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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 0.50212
Validation:	Loss 0.47752	Accuracy 1.00000
Epoch [  2]: Loss 0.40272
Validation:	Loss 0.39338	Accuracy 1.00000
Epoch [  3]: Loss 0.32381
Validation:	Loss 0.30736	Accuracy 1.00000
Epoch [  4]: Loss 0.24327
Validation:	Loss 0.22737	Accuracy 1.00000
Epoch [  5]: Loss 0.18087
Validation:	Loss 0.17146	Accuracy 1.00000
Epoch [  6]: Loss 0.13492
Validation:	Loss 0.13105	Accuracy 1.00000
Epoch [  7]: Loss 0.10223
Validation:	Loss 0.09862	Accuracy 1.00000
Epoch [  8]: Loss 0.07632
Validation:	Loss 0.07353	Accuracy 1.00000
Epoch [  9]: Loss 0.05721
Validation:	Loss 0.05620	Accuracy 1.00000
Epoch [ 10]: Loss 0.04477
Validation:	Loss 0.04500	Accuracy 1.00000
Epoch [ 11]: Loss 0.03676
Validation:	Loss 0.03743	Accuracy 1.00000
Epoch [ 12]: Loss 0.03070
Validation:	Loss 0.03173	Accuracy 1.00000
Epoch [ 13]: Loss 0.02613
Validation:	Loss 0.02675	Accuracy 1.00000
Epoch [ 14]: Loss 0.02222
Validation:	Loss 0.02317	Accuracy 1.00000
Epoch [ 15]: Loss 0.01975
Validation:	Loss 0.02092	Accuracy 1.00000
Epoch [ 16]: Loss 0.01773
Validation:	Loss 0.01913	Accuracy 1.00000
Epoch [ 17]: Loss 0.01638
Validation:	Loss 0.01759	Accuracy 1.00000
Epoch [ 18]: Loss 0.01503
Validation:	Loss 0.01622	Accuracy 1.00000
Epoch [ 19]: Loss 0.01387
Validation:	Loss 0.01495	Accuracy 1.00000
Epoch [ 20]: Loss 0.01274
Validation:	Loss 0.01369	Accuracy 1.00000
Epoch [ 21]: Loss 0.01168
Validation:	Loss 0.01231	Accuracy 1.00000
Epoch [ 22]: Loss 0.01036
Validation:	Loss 0.01080	Accuracy 1.00000
Epoch [ 23]: Loss 0.00900
Validation:	Loss 0.00919	Accuracy 1.00000
Epoch [ 24]: Loss 0.00764
Validation:	Loss 0.00767	Accuracy 1.00000
Epoch [ 25]: Loss 0.00646
Validation:	Loss 0.00644	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 0.65785
Validation:	Loss 0.62853	Accuracy 0.42188
Epoch [  2]: Loss 0.56226
Validation:	Loss 0.56215	Accuracy 0.42188
Epoch [  3]: Loss 0.49695
Validation:	Loss 0.51020	Accuracy 0.42188
Epoch [  4]: Loss 0.44895
Validation:	Loss 0.46571	Accuracy 1.00000
Epoch [  5]: Loss 0.40329
Validation:	Loss 0.42574	Accuracy 1.00000
Epoch [  6]: Loss 0.36321
Validation:	Loss 0.38633	Accuracy 1.00000
Epoch [  7]: Loss 0.32667
Validation:	Loss 0.34394	Accuracy 1.00000
Epoch [  8]: Loss 0.28701
Validation:	Loss 0.29675	Accuracy 1.00000
Epoch [  9]: Loss 0.24235
Validation:	Loss 0.24638	Accuracy 1.00000
Epoch [ 10]: Loss 0.19752
Validation:	Loss 0.19851	Accuracy 1.00000
Epoch [ 11]: Loss 0.15762
Validation:	Loss 0.16014	Accuracy 1.00000
Epoch [ 12]: Loss 0.12744
Validation:	Loss 0.13141	Accuracy 1.00000
Epoch [ 13]: Loss 0.10497
Validation:	Loss 0.10912	Accuracy 1.00000
Epoch [ 14]: Loss 0.08773
Validation:	Loss 0.09177	Accuracy 1.00000
Epoch [ 15]: Loss 0.07436
Validation:	Loss 0.07852	Accuracy 1.00000
Epoch [ 16]: Loss 0.06454
Validation:	Loss 0.06834	Accuracy 1.00000
Epoch [ 17]: Loss 0.05638
Validation:	Loss 0.06024	Accuracy 1.00000
Epoch [ 18]: Loss 0.05003
Validation:	Loss 0.05384	Accuracy 1.00000
Epoch [ 19]: Loss 0.04459
Validation:	Loss 0.04861	Accuracy 1.00000
Epoch [ 20]: Loss 0.04057
Validation:	Loss 0.04428	Accuracy 1.00000
Epoch [ 21]: Loss 0.03710
Validation:	Loss 0.04061	Accuracy 1.00000
Epoch [ 22]: Loss 0.03424
Validation:	Loss 0.03749	Accuracy 1.00000
Epoch [ 23]: Loss 0.03138
Validation:	Loss 0.03478	Accuracy 1.00000
Epoch [ 24]: Loss 0.02947
Validation:	Loss 0.03239	Accuracy 1.00000
Epoch [ 25]: Loss 0.02765
Validation:	Loss 0.03028	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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