gruLayer

Gated recurrent unit (GRU) layer for recurrent neural network (RNN)

Description

A GRU layer is an RNN layer that learns dependencies between time steps in time-series and sequence data.

Creation

Syntax

layer = gruLayer(numHiddenUnits)

layer = gruLayer(numHiddenUnits,Name,Value)

Description

layer = gruLayer(numHiddenUnits) creates a GRU layer and sets the NumHiddenUnits property.

layer = gruLayer(numHiddenUnits,Name,Value) sets additional OutputMode, Activations, State, Parameters and Initialization, Learning 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

GRU

NumHiddenUnits — Number of hidden units

positive integer

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 that the layer remembers between time steps (the hidden state). The hidden state can contain information from all the previous time steps, regardless of the sequence length. If the number of hidden units is too large, then the layer can overfit to the training data. The hidden state does not limit the number of time steps that the layer processes in an iteration.

The layer outputs data with NumHiddenUnits channels.

To set this property, use the numHiddenUnits argument when you create the GRULayer object. After you create a GRULayer object, this property is read-only.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

OutputMode — Output mode

"sequence" (default) | "last"

Output mode, specified as one of these values:

• "sequence" — Output the complete sequence.

• "last" — Output the last time step of the sequence.

The GRULayer object stores this property as a character vector.

To set this property, use the corresponding name-value argument when you create the GRULayer object. After you create a GRULayer object, this property is read-only.

HasStateInputs — Flag for state inputs to layer

0 (false) (default) | 1 (true)

Flag for state inputs to the layer, specified as 0 (false) or 1 (true).

If the HasStateInputs property is 0 (false), then the layer has one input with the name "in", which corresponds to the input data. In this case, the layer uses the HiddenState property for the layer operation.

If the HasStateInputs property is 1 (true), then the layer has two inputs with the names "in" and "hidden", which correspond to the input data and hidden state, respectively. In this case, the layer uses the values that the network passes to these inputs for the layer operation. If HasStateInputs is 1 (true), then the HiddenState property must be empty.

To set this property, use the corresponding name-value argument when you create the GRULayer object. After you create a GRULayer object, this property is read-only.

HasStateOutputs — Flag for state outputs from layer

0 (false) (default) | 1 (true)

Flag for state outputs from the layer, specified as 0 (false) or 1 (true).

If the HasStateOutputs property is 0 (false), then the layer has one output with the name "out", which corresponds to the output data.

If the HasStateOutputs property is 1 (true), then the layer has two outputs with the names "out" and "hidden", which correspond to the output data and hidden state, respectively. In this case, the layer also outputs the state values computed during the layer operation.

To set this property, use the corresponding name-value argument when you create the GRULayer object. After you create a GRULayer object, this property is read-only.

ResetGateMode — Reset gate mode

"after-multiplication" (default) | "before-multiplication" | "recurrent-bias-after-multiplication"

Reset gate mode, specified as one of these values:

• "after-multiplication" — Apply the reset gate after matrix multiplication. This option is cuDNN compatible.

• "before-multiplication" — Apply the reset gate before matrix multiplication.

• "recurrent-bias-after-multiplication" — Apply the reset gate after matrix multiplication and use an additional set of bias terms for the recurrent weights.

For more information about the reset gate calculations, see Gated Recurrent Unit Layer.

Before R2023a: dlnetwork objects support GRU layers with the ResetGateMode set to "after-multiplication" only.

InputSize — Input size

Read-only: "auto" (default) | positive integer

This property is read-only.

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

If InputSize is "auto", then the GRULayer object stores this property as a character vector.

Data Types: double | char | string

Activations

StateActivationFunction — Activation function to update hidden state

"tanh" (default) | "softsign" | "relu"

Activation function to update the hidden state, specified as one of these values:

• "tanh" — Use the hyperbolic tangent function (tanh).

