# lstmLayer

Long short-term memory (LSTM) layer

## Description

An LSTM layer learns long-term dependencies between time steps in time series and sequence data.

The layer performs additive interactions, which can help improve gradient flow over long sequences during training.

## Creation

### Description

example

layer = lstmLayer(numHiddenUnits) creates an LSTM layer and sets the NumHiddenUnits property.

example

layer = lstmLayer(numHiddenUnits,Name,Value) sets additional OutputMode, Activations, State, Parameters and Initialization, Learn Rate and Regularization, and Name properties using one or more name-value pair arguments. You can specify multiple name-value pair arguments. Enclose each property name in quotes.

## Properties

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### LSTM

Number of hidden units (also known as the hidden size), specified as a positive integer.

The number of hidden units corresponds to the amount of information remembered between time steps (the hidden state). The hidden state can contain information from all previous time steps, regardless of the sequence length. If the number of hidden units is too large, then the layer might overfit to the training data. This value can vary from a few dozen to a few thousand.

The hidden state does not limit the number of time steps that are processed in an iteration. To split your sequences into smaller sequences for training, use the 'SequenceLength' option in trainingOptions.

Example: 200

Format of output, specified as one of the following:

• 'sequence' – Output the complete sequence.

• 'last' – Output the last time step of the sequence.

Input size, specified as a positive integer or 'auto'. If InputSize is 'auto', then the software automatically assigns the input size at training time.

Example: 100

### Activations

Activation function to update the cell and hidden state, specified as one of the following:

• 'tanh' – Use the hyperbolic tangent function (tanh).

• 'softsign' – Use the softsign function $\text{softsign}\left(x\right)=\frac{x}{1+|x|}$.

The layer uses this option as the function ${\sigma }_{c}$ in the calculations to update the cell and hidden state. For more information on how activation functions are used in an LSTM layer, see Long Short-Term Memory Layer.

Activation function to apply to the gates, specified as one of the following:

• 'sigmoid' – Use the sigmoid function $\sigma \left(x\right)={\left(1+{e}^{-x}\right)}^{-1}$.

• 'hard-sigmoid' – Use the hard sigmoid function

The layer uses this option as the function ${\sigma }_{g}$ in the calculations for the layer gates.

### State

Initial value of the cell state, specified as a NumHiddenUnits-by-1 numeric vector. This value corresponds to the cell state at time step 0.

After setting this property, calls to the resetState function set the cell state to this value.

Initial value of the hidden state, specified as a NumHiddenUnits-by-1 numeric vector. This value corresponds to the hidden state at time step 0.

After setting this property, calls to the resetState function set the hidden state to this value.

### Parameters and Initialization

Function to initialize the input weights, specified as one of the following:

• 'glorot' – Initialize the input weights with the Glorot initializer [4] (also known as Xavier initializer). The Glorot initializer independently samples from a uniform distribution with zero mean and variance 2/(InputSize + numOut), where numOut = 4*NumHiddenUnits.

• 'he' – Initialize the input weights with the He initializer [5]. The He initializer samples from a normal distribution with zero mean and variance 2/InputSize.

• 'orthogonal' – Initialize the input weights with Q, the orthogonal matrix given by the QR decomposition of Z = QR for a random matrix Z sampled from a unit normal distribution. [6]

• 'narrow-normal' – Initialize the input weights by independently sampling from a normal distribution with zero mean and standard deviation 0.01.

• 'zeros' – Initialize the input weights with zeros.

• 'ones' – Initialize the input weights with ones.

• Function handle – Initialize the input weights with a custom function. If you specify a function handle, then the function must be of the form weights = func(sz), where sz is the size of the input weights.

The layer only initializes the input weights when the InputWeights property is empty.

Data Types: char | string | function_handle

Function to initialize the recurrent weights, specified as one of the following:

• 'orthogonal' – Initialize the recurrent weights with Q, the orthogonal matrix given by the QR decomposition of Z = QR for a random matrix Z sampled from a unit normal distribution. [6]

• 'glorot' – Initialize the recurrent weights with the Glorot initializer [4] (also known as Xavier initializer). The Glorot initializer independently samples from a uniform distribution with zero mean and variance 2/(numIn + numOut), where numIn = NumHiddenUnits and numOut = 4*NumHiddenUnits.

