17:49 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-16.0.6 (ORCJIT, znver3)
Threads: 4 default, 0 interactive, 2 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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