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

• "relu" (since R2024b) — Use the rectified linear unit (ReLU) function $$\text{ReLU}(x)=\{\begin{array}{cc}x,& x>0\\ 0,& x\le 0\end{array}$$.

The software uses this option as the function $${\sigma }_s$$ in the calculations to update the hidden state.

The GRULayer object stores this property as a character vector.

To set this property, use the corresponding name-value argument when you create the GRULayer object. After you create a GRULayer object, this property is read-only.

GateActivationFunction — Activation function to apply to gates

"sigmoid" (default) | "hard-sigmoid"

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

• "sigmoid" — Use the sigmoid function, $$\sigma (x)={(1+e^{-x})}^{-1}$$.

• "hard-sigmoid" — Use the hard sigmoid function,

  $$\sigma (x)=\{\begin{array}{cc}\begin{array}{l}0\hfill \\ 0.2x+0.5\hfill \\ 1\hfill \end{array}& \begin{array}{l}\text{if }x<-2.5\hfill \\ \text{if}-2.5\le x\le 2.5\hfill \\ \text{if }x>2.5\hfill \end{array}\end{array}.$$

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

The GRULayer object stores this property as a character vector.

To set this property, use the corresponding name-value argument when you create the GRULayer object. After you create a GRULayer object, this property is read-only.

State

HiddenState — Hidden state

[] (default) | numeric vector

Hidden state to use in the layer operation, specified as a NumHiddenUnits-by-1 numeric vector. This value corresponds to the initial hidden state when data is passed to the layer.

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

If HasStateInputs is 1 (true), then the HiddenState property must be empty.

Data Types: single | double

Parameters and Initialization

InputWeightsInitializer — Function to initialize input weights

"glorot" (default) | "he" | "orthogonal" | "narrow-normal" | "zeros" | "ones" | function handle

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

• "glorot" — Initialize the input weights with the Glorot initializer [2] (also known as Xavier initializer). The Glorot initializer independently samples from a uniform distribution with a mean of zero and a variance of 2/(InputSize + numOut), where numOut = 3*NumHiddenUnits.

• "he" — Initialize the input weights with the He initializer [3]. The He initializer samples from a normal distribution with a mean of zero and a variance of 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. [4]

• "narrow-normal" — Initialize the input weights by independently sampling from a normal distribution with a mean of zero and a standard deviation of 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.

The GRULayer object stores this property as a character vector or a function handle.

Data Types: char | string | function_handle

RecurrentWeightsInitializer — Function to initialize recurrent weights

"orthogonal" (default) | "glorot" | "he" | "narrow-normal" | "zeros" | "ones" | 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. [4]

• "glorot" — Initialize the recurrent weights with the Glorot initializer [2] (also known as Xavier initializer). The Glorot initializer independently samples from a uniform distribution with a mean of zero and a variance of 2/(numIn + numOut), where numIn = NumHiddenUnits and numOut = 3*NumHiddenUnits.

• "he" — Initialize the recurrent weights with the He initializer [3]. The He initializer samples from a normal distribution with a mean of zero and a variance of 2/NumHiddenUnits.

• "narrow-normal" — Initialize the recurrent weights by independently sampling from a normal distribution with a mean of zero and a standard deviation of 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.

The GRULayer object stores this property as a character vector or a function handle.

Data Types: char | string | function_handle

BiasInitializer — Function to initialize bias

"zeros" (default) | "narrow-normal" | "ones" | function handle

Function to initialize the bias, specified as one of these values:

• "zeros" — Initialize the bias with zeros.

• "narrow-normal" — Initialize the bias by independently sampling from a normal distribution with a mean of zero 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 have the form bias = func(sz), where sz is the size of the bias.

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

The GRULayer object stores this property as a character vector or a function handle.

Data Types: char | string | function_handle

InputWeights — Input weights

[] (default) | matrix

Input weights, specified as a matrix.

