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Long short-term memory (LSTM) layer

An LSTM layer is a recurrent neural network (RNN) layer that enables support for time series and sequence data in a network. The layer performs additive interactions, which can help improve gradient flow over long sequences during training. LSTM layers are best suited for learning *long-term dependencies* (dependencies from distant time steps).

`layer = lstmLayer(numHiddenUnits)`

`layer = lstmLayer(numHiddenUnits,Name,Value)`

creates an LSTM layer and sets the `layer`

= lstmLayer(`numHiddenUnits`

)`NumHiddenUnits`

property.

sets additional LSTM Parameters properties
as well as Learn Rate and
L2 Factors properties using one or more name-value pair arguments.
You can specify multiple name-value pair arguments. Enclose each property name
in quotes.`layer`

= lstmLayer(`numHiddenUnits`

,`Name,Value`

)

`Name`

— Layer name`''`

(default) | character vectorLayer name, specified as a character vector. If `Name`

is set to
`''`

, then the software automatically assigns a name at training
time.

**Data Types: **`char`

`InputSize`

— Input size`'auto'`

(default) | positive integer 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

`NumHiddenUnits`

— Number of hidden unitspositive integer

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

**Example: ** 200

`OutputMode`

— Format of output`'sequence'`

(default) | `'last'`

Format of output, specified as one of the following:

`'sequence'`

– Output the complete sequence.`'last'`

– Output the last time step of the sequence.

`BiasLearnRateFactor`

— Learning rate factor for biases1 (default) | nonnegative scalar | 1-by-4 numeric vector

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 the 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 matrices in `Bias`

, specify a 1-by-4
vector. The entries of `BiasLearnRateFactor`

correspond to the learning rate factor of the following:

Input gate

Forget gate

Layer input

Output gate

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

**Example: **
`2`

**Example: **
`[1 2 1 1]`

`BiasL2Factor`

— L2 regularization factor for biases0 (default) | nonnegative scalar | 1-by-4 numeric vector

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 learning rate for the biases in the layer. For example, if `BiasL2Factor`

is 2, then the L2 regularization for the biases in the 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 matrices in `Bias`

, specify a 1-by-4
vector. The entries of `BiasL2Factor`

correspond to
the L2 regularization factor of the following:

Input gate

Forget gate

Layer input

Output gate

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

**Example: **
`2`

**Example: **
`[1 2 1 1]`

`InputWeightsLearnRateFactor`

— Learning rate factor for input weights1 (default) | numeric scalar | 1-by-4 numeric vector

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:

Input gate

Forget gate

Layer input

Output gate

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

**Example: **`2`

**Example: **
`[1 2 1 1]`

`InputWeightsL2Factor`

— L2 regularization factor for input weights1 (default) | numeric scalar | 1-by-4 numeric vector

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:

Input gate

Forget gate

Layer input

Output gate

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

**Example: **`2`

**Example: **
`[1 2 1 1]`

`RecurrentWeightsLearnRateFactor`

— Learning rate factor for recurrent weights1 (default) | numeric scalar | 1-by-4 numeric vector

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:

Input gate

Forget gate

Layer input

Output gate

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

**Example: **`2`

**Example: **
`[1 2 1 1]`

`RecurrentWeightsL2Factor`

— L2 regularization factor for recurrent weights1 (default) | numeric scalar | 1-by-4 numeric vector

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:

Input gate

Forget gate

Layer input

Output gate

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

**Example: **`2`

**Example: **
`[1 2 1 1]`

`CellState`

— Initial value of cell statenumeric vector

Initial value of the cell state, specified as a
`NumHiddenUnits`

-by-1 numeric vector.

`OutputState`

— Initial value of the output statenumeric vector

Initial value of the output state, specified as a
`NumHiddenUnits`

-by-1 numeric vector.

`Bias`

— Layer biasesnumeric vector

Layer biases for the LSTM layer, specified as a
`4*NumHiddenUnits`

-by-1 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:

Input gate

Forget gate

Layer input

Output gate

`InputWeights`

— Input weightsmatrix

Input weights, specified as a
`4*NumHiddenUnits`

-by-`InputSize`

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:

Input gate

Forget gate

Layer input

Output gate

`RecurrentWeights`

— Recurrent weightsmatrix

Recurrent weights, specified as a
`4*NumHiddenUnits`

-by-`NumHiddenUnits`

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:

Input gate

Forget gate

Layer input

Output gate

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' Learnable Parameters InputWeights: [] RecurrentWeights: [] Bias: [] State Parameters HiddenState: [] CellState: [] Show all properties

Include an LSTM layer in a `Layer`

array.

```
layers = [ ...
sequenceInputLayer(12)
lstmLayer(100)
fullyConnectedLayer(9)
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 feature dimension 12. `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") legend("Feature " + string(1:12),'Location','northeastoutside')

Define the LSTM network architecture. Specify the input size 12 (the dimension of the input data). Specify an LSTM layer to have 100 hidden units and output the last element of the sequence. Finally, specify 9 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 = 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

Specify the training options. Specify the solver to be `'adam'`

and `'GradientThreshold'`

to be 1. Set the mini-batch size to 27, and set the maximum number of epochs to 100.

Because the mini-batches are small with short sequences, training is better suited for the CPU. Specify `'ExecutionEnvironment'`

to be `'cpu'`

. To train on a GPU, if available, set `'ExecutionEnvironment'`

to `'auto'`

(the default value).

maxEpochs = 100; miniBatchSize = 27; options = trainingOptions('adam', ... 'ExecutionEnvironment','cpu', ... 'MaxEpochs',maxEpochs, ... 'MiniBatchSize',miniBatchSize, ... 'GradientThreshold',1, ... 'Verbose',0, ... '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. Set the mini-batch size to 27.