• 'he' – Initialize the recurrent weights with the He initializer [5]. The He initializer samples from a normal distribution with zero mean and variance 2/NumHiddenUnits.

• 'narrow-normal' – Initialize the recurrent weights by independently sampling from a normal distribution with zero mean and standard deviation 0.01.

• 'zeros' – Initialize the recurrent weights with zeros.

• 'ones' – Initialize the recurrent weights with ones.

• Function handle – Initialize the recurrent weights with a custom function. If you specify a function handle, then the function must be of the form weights = func(sz), where sz is the size of the recurrent weights.

The layer only initializes the recurrent weights when the RecurrentWeights property is empty.

Data Types: char | string | function_handle

Function to initialize the bias, specified as one of the following:

• 'unit-forget-gate' – Initialize the forget gate bias with ones and the remaining biases with zeros.

• 'narrow-normal' – Initialize the bias by independently sampling from a normal distribution with zero mean and standard deviation 0.01.

• 'ones' – Initialize the bias with ones.

• Function handle – Initialize the bias with a custom function. If you specify a function handle, then the function must be of the form bias = func(sz), where sz is the size of the bias.

The layer only initializes the bias when the Bias property is empty.

Data Types: char | string | function_handle

Input weights, specified as a matrix.

The input weight matrix is a concatenation of the four input weight matrices for the components (gates) in the LSTM layer. The four matrices are concatenated vertically in the following order:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

The input weights are learnable parameters. When training a network, if InputWeights is nonempty, then trainNetwork uses the InputWeights property as the initial value. If InputWeights is empty, then trainNetwork uses the initializer specified by InputWeightsInitializer.

At training time, InputWeights is a 4*NumHiddenUnits-by-InputSize matrix.

Recurrent weights, specified as a matrix.

The recurrent weight matrix is a concatenation of the four recurrent weight matrices for the components (gates) in the LSTM layer. The four matrices are vertically concatenated in the following order:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

The recurrent weights are learnable parameters. When training a network, if RecurrentWeights is nonempty, then trainNetwork uses the RecurrentWeights property as the initial value. If RecurrentWeights is empty, then trainNetwork uses the initializer specified by RecurrentWeightsInitializer.

At training time RecurrentWeights is a 4*NumHiddenUnits-by-NumHiddenUnits matrix.

Layer biases for the LSTM layer, specified as a numeric vector.

The bias vector is a concatenation of the four bias vectors for the components (gates) in the LSTM layer. The four vectors are concatenated vertically in the following order:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

The layer biases are learnable parameters. When training a network, if Bias is nonempty, then trainNetwork uses the Bias property as the initial value. If Bias is empty, then trainNetwork uses the initializer specified by BiasInitializer.

At training time, Bias is a 4*NumHiddenUnits-by-1 numeric vector.

### Learn Rate and Regularization

Learning rate factor for the input weights, specified as a numeric scalar or a 1-by-4 numeric vector.

The software multiplies this factor by the global learning rate to determine the learning rate factor for the input weights of the layer. For example, if InputWeightsLearnRateFactor is 2, then the learning rate factor for the input weights of the layer is twice the current global learning rate. The software determines the global learning rate based on the settings specified with the trainingOptions function.

To control the value of the learning rate factor for the four individual matrices in InputWeights, specify a 1-by-4 vector. The entries of InputWeightsLearnRateFactor correspond to the learning rate factor of the following:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

To specify the same value for all the matrices, specify a nonnegative scalar.

Example: 2

Example: [1 2 1 1]

Learning rate factor for the recurrent weights, specified as a numeric scalar or a 1-by-4 numeric vector.

The software multiplies this factor by the global learning rate to determine the learning rate for the recurrent weights of the layer. For example, if RecurrentWeightsLearnRateFactor is 2, then the learning rate for the recurrent weights of the layer is twice the current global learning rate. The software determines the global learning rate based on the settings specified with the trainingOptions function.