The input weight matrix is a concatenation of the three input weight matrices for the components in the GRU layer. The three matrices are concatenated vertically in the following order:

1. Reset gate

2. Update gate

3. Candidate state

The input weights are learnable parameters. When you train a neural network using the trainnet function, if InputWeights is nonempty, then the software uses the InputWeights property as the initial value. If InputWeights is empty, then the software uses the initializer specified by InputWeightsInitializer.

At training time, InputWeights is a 3*NumHiddenUnits-by-InputSize matrix.

RecurrentWeights — Recurrent weights

[] (default) | matrix

Recurrent weights, specified as a matrix.

The recurrent weight matrix is a concatenation of the three recurrent weight matrices for the components in the GRU layer. The three matrices are vertically concatenated in the following order:

1. Reset gate

2. Update gate

3. Candidate state

The recurrent weights are learnable parameters. When you train an RNN using the trainnet function, if RecurrentWeights is nonempty, then the software uses the RecurrentWeights property as the initial value. If RecurrentWeights is empty, then the software uses the initializer specified by RecurrentWeightsInitializer.

At training time RecurrentWeights is a 3*NumHiddenUnits-by-NumHiddenUnits matrix.

Bias — Layer biases

[] (default) | numeric vector

Layer biases, specified as a numeric vector.

If ResetGateMode is "after-multiplication" or "before-multiplication", then the bias vector is a concatenation of three bias vectors for the components in the layer operation. The layer concatenates the vectors vertically in this order:

1. Reset gate

2. Update gate

3. Candidate state

In this case, at training time, Bias is a 3*NumHiddenUnits-by-1 numeric vector.

If ResetGateMode is "recurrent-bias-after-multiplication", then the bias vector is a concatenation of six bias vectors for the components in the GRU layer. The layer concatenates the vectors vertically in this order:

1. Reset gate

2. Update gate

3. Candidate state

4. Reset gate (recurrent bias)

5. Update gate (recurrent bias)

6. Candidate state (recurrent bias)

In this case, at training time, Bias is a 6*NumHiddenUnits-by-1 numeric vector.

The layer biases are learnable parameters. When you train a neural network, if Bias is nonempty, then the trainnet function uses the Bias property as the initial value. If Bias is empty, then software uses the initializer specified by BiasInitializer.

For more information about the reset gate calculations, see Gated Recurrent Unit Layer.

Learning Rate and Regularization

InputWeightsLearnRateFactor — Learning rate factor for input weights

1 (default) | numeric scalar | 1-by-3 numeric vector

Learning rate factor for the input weights, specified as a numeric scalar or a 1-by-3 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 you specify with the trainingOptions function.

To control the value of the learning rate factor for the three individual matrices in InputWeights, specify a 1-by-3 vector. The entries of InputWeightsLearnRateFactor correspond to the learning rate factor of these values:

1. Reset gate

2. Update gate

3. Candidate state

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

Example: 2

Example: [1 2 1]

RecurrentWeightsLearnRateFactor — Learning rate factor for recurrent weights

1 (default) | numeric scalar | 1-by-3 numeric vector

Learning rate factor for the recurrent weights, specified as a numeric scalar or a 1-by-3 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 you specify using the trainingOptions function.

To control the value of the learning rate factor for the three individual matrices in RecurrentWeights, specify a 1-by-3 vector. The entries of RecurrentWeightsLearnRateFactor correspond to the learning rate factor of these values:

1. Reset gate

2. Update gate

3. Candidate state

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

Example: 2

Example: [1 2 1]

BiasLearnRateFactor — Learning rate factor for biases

1 (default) | nonnegative scalar | 1-by-3 numeric vector

Learning rate factor for the biases, specified as a nonnegative scalar or a 1-by-3 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 you specify using the trainingOptions function.

To control the value of the learning rate factor for the three individual vectors in Bias, specify a 1-by-3 vector. The entries of BiasLearnRateFactor correspond to the learning rate factor of these values:

1. Reset gate

2. Update gate

3. Candidate state

If ResetGateMode is "recurrent-bias-after-multiplication", then the software uses the same vector for the recurrent bias vectors.

