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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 0.87522
Validation:	Loss 0.78992	Accuracy 0.00000
Epoch [  2]: Loss 0.75719
Validation:	Loss 0.71213	Accuracy 0.36719
Epoch [  3]: Loss 0.68375
Validation:	Loss 0.65675	Accuracy 0.46094
Epoch [  4]: Loss 0.62879
Validation:	Loss 0.60832	Accuracy 0.46094
Epoch [  5]: Loss 0.57977
Validation:	Loss 0.56161	Accuracy 1.00000
Epoch [  6]: Loss 0.52951
Validation:	Loss 0.50644	Accuracy 1.00000
Epoch [  7]: Loss 0.46817
Validation:	Loss 0.44978	Accuracy 1.00000
Epoch [  8]: Loss 0.41097
Validation:	Loss 0.39480	Accuracy 1.00000
Epoch [  9]: Loss 0.35755
Validation:	Loss 0.34201	Accuracy 1.00000
Epoch [ 10]: Loss 0.30762
Validation:	Loss 0.29316	Accuracy 1.00000
Epoch [ 11]: Loss 0.26208
Validation:	Loss 0.25332	Accuracy 1.00000
Epoch [ 12]: Loss 0.22626
Validation:	Loss 0.22281	Accuracy 1.00000
Epoch [ 13]: Loss 0.19777
Validation:	Loss 0.19735	Accuracy 1.00000
Epoch [ 14]: Loss 0.17590
Validation:	Loss 0.17602	Accuracy 1.00000
Epoch [ 15]: Loss 0.15807
Validation:	Loss 0.15768	Accuracy 1.00000
Epoch [ 16]: Loss 0.14291
Validation:	Loss 0.14193	Accuracy 1.00000
Epoch [ 17]: Loss 0.12718
Validation:	Loss 0.12795	Accuracy 1.00000
Epoch [ 18]: Loss 0.11439
Validation:	Loss 0.11482	Accuracy 1.00000
Epoch [ 19]: Loss 0.10161
Validation:	Loss 0.10133	Accuracy 1.00000
Epoch [ 20]: Loss 0.08974
Validation:	Loss 0.08561	Accuracy 1.00000
Epoch [ 21]: Loss 0.07398
Validation:	Loss 0.06834	Accuracy 1.00000
Epoch [ 22]: Loss 0.05864
Validation:	Loss 0.05537	Accuracy 1.00000
Epoch [ 23]: Loss 0.04873
Validation:	Loss 0.04711	Accuracy 1.00000
Epoch [ 24]: Loss 0.04207
Validation:	Loss 0.04080	Accuracy 1.00000
Epoch [ 25]: Loss 0.03617
Validation:	Loss 0.03522	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 0.64236
Validation:	Loss 0.60504	Accuracy 0.50000
Epoch [  2]: Loss 0.57763
Validation:	Loss 0.54052	Accuracy 1.00000
Epoch [  3]: Loss 0.50355
Validation:	Loss 0.44802	Accuracy 1.00000
Epoch [  4]: Loss 0.40310
Validation:	Loss 0.34010	Accuracy 1.00000
Epoch [  5]: Loss 0.29222
Validation:	Loss 0.22399	Accuracy 1.00000
Epoch [  6]: Loss 0.18376
Validation:	Loss 0.13786	Accuracy 1.00000
Epoch [  7]: Loss 0.11304
Validation:	Loss 0.08601	Accuracy 1.00000
Epoch [  8]: Loss 0.07478
Validation:	Loss 0.06107	Accuracy 1.00000
Epoch [  9]: Loss 0.05445
Validation:	Loss 0.04633	Accuracy 1.00000
Epoch [ 10]: Loss 0.04223
Validation:	Loss 0.03708	Accuracy 1.00000
Epoch [ 11]: Loss 0.03453
Validation:	Loss 0.03095	Accuracy 1.00000
Epoch [ 12]: Loss 0.02909
Validation:	Loss 0.02658	Accuracy 1.00000
Epoch [ 13]: Loss 0.02516
Validation:	Loss 0.02331	Accuracy 1.00000
Epoch [ 14]: Loss 0.02229
Validation:	Loss 0.02078	Accuracy 1.00000
Epoch [ 15]: Loss 0.01992
Validation:	Loss 0.01876	Accuracy 1.00000
Epoch [ 16]: Loss 0.01811
Validation:	Loss 0.01709	Accuracy 1.00000
Epoch [ 17]: Loss 0.01649
Validation:	Loss 0.01569	Accuracy 1.00000
Epoch [ 18]: Loss 0.01523
Validation:	Loss 0.01449	Accuracy 1.00000
Epoch [ 19]: Loss 0.01406
Validation:	Loss 0.01345	Accuracy 1.00000
Epoch [ 20]: Loss 0.01308
Validation:	Loss 0.01254	Accuracy 1.00000
Epoch [ 21]: Loss 0.01219
Validation:	Loss 0.01173	Accuracy 1.00000
Epoch [ 22]: Loss 0.01143
Validation:	Loss 0.01100	Accuracy 1.00000
Epoch [ 23]: Loss 0.01073
Validation:	Loss 0.01034	Accuracy 1.00000
Epoch [ 24]: Loss 0.01009
Validation:	Loss 0.00974	Accuracy 1.00000
Epoch [ 25]: Loss 0.00952
Validation:	Loss 0.00920	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 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 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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