To control the value of the learning rate factor for the four individual matrices in RecurrentWeights, specify a 1-by-4 vector. The entries of RecurrentWeightsLearnRateFactor correspond to the learning rate factor of the following:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

To specify the same value for all the matrices, specify a nonnegative scalar.

Example: 2

Example: [1 2 1 1]

Learning rate factor for the biases, specified as a nonnegative scalar or a 1-by-4 numeric vector.

The software multiplies this factor by the global learning rate to determine the learning rate for the biases in this layer. For example, if BiasLearnRateFactor is 2, then the learning rate for the biases in the layer is twice the current global learning rate. The software determines the global learning rate based on the settings specified with the trainingOptions function.

To control the value of the learning rate factor for the four individual vectors in Bias, specify a 1-by-4 vector. The entries of BiasLearnRateFactor correspond to the learning rate factor of the following:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

To specify the same value for all the vectors, specify a nonnegative scalar.

Example: 2

Example: [1 2 1 1]

L2 regularization factor for the input weights, specified as a numeric scalar or a 1-by-4 numeric vector.

The software multiplies this factor by the global L2 regularization factor to determine the L2 regularization factor for the input weights of the layer. For example, if InputWeightsL2Factor is 2, then the L2 regularization factor for the input weights of the layer is twice the current global L2 regularization factor. The software determines the L2 regularization factor based on the settings specified with the trainingOptions function.

To control the value of the L2 regularization factor for the four individual matrices in InputWeights, specify a 1-by-4 vector. The entries of InputWeightsL2Factor correspond to the L2 regularization factor of the following:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

To specify the same value for all the matrices, specify a nonnegative scalar.

Example: 2

Example: [1 2 1 1]

L2 regularization factor for the recurrent weights, specified as a numeric scalar or a 1-by-4 numeric vector.

The software multiplies this factor by the global L2 regularization factor to determine the L2 regularization factor for the recurrent weights of the layer. For example, if RecurrentWeightsL2Factor is 2, then the L2 regularization factor for the recurrent weights of the layer is twice the current global L2 regularization factor. The software determines the L2 regularization factor based on the settings specified with the trainingOptions function.

To control the value of the L2 regularization factor for the four individual matrices in RecurrentWeights, specify a 1-by-4 vector. The entries of RecurrentWeightsL2Factor correspond to the L2 regularization factor of the following:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

To specify the same value for all the matrices, specify a nonnegative scalar.

Example: 2

Example: [1 2 1 1]

L2 regularization factor for the biases, specified as a nonnegative scalar or a 1-by-4 numeric vector.

The software multiplies this factor by the global L2 regularization factor to determine the L2 regularization for the biases in this layer. For example, if BiasL2Factor is 2, then the L2 regularization for the biases in this layer is twice the global L2 regularization factor. You can specify the global L2 regularization factor using the trainingOptions function.

To control the value of the L2 regularization factor for the four individual vectors in Bias, specify a 1-by-4 vector. The entries of BiasL2Factor correspond to the L2 regularization factor of the following:

1. Input gate

2. Forget gate

3. Cell candidate

4. Output gate

To specify the same value for all the vectors, specify a nonnegative scalar.

Example: 2

Example: [1 2 1 1]

### Layer

Layer name, specified as a character vector or a string scalar. If Name is set to '', then the software automatically assigns a name at training time.

Data Types: char | string

Number of inputs of the layer. This layer accepts a single input only.

Data Types: double

Input names of the layer. This layer accepts a single input only.

Data Types: cell

Number of outputs of the layer. This layer has a single output only.

Data Types: double

Output names of the layer. This layer has a single output only.