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

Example: 2

Example: [1 2 1]

InputWeightsL2Factor — L₂ regularization factor for input weights

1 (default) | numeric scalar | 1-by-3 numeric vector

L₂ regularization factor for the input weights, specified as a numeric scalar or a 1-by-3 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 you specify using the trainingOptions function.

To control the value of the L₂ regularization factor for the three individual matrices in InputWeights, specify a 1-by-3 vector. The entries of InputWeightsL2Factor correspond to the L₂ regularization factor of these values:

1. Reset gate

2. Update gate

3. Candidate state

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

Example: 2

Example: [1 2 1]

RecurrentWeightsL2Factor — L₂ regularization factor for recurrent weights

1 (default) | numeric scalar | 1-by-3 numeric vector

L₂ regularization factor for the recurrent weights, specified as a numeric scalar or a 1-by-3 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 you specify using the trainingOptions function.

To control the value of the L₂ regularization factor for the three individual matrices in RecurrentWeights, specify a 1-by-3 vector. The entries of RecurrentWeightsL2Factor correspond to the L₂ regularization factor of these values:

1. Reset gate

2. Update gate

3. Candidate state

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

Example: 2

Example: [1 2 1]

BiasL2Factor — L₂ regularization factor for biases

0 (default) | nonnegative scalar | 1-by-3 numeric vector

L₂ regularization factor for the biases, specified as a nonnegative scalar or a 1-by-3 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. The software determines the global L₂ regularization factor based on the settings you specify using the trainingOptions function.

To control the value of the L₂ regularization factor for the individual vectors in Bias, specify a 1-by-3 vector. The entries of BiasL2Factor correspond to the L₂ regularization factor of these values:

1. Reset gate

2. Update gate

3. Candidate state

If ResetGateMode is "recurrent-bias-after-multiplication", then the software uses the same vector for the recurrent bias vectors.

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

Example: 2

Example: [1 2 1]

Layer

Name — Layer name

'' (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to unnamed layers.

The GRULayer object stores this property as a character vector.

Data Types: char | string

NumInputs — Number of inputs

Read-only: 1 | 2

This property is read-only.

Number of inputs to the layer.

If the HasStateInputs property is 0 (false), then the layer has one input with the name "in", which corresponds to the input data. In this case, the layer uses the HiddenState property for the layer operation.

If the HasStateInputs property is 1 (true), then the layer has two inputs with the names "in" and "hidden", which correspond to the input data and hidden state, respectively. In this case, the layer uses the values that the network passes to these inputs for the layer operation. If HasStateInputs is 1 (true), then the HiddenState property must be empty.

Data Types: double

InputNames — Layer input names

Read-only: "in" | ["in" "hidden"]

This property is read-only.

Layer input names.

If the HasStateInputs property is 0 (false), then the layer has one input with the name "in", which corresponds to the input data. In this case, the layer uses the HiddenState property for the layer operation.

If the HasStateInputs property is 1 (true), then the layer has two inputs with the names "in" and "hidden", which correspond to the input data and hidden state, respectively. In this case, the layer uses the values that the network passes to these inputs for the layer operation. If HasStateInputs is 1 (true), then the HiddenState property must be empty.

The GRULayer object stores this property as a cell array of character vectors.

NumOutputs — Number of outputs

Read-only: 1 | 2

This property is read-only.

Number of outputs from the layer.

If the HasStateOutputs property is 0 (false), then the layer has one output with the name "out", which corresponds to the output data.

If the HasStateOutputs property is 1 (true), then the layer has two outputs with the names "out" and "hidden", which correspond to the output data and hidden state, respectively. In this case, the layer also outputs the state values computed during the layer operation.

Data Types: double

OutputNames — Layer output names

Read-only: "out" | ["out" "hidden"]

This property is read-only.

Layer output names.

If the HasStateOutputs property is 0 (false), then the layer has one output with the name "out", which corresponds to the output data.

