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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)
    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.

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 ? 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 0.88854
Validation:	Loss 0.75411	Accuracy 0.36719
Epoch [  2]: Loss 0.70946
Validation:	Loss 0.66796	Accuracy 0.48438
Epoch [  3]: Loss 0.62661
Validation:	Loss 0.58999	Accuracy 0.48438
Epoch [  4]: Loss 0.55360
Validation:	Loss 0.51582	Accuracy 1.00000
Epoch [  5]: Loss 0.47858
Validation:	Loss 0.44289	Accuracy 1.00000
Epoch [  6]: Loss 0.40760
Validation:	Loss 0.37303	Accuracy 1.00000
Epoch [  7]: Loss 0.33749
Validation:	Loss 0.30100	Accuracy 1.00000
Epoch [  8]: Loss 0.26765
Validation:	Loss 0.23172	Accuracy 1.00000
Epoch [  9]: Loss 0.20039
Validation:	Loss 0.16783	Accuracy 1.00000
Epoch [ 10]: Loss 0.14354
Validation:	Loss 0.12010	Accuracy 1.00000
Epoch [ 11]: Loss 0.10601
Validation:	Loss 0.09379	Accuracy 1.00000
Epoch [ 12]: Loss 0.08566
Validation:	Loss 0.07839	Accuracy 1.00000
Epoch [ 13]: Loss 0.07254
Validation:	Loss 0.06754	Accuracy 1.00000
Epoch [ 14]: Loss 0.06324
Validation:	Loss 0.05935	Accuracy 1.00000
Epoch [ 15]: Loss 0.05585
Validation:	Loss 0.05291	Accuracy 1.00000
Epoch [ 16]: Loss 0.04993
Validation:	Loss 0.04763	Accuracy 1.00000
Epoch [ 17]: Loss 0.04523
Validation:	Loss 0.04309	Accuracy 1.00000
Epoch [ 18]: Loss 0.04083
Validation:	Loss 0.03886	Accuracy 1.00000
Epoch [ 19]: Loss 0.03659
Validation:	Loss 0.03421	Accuracy 1.00000
Epoch [ 20]: Loss 0.03180
Validation:	Loss 0.02898	Accuracy 1.00000
Epoch [ 21]: Loss 0.02668
Validation:	Loss 0.02415	Accuracy 1.00000
Epoch [ 22]: Loss 0.02260
Validation:	Loss 0.02100	Accuracy 1.00000
Epoch [ 23]: Loss 0.01998
Validation:	Loss 0.01887	Accuracy 1.00000
Epoch [ 24]: Loss 0.01813
Validation:	Loss 0.01731	Accuracy 1.00000
Epoch [ 25]: Loss 0.01671
Validation:	Loss 0.01608	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 0.63524
Validation:	Loss 0.52548	Accuracy 1.00000
Epoch [  2]: Loss 0.46960
Validation:	Loss 0.40427	Accuracy 1.00000
Epoch [  3]: Loss 0.36310
Validation:	Loss 0.31086	Accuracy 1.00000
Epoch [  4]: Loss 0.27445
Validation:	Loss 0.22634	Accuracy 1.00000
Epoch [  5]: Loss 0.19627
Validation:	Loss 0.15634	Accuracy 1.00000
Epoch [  6]: Loss 0.13670
Validation:	Loss 0.10843	Accuracy 1.00000
Epoch [  7]: Loss 0.09646
Validation:	Loss 0.07790	Accuracy 1.00000
Epoch [  8]: Loss 0.07040
Validation:	Loss 0.05787	Accuracy 1.00000
Epoch [  9]: Loss 0.05277
Validation:	Loss 0.04393	Accuracy 1.00000
Epoch [ 10]: Loss 0.04038
Validation:	Loss 0.03388	Accuracy 1.00000
Epoch [ 11]: Loss 0.03149
Validation:	Loss 0.02734	Accuracy 1.00000
Epoch [ 12]: Loss 0.02571
Validation:	Loss 0.02263	Accuracy 1.00000
Epoch [ 13]: Loss 0.02130
Validation:	Loss 0.01896	Accuracy 1.00000
Epoch [ 14]: Loss 0.01789
Validation:	Loss 0.01604	Accuracy 1.00000
Epoch [ 15]: Loss 0.01509
Validation:	Loss 0.01355	Accuracy 1.00000
Epoch [ 16]: Loss 0.01271
Validation:	Loss 0.01143	Accuracy 1.00000
Epoch [ 17]: Loss 0.01081
Validation:	Loss 0.00987	Accuracy 1.00000
Epoch [ 18]: Loss 0.00940
Validation:	Loss 0.00871	Accuracy 1.00000
Epoch [ 19]: Loss 0.00835
Validation:	Loss 0.00779	Accuracy 1.00000
Epoch [ 20]: Loss 0.00747
Validation:	Loss 0.00701	Accuracy 1.00000
Epoch [ 21]: Loss 0.00676
Validation:	Loss 0.00637	Accuracy 1.00000
Epoch [ 22]: Loss 0.00615
Validation:	Loss 0.00583	Accuracy 1.00000
Epoch [ 23]: Loss 0.00566
Validation:	Loss 0.00540	Accuracy 1.00000
Epoch [ 24]: Loss 0.00527
Validation:	Loss 0.00505	Accuracy 1.00000
Epoch [ 25]: Loss 0.00493
Validation:	Loss 0.00475	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 1.12.6
Commit 15346901f00 (2026-04-09 19:20 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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