Data Types: cell

## Examples

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Create an LSTM layer with the name 'lstm1' and 100 hidden units.

layer = lstmLayer(100,'Name','lstm1')
layer =
LSTMLayer with properties:

Name: 'lstm1'

Hyperparameters
InputSize: 'auto'
NumHiddenUnits: 100
OutputMode: 'sequence'
StateActivationFunction: 'tanh'
GateActivationFunction: 'sigmoid'

Learnable Parameters
InputWeights: []
RecurrentWeights: []
Bias: []

State Parameters
HiddenState: []
CellState: []

Show all properties

Include an LSTM layer in a Layer array.

inputSize = 12;
numHiddenUnits = 100;
numClasses = 9;

layers = [ ...
sequenceInputLayer(inputSize)
lstmLayer(numHiddenUnits)
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer]
layers =
5x1 Layer array with layers:

1   ''   Sequence Input          Sequence input with 12 dimensions
2   ''   LSTM                    LSTM with 100 hidden units
3   ''   Fully Connected         9 fully connected layer
4   ''   Softmax                 softmax
5   ''   Classification Output   crossentropyex

Train a deep learning LSTM network for sequence-to-label classification.

Load the Japanese Vowels data set as described in [1] and [2]. XTrain is a cell array containing 270 sequences of varying length with 12 features corresponding to LPC cepstrum coefficients. Y is a categorical vector of labels 1,2,...,9. The entries in XTrain are matrices with 12 rows (one row for each feature) and a varying number of columns (one column for each time step).

[XTrain,YTrain] = japaneseVowelsTrainData;

Visualize the first time series in a plot. Each line corresponds to a feature.

figure
plot(XTrain{1}')
title("Training Observation 1")
numFeatures = size(XTrain{1},1);
legend("Feature " + string(1:numFeatures),'Location','northeastoutside')

Define the LSTM network architecture. Specify the input size as 12 (the number of features of the input data). Specify an LSTM layer to have 100 hidden units and to output the last element of the sequence. Finally, specify nine classes by including a fully connected layer of size 9, followed by a softmax layer and a classification layer.

inputSize = 12;
numHiddenUnits = 100;
numClasses = 9;

layers = [ ...
sequenceInputLayer(inputSize)
lstmLayer(numHiddenUnits,'OutputMode','last')
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer]
layers =
5×1 Layer array with layers:

1   ''   Sequence Input          Sequence input with 12 dimensions
2   ''   LSTM                    LSTM with 100 hidden units
3   ''   Fully Connected         9 fully connected layer
4   ''   Softmax                 softmax
5   ''   Classification Output   crossentropyex

Specify the training options. Specify the solver as 'adam' and 'GradientThreshold' as 1. Set the mini-batch size to 27 and set the maximum number of epochs to 70.

Because the mini-batches are small with short sequences, the CPU is better suited for training. Set 'ExecutionEnvironment' to 'cpu'. To train on a GPU, if available, set 'ExecutionEnvironment' to 'auto' (the default value).

maxEpochs = 70;
miniBatchSize = 27;

'ExecutionEnvironment','cpu', ...
'MaxEpochs',maxEpochs, ...
'MiniBatchSize',miniBatchSize, ...
'Verbose',false, ...
'Plots','training-progress');

Train the LSTM network with the specified training options.

net = trainNetwork(XTrain,YTrain,layers,options);

Load the test set and classify the sequences into speakers.

[XTest,YTest] = japaneseVowelsTestData;

Classify the test data. Specify the same mini-batch size used for training.

YPred = classify(net,XTest,'MiniBatchSize',miniBatchSize);

Calculate the classification accuracy of the predictions.

acc = sum(YPred == YTest)./numel(YTest)
acc = 0.9514

To create an LSTM network for sequence-to-label classification, create a layer array containing a sequence input layer, an LSTM layer, a fully connected layer, a softmax layer, and a classification output layer.

Set the size of the sequence input layer to the number of features of the input data. Set the size of the fully connected layer to the number of classes. You do not need to specify the sequence length.

For the LSTM layer, specify the number of hidden units and the output mode 'last'.

numFeatures = 12;
numHiddenUnits = 100;
numClasses = 9;
layers = [ ...
sequenceInputLayer(numFeatures)
lstmLayer(numHiddenUnits,'OutputMode','last')
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer];

For an example showing how to train an LSTM network for sequence-to-label classification and classify new data, see Sequence Classification Using Deep Learning.