If the HasStateOutputs property is 1 (true), then the layer has two outputs with the names "out" and "hidden", which correspond to the output data and hidden state, respectively. In this case, the layer also outputs the state values computed during the layer operation.

The GRULayer object stores this property as a cell array of character vectors.

Examples

Create GRU Layer

Create a GRU layer with the name gru1 and 100 hidden units.

layer = gruLayer(100,Name="gru1")

layer = 
  GRULayer with properties:

                       Name: 'gru1'
                 InputNames: {'in'}
                OutputNames: {'out'}
                  NumInputs: 1
                 NumOutputs: 1
             HasStateInputs: 0
            HasStateOutputs: 0

   Hyperparameters
                  InputSize: 'auto'
             NumHiddenUnits: 100
                 OutputMode: 'sequence'
    StateActivationFunction: 'tanh'
     GateActivationFunction: 'sigmoid'
              ResetGateMode: 'after-multiplication'

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

   State Parameters
                HiddenState: []

  Show all properties

Include a GRU layer in a Layer array.

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

layers = [ ...
    sequenceInputLayer(inputSize)
    gruLayer(numHiddenUnits)
    fullyConnectedLayer(numClasses)
    softmaxLayer]

layers = 
  4×1 Layer array with layers:

     1   ''   Sequence Input    Sequence input with 12 dimensions
     2   ''   GRU               GRU with 100 hidden units
     3   ''   Fully Connected   9 fully connected layer
     4   ''   Softmax           softmax

Algorithms

Gated Recurrent Unit Layer

A GRU layer is an RNN layer that learns dependencies between time steps in time-series and sequence data.

The hidden state of the layer at time step t contains the output of the GRU layer for this time step. At each time step, the layer adds information to or removes information from the state. The layer controls these updates using gates.

These components control the hidden state of the layer.

Component	Purpose
Reset gate (r)	Control level of state reset
Update gate (z)	Control level of state update
Candidate state ($$\tilde{h}$$)	Control level of update added to hidden state

The learnable weights of a GRU layer are the input weights W (InputWeights), the recurrent weights R (RecurrentWeights), and the bias b (Bias). If the ResetGateMode property is "recurrent-bias-after-multiplication", then the gate and state calculations require two sets of bias values. The matrices W and R are concatenations of the input weights and the recurrent weights of each component, respectively. The layer concatenates the matrices in this order:

$$W=\left[\begin{array}{c}{W}_r\\ W_z\\ W_{\tilde{h}}\end{array}\right],R=\left[\begin{array}{c}{R}_r\\ R_z\\ R_{\tilde{h}}\end{array}\right],$$

where r, z, and $$\tilde{h}$$ denote the reset gate, update gate, and candidate state, respectively.

The bias vector depends on the ResetGateMode property. If ResetGateMode is "after-multiplication" or "before-multiplication", then the bias vector is a concatenation of three vectors:

$$b=\left[\begin{array}{c}{b}_{W_r}\\ b_{W_z}\\ b_{W_{\tilde{h}}}\end{array}\right],$$

where the subscript W indicates that this bias corresponds to the input weights multiplication.

If ResetGateMode is "recurrent-bias-after-multiplication", then the bias vector is a concatenation of six vectors:

$$b=\left[\begin{array}{c}{b}_{W_r}\\ b_{W_z}\\ b_{W_{\tilde{h}}}\\ b_{R_r}\\ b_{R_z}\\ b_{R_{\tilde{h}}}\end{array}\right],$$

where the subscript R indicates that this is the bias corresponding to the recurrent weights multiplication.

The hidden state at time step t is given by this equation:

$$h_t=(1-z_t)\odot {\tilde{h}}_t+z_t\odot h_{t-1}.$$

These formulas describe the components at time step t.

