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SciML.ai

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
Precompiling packages...
   1345.2 ms  ✓ StructUtilsTablesExt (serial)
  1 dependency successfully precompiled in 1 seconds

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 0.65871
Validation:	Loss 0.57337	Accuracy 1.00000
Epoch [  2]: Loss 0.51965
Validation:	Loss 0.47206	Accuracy 1.00000
Epoch [  3]: Loss 0.42746
Validation:	Loss 0.39525	Accuracy 1.00000
Epoch [  4]: Loss 0.35721
Validation:	Loss 0.33374	Accuracy 1.00000
Epoch [  5]: Loss 0.30053
Validation:	Loss 0.28084	Accuracy 1.00000
Epoch [  6]: Loss 0.24692
Validation:	Loss 0.22898	Accuracy 1.00000
Epoch [  7]: Loss 0.19862
Validation:	Loss 0.17643	Accuracy 1.00000
Epoch [  8]: Loss 0.15031
Validation:	Loss 0.13364	Accuracy 1.00000
Epoch [  9]: Loss 0.11677
Validation:	Loss 0.10542	Accuracy 1.00000
Epoch [ 10]: Loss 0.09464
Validation:	Loss 0.08715	Accuracy 1.00000
Epoch [ 11]: Loss 0.07875
Validation:	Loss 0.07397	Accuracy 1.00000
Epoch [ 12]: Loss 0.06772
Validation:	Loss 0.06363	Accuracy 1.00000
Epoch [ 13]: Loss 0.05804
Validation:	Loss 0.05510	Accuracy 1.00000
Epoch [ 14]: Loss 0.05057
Validation:	Loss 0.04767	Accuracy 1.00000
Epoch [ 15]: Loss 0.04344
Validation:	Loss 0.04112	Accuracy 1.00000
Epoch [ 16]: Loss 0.03747
Validation:	Loss 0.03552	Accuracy 1.00000
Epoch [ 17]: Loss 0.03269
Validation:	Loss 0.03077	Accuracy 1.00000
Epoch [ 18]: Loss 0.02825
Validation:	Loss 0.02692	Accuracy 1.00000
Epoch [ 19]: Loss 0.02495
Validation:	Loss 0.02395	Accuracy 1.00000
Epoch [ 20]: Loss 0.02238
Validation:	Loss 0.02158	Accuracy 1.00000
Epoch [ 21]: Loss 0.02019
Validation:	Loss 0.01963	Accuracy 1.00000
Epoch [ 22]: Loss 0.01854
Validation:	Loss 0.01798	Accuracy 1.00000
Epoch [ 23]: Loss 0.01698
Validation:	Loss 0.01657	Accuracy 1.00000
Epoch [ 24]: Loss 0.01567
Validation:	Loss 0.01536	Accuracy 1.00000
Epoch [ 25]: Loss 0.01458
Validation:	Loss 0.01431	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 0.64623
Validation:	Loss 0.55919	Accuracy 1.00000
Epoch [  2]: Loss 0.49907
Validation:	Loss 0.42724	Accuracy 1.00000
Epoch [  3]: Loss 0.38643
Validation:	Loss 0.33868	Accuracy 1.00000
Epoch [  4]: Loss 0.30954
Validation:	Loss 0.27054	Accuracy 1.00000
Epoch [  5]: Loss 0.24704
Validation:	Loss 0.21202	Accuracy 1.00000
Epoch [  6]: Loss 0.18944
Validation:	Loss 0.16146	Accuracy 1.00000
Epoch [  7]: Loss 0.14313
Validation:	Loss 0.12125	Accuracy 1.00000
Epoch [  8]: Loss 0.10884
Validation:	Loss 0.09348	Accuracy 1.00000
Epoch [  9]: Loss 0.08532
Validation:	Loss 0.07583	Accuracy 1.00000
Epoch [ 10]: Loss 0.07003
Validation:	Loss 0.06394	Accuracy 1.00000
Epoch [ 11]: Loss 0.06021
Validation:	Loss 0.05529	Accuracy 1.00000
Epoch [ 12]: Loss 0.05224
Validation:	Loss 0.04861	Accuracy 1.00000
Epoch [ 13]: Loss 0.04622
Validation:	Loss 0.04327	Accuracy 1.00000
Epoch [ 14]: Loss 0.04117
Validation:	Loss 0.03892	Accuracy 1.00000
Epoch [ 15]: Loss 0.03760
Validation:	Loss 0.03530	Accuracy 1.00000
Epoch [ 16]: Loss 0.03394
Validation:	Loss 0.03226	Accuracy 1.00000
Epoch [ 17]: Loss 0.03108
Validation:	Loss 0.02969	Accuracy 1.00000
Epoch [ 18]: Loss 0.02867
Validation:	Loss 0.02745	Accuracy 1.00000
Epoch [ 19]: Loss 0.02675
Validation:	Loss 0.02549	Accuracy 1.00000
Epoch [ 20]: Loss 0.02478
Validation:	Loss 0.02376	Accuracy 1.00000
Epoch [ 21]: Loss 0.02301
Validation:	Loss 0.02224	Accuracy 1.00000
Epoch [ 22]: Loss 0.02146
Validation:	Loss 0.02089	Accuracy 1.00000
Epoch [ 23]: Loss 0.02031
Validation:	Loss 0.01967	Accuracy 1.00000
Epoch [ 24]: Loss 0.01929
Validation:	Loss 0.01857	Accuracy 1.00000
Epoch [ 25]: Loss 0.01814
Validation:	Loss 0.01757	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 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 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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