```
miniBatchSize = 27;
YPred = classify(net,XTest,'MiniBatchSize',miniBatchSize);
```

Calculate the classification accuracy of the predictions.

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

acc = 0.9216

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.

Specify the size of the sequence input layer to be the feature dimension of the input data. Specify the size of the fully connected layer to be the number of classes.

For the LSTM layer, choose an output size, and specify the output mode `'last'`

.

inputSize = 12; numHiddenUnits = 100; numClasses = 9; layers = [ ... sequenceInputLayer(inputSize) 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 regression, use the same architecture for sequence-to-labe classification, but set the output mode of the LSTM layer to 'sequence'.

inputSize = 12; numHiddenUnits = 100; numClasses = 9; layers = [ ... sequenceInputLayer(inputSize) 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.

Specify the size of the sequence input layer to be the feature dimension of the input data. Specify the size of the fully connected layer to be the number of responses.

For the LSTM layer, choose an output size, and specify the output mode `'last'`

.

inputSize = 12; outputSize = 125; numResponses = 1; layers = [ ... sequenceInputLayer(inputSize) lstmLayer(outputSize,'OutputMode','last') fullyConnectedLayer(numResponses) regressionLayer];

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

.

inputSize = 12; outputSize = 125; numResponses = 1; layers = [ ... sequenceInputLayer(inputSize) lstmLayer(outputSize,'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.

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

.

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

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

.

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

An LSTM layer is a recurrent neural network (RNN) layer that enables support for time series and sequence data in a network. The layer performs additive interactions, which can help improve gradient flow over long sequences during training. LSTM layers are best suited for learning *long-term dependencies* (dependencies from distant time steps).

The state of the layer consists of the *output state* (also known as the
*hidden state*) and the *cell state*. The output
state at time step *t* contains the output of the LSTM layer for this time
step. The cell state contains information learned from the previous time steps. At each time
step, the layer adds information to or removes information from the cell state, where the
layer controls these updates using *gates*.

This table summarizes the components that control the cell state and output state of the layer.

Component | Purpose |
---|---|

Input gate (i) | Control level of cell state update |

Forget gate (f) | Control level of cell state reset (forget) |

Layer input (g) | Add information to cell state |

Output gate (o) | Control level of cell state added to output state |

This diagram illustrates the flow of data at time step *t*. The diagram
highlights how the gates forget, update, and output the cell and output states.

The learnable weights of an LSTM layer are the input weights *W*
(`InputWeights`

), the recurrent weights *R*
(`RecurrentWeights`

), and the bias *b*
(`Bias`

). The matrices *W*, *R*,
and *b* are concatenations of the input weights, the recurrent weights, and
the bias of each component, respectively. These matrices are concatenated as follows:

$$W=\left[\begin{array}{c}{W}_{i}\\ {W}_{f}\\ {W}_{g}\\ {W}_{o}\end{array}\right],R=\left[\begin{array}{c}{R}_{i}\\ {R}_{f}\\ {R}_{g}\\ {R}_{o}\end{array}\right],b=\left[\begin{array}{c}{b}_{i}\\ {b}_{f}\\ {b}_{g}\\ {b}_{o}\end{array}\right],$$

where *i*, *f*, *g*, and
*o* denote the input gate, forget gate, layer input, and output gate,
respectively.

The cell state at time step *t* is given by

$${c}_{t}={f}_{t}\odot {c}_{t-1}+{i}_{t}\odot {g}_{t},$$

The output (hidden) state at time step *t* is given by

$${h}_{t}={o}_{t}\odot \text{tanh}({c}_{t}).$$

This table shows the formula for each component at time step
*t*.

Component | Formula |
---|---|

Input gate | $${i}_{t}=\sigma ({W}_{i}{x}_{t}+\text{}{\text{R}}_{i}{h}_{t-1}+{b}_{i})$$ |

Forget gate | $${f}_{t}=\sigma ({W}_{f}{x}_{t}+\text{}{\text{R}}_{f}{h}_{t-1}+{b}_{f})$$ |

Layer input | $${g}_{t}=\text{tanh}({W}_{g}{x}_{t}+\text{}{\text{R}}_{g}{h}_{t-1}+{b}_{g})$$ |

Output gate | $${o}_{t}=\sigma ({W}_{o}{x}_{t}+\text{}{\text{R}}_{o}{h}_{t-1}+{b}_{o})$$ |

Here, denotes the sigmoid function given by .

[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.

`bilstmLayer`

| `classifyAndUpdateState`

| `predictAndUpdateState`

| `resetState`

| `sequenceInputLayer`

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