Component		ResetGateMode	Formula
Reset gate		"after-multiplication"	$$r_t={\sigma }_g\left(W_r{x}_t+b_{W_r}+\text{}{R}_r{h}_{t-1}\right)$$
		"before-multiplication"
		"recurrent-bias-after-multiplication"	$$r_t={\sigma }_g\left(W_r{x}_t+b_{W_r}+\text{}{R}_r{h}_{t-1}+b_{R_r}\right)$$
Update gate		"after-multiplication"	$$z_t={\sigma }_g\left(W_z{x}_t+b_{W_z}+\text{}{R}_z{h}_{t-1}\right)$$
		"before-multiplication"
		"recurrent-bias-after-multiplication"	$$z_t={\sigma }_g\left(W_z{x}_t+b_{W_z}+\text{}{R}_z{h}_{t-1}+b_{R_z}\right)$$
Candidate state		"after-multiplication"	$${\tilde{h}}_t={\sigma }_s\left(W_{\tilde{h}}{x}_t+b_{W_{\tilde{h}}}+r_t\odot \text{}({\text{R}}_{\tilde{h}}{h}_{t-1})\right)$$
		"before-multiplication"	$${\tilde{h}}_t={\sigma }_s\left(W_{\tilde{h}}{x}_t+b_{W_{\tilde{h}}}+R_{\tilde{h}}(r_t\odot \text{}{h}_{t-1})\right)$$
		"recurrent-bias-after-multiplication"	$${\tilde{h}}_t={\sigma }_s\left(W_{\tilde{h}}{x}_t+b_{W_{\tilde{h}}}+r_t\odot \text{}\left({\text{R}}_{\tilde{h}}{h}_{t-1}+b_{R_{\tilde{h}}}\right)\right)$$

In these calculations, $${\sigma }_g$$ and $${\sigma }_s$$ denote the gate and state activation functions, respectively. The gruLayer function, by default, uses the sigmoid function given by $$\sigma (x)={(1+e^{-x})}^{-1}$$ to compute the gate activation function and the hyperbolic tangent function (tanh) to compute the state activation function. To specify the state and gate activation functions, use the StateActivationFunction and GateActivationFunction properties, respectively.

Layer Input and Output Formats

Layers in a layer array or layer graph pass data to subsequent layers as formatted dlarray objects. The format of a dlarray object is a string of characters in which each character describes the corresponding dimension of the data. The format consists of one or more of these characters:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, you can describe 2-D image data that is represented as a 4-D array, where the first two dimensions correspond to the spatial dimensions of the images, the third dimension corresponds to the channels of the images, and the fourth dimension corresponds to the batch dimension, as having the format "SSCB" (spatial, spatial, channel, batch).

You can interact with these dlarray objects in automatic differentiation workflows, such as those for developing a custom layer, using a functionLayer object, or using the forward and predict functions with dlnetwork objects.

This table shows the supported input formats of GRULayer objects and the corresponding output format. If the software passes the output of the layer to a custom layer that does not inherit from the nnet.layer.Formattable class, or a FunctionLayer object with the Formattable property set to 0 (false), then the layer receives an unformatted dlarray object with dimensions ordered according to the formats in this table. The formats listed here are only a subset. The layer may support additional formats such as formats with additional "S" (spatial) or "U" (unspecified) dimensions.

Input Format	OutputMode	Output Format
"CB" (channel, batch)	"sequence"	"CB" (channel, batch)
	"last"
"CBT" (channel, batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)
"SB" (spatial, batch)	"sequence"	"CB" (channel, batch)
	"last"

In dlnetwork objects, GRULayer objects also support these input and output format combinations.