To create an LSTM network for sequence-to-sequence classification, use the same architecture as for sequence-to-label classification, but set the output mode of the LSTM layer to 'sequence'.

numFeatures = 12;
numHiddenUnits = 100;
numClasses = 9;
layers = [ ...
sequenceInputLayer(numFeatures)
lstmLayer(numHiddenUnits,'OutputMode','sequence')
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer];

To create an LSTM network for sequence-to-one regression, create a layer array containing a sequence input layer, an LSTM layer, a fully connected layer, and a regression output layer.

Set the size of the sequence input layer to the number of features of the input data. Set the size of the fully connected layer to the number of responses. You do not need to specify the sequence length.

For the LSTM layer, specify the number of hidden units and the output mode 'last'.

numFeatures = 12;
numHiddenUnits = 125;
numResponses = 1;

layers = [ ...
sequenceInputLayer(numFeatures)
lstmLayer(numHiddenUnits,'OutputMode','last')
fullyConnectedLayer(numResponses)
regressionLayer];

To create an LSTM network for sequence-to-sequence regression, use the same architecture as for sequence-to-one regression, but set the output mode of the LSTM layer to 'sequence'.

numFeatures = 12;
numHiddenUnits = 125;
numResponses = 1;

layers = [ ...
sequenceInputLayer(numFeatures)
lstmLayer(numHiddenUnits,'OutputMode','sequence')
fullyConnectedLayer(numResponses)
regressionLayer];

For an example showing how to train an LSTM network for sequence-to-sequence regression and predict on new data, see Sequence-to-Sequence Regression Using Deep Learning.

You can make LSTM networks deeper by inserting extra LSTM layers with the output mode 'sequence' before the LSTM layer. To prevent overfitting, you can insert dropout layers after the LSTM layers.

For sequence-to-label classification networks, the output mode of the last LSTM layer must be 'last'.

numFeatures = 12;
numHiddenUnits1 = 125;
numHiddenUnits2 = 100;
numClasses = 9;
layers = [ ...
sequenceInputLayer(numFeatures)
lstmLayer(numHiddenUnits1,'OutputMode','sequence')
dropoutLayer(0.2)
lstmLayer(numHiddenUnits2,'OutputMode','last')
dropoutLayer(0.2)
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer];

For sequence-to-sequence classification networks, the output mode of the last LSTM layer must be 'sequence'.

numFeatures = 12;
numHiddenUnits1 = 125;
numHiddenUnits2 = 100;
numClasses = 9;
layers = [ ...
sequenceInputLayer(numFeatures)
lstmLayer(numHiddenUnits1,'OutputMode','sequence')
dropoutLayer(0.2)
lstmLayer(numHiddenUnits2,'OutputMode','sequence')
dropoutLayer(0.2)
fullyConnectedLayer(numClasses)
softmaxLayer
classificationLayer];

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## Compatibility Considerations

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Behavior changed in R2019a

Behavior changed in R2019a

## References

[1] M. Kudo, J. Toyama, and M. Shimbo. "Multidimensional Curve Classification Using Passing-Through Regions." Pattern Recognition Letters. Vol. 20, No. 11–13, pages 1103–1111.

[2] UCI Machine Learning Repository: Japanese Vowels Dataset. https://archive.ics.uci.edu/ml/datasets/Japanese+Vowels

[3] Hochreiter, S, and J. Schmidhuber, 1997. Long short-term memory. Neural computation, 9(8), pp.1735–1780.

[4] Glorot, Xavier, and Yoshua Bengio. "Understanding the Difficulty of Training Deep Feedforward Neural Networks." In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 249–356. Sardinia, Italy: AISTATS, 2010.

[5] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification." In Proceedings of the 2015 IEEE International Conference on Computer Vision, 1026–1034. Washington, DC: IEEE Computer Vision Society, 2015.

[6] Saxe, Andrew M., James L. McClelland, and Surya Ganguli. "Exact solutions to the nonlinear dynamics of learning in deep linear neural networks." arXiv preprint arXiv:1312.6120 (2013).

## Extended Capabilities

Introduced in R2017b