Input Format	OutputMode	Output Format
"SCB" (spatial, channel, batch)	"sequence"	"CB" (channel, batch)
	"last"
"SSCB" (spatial, spatial, channel, batch)	"sequence"
	"last"
"SSSCB" (spatial, spatial, spatial, channel, batch)	"sequence"
	"last"
"SCBT" (spatial, channel, batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)
"SSCBT" (spatial, spatial, channel, batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)
"SSSCBT" (spatial, spatial, spatial, channel, batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)
"SC" (spatial, channel)	"sequence"	"CU" (channel, unspecified)
	"last"
"SSC" (spatial, spatial, channel)	"sequence"
	"last"
"SSSC" (spatial, spatial, spatial, channel)	"sequence"
	"last"
"CT" (channel, time)	"sequence"	"CT" (channel, time)
	"last"	"CU" (channel, unspecified)
"SCT" (spatial, channel, time)	"sequence"	"CT" (channel, time)
	"last"	"CU" (channel, unspecified)
"SSCT" (spatial, spatial, channel, time)	"sequence"	"CT" (channel, time)
	"last"	"CU" (channel, unspecified)
"SSSCT" (spatial, spatial, channel, time)	"sequence"	"CT" (channel, time)
	"last"	"CU" (channel, unspecified)
"SSB" (spatial, spatial, batch)	"sequence"	"CB" (channel, batch)
	"last"
"SSSB" (spatial, spatial, spatial, batch)	"sequence"
	"last"
"BT" (batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)
"SBT" (spatial, batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)
"SSBT" (spatial, spatial, batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)
"SSSBT" (spatial, spatial, spatial, batch, time)	"sequence"	"CBT" (channel, batch, time)
	"last"	"CB" (channel, batch)

If the HasStateInputs property is 1 (true), then the layer has two additional inputs with the names "hidden" and "cell", which correspond to the hidden state and cell state, respectively. These additional inputs expect input format "CB" (channel, batch).

If the HasStateOutputs property is 1 (true), then the layer has two additional outputs with names "hidden" and "cell", which correspond to the hidden state and cell state, respectively. These additional outputs have output format "CB" (channel, batch).

References

[1] Cho, Kyunghyun, Bart Van Merriënboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. "Learning phrase representations using RNN encoder-decoder for statistical machine translation." arXiv preprint arXiv:1406.1078 (2014).

[2] 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. https://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf

[3] He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. "Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification." In 2015 IEEE International Conference on Computer Vision (ICCV), 1026–34. Santiago, Chile: IEEE, 2015. https://doi.org/10.1109/ICCV.2015.123

[4] Saxe, Andrew M., James L. McClelland, and Surya Ganguli. "Exact Solutions to the Nonlinear Dynamics of Learning in Deep Linear Neural Networks.” Preprint, submitted February 19, 2014. https://arxiv.org/abs/1312.6120.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• For code generation in general, the HasStateInputs and HasStateOutputs properties must be set to 0 (false).

• Code generation does not support passing dlarray objects with unspecified (U) dimensions to this layer.

• For code generation, you must pass a dlarray object with a channel (C) dimension as the input to this layer. For example, code generation supports data format such as "SSC" or "SSCBT".

• When generating code with Intel^® MKL-DNN or ARM^® Compute Library:

  • The StateActivationFunction property must be set to "tanh".

  • The GateActivationFunction property must be set to "sigmoid".

  • The ResetGateMode property must be set to "after-multiplication" or "recurrent-bias-after-multiplication".

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• The HasStateInputs and HasStateOutputs properties must be set to 0 (false).

• Code generation does not support passing dlarray objects with unspecified (U) dimensions to this layer.

• For code generation, you must pass a dlarray object with a channel (C) dimension as the input to this layer. For example, code generation supports data format such as "SSC" or "SSCBT".

• When generating code with NVIDIA^® TensorRT or CUDA deep neural network (cuDNN) library:

  • The StateActivationFunction property must be set to "tanh".

  • The GateActivationFunction property must be set to "sigmoid".

  • The ResetGateMode property must be set to "after-multiplication" or "recurrent-bias-after-multiplication".

Version History

Introduced in R2020a

R2024b: Specify the ReLU state activation function

To specify the ReLU state activation function, set the StateActivationFunction property to "relu".

R2023a: Specify reset gate mode for GRU layers in dlnetwork objects

For GRU layers in dlnetwork objects, specify the reset gate mode using the ResetGateMode property.