# RNN#

## RNN - 14#

Version

• name: RNN (GitHub)

• domain: main

• since_version: 14

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 14.

Summary

Computes an one-layer simple RNN. This operator is usually supported via some custom implementation such as CuDNN.

Notations:

X - input tensor

i - input gate

t - time step (t-1 means previous time step)

Wi - W parameter weight matrix for input gate

Ri - R recurrence weight matrix for input gate

Wbi - W parameter bias vector for input gate

Rbi - R parameter bias vector for input gate

WBi - W parameter weight matrix for backward input gate

RBi - R recurrence weight matrix for backward input gate

WBbi - WR bias vectors for backward input gate

RBbi - RR bias vectors for backward input gate

H - Hidden state

num_directions - 2 if direction == bidirectional else 1

Activation functions:

Relu(x) - max(0, x)

Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})

Sigmoid(x) - 1/(1 + e^{-x})

(NOTE: Below are optional)

Affine(x) - alpha*x + beta

LeakyRelu(x) - x if x >= 0 else alpha * x

ThresholdedRelu(x) - x if x >= alpha else 0

ScaledTanh(x) - alpha*Tanh(beta*x)

HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)

Elu(x) - x if x >= 0 else alpha*(e^x - 1)

Softsign(x) - x/(1 + |x|)

Softplus(x) - log(1 + e^x)

Equations (Default: f=Tanh):

• Ht = f(Xt*(Wi^T) + Ht-1*(Ri^T) + Wbi + Rbi)

This operator has optional inputs/outputs. See ONNX for more details about the representation of optional arguments. An empty string may be used in the place of an actual argument’s name to indicate a missing argument. Trailing optional arguments (those not followed by an argument that is present) may also be simply omitted.

Attributes

• activation_alpha: Optional scaling values used by some activation functions. The values are consumed in the order of activation functions, for example (f, g, h) in LSTM. Default values are the same as of corresponding ONNX operators.For example with LeakyRelu, the default alpha is 0.01.

• activation_beta: Optional scaling values used by some activation functions. The values are consumed in the order of activation functions, for example (f, g, h) in LSTM. Default values are the same as of corresponding ONNX operators.

• activations: One (or two if bidirectional) activation function for input gate. The activation function must be one of the activation functions specified above. Optional: Default Tanh if not specified. Default value is `[b'Tanh' b'Tanh']`.

• clip: Cell clip threshold. Clipping bounds the elements of a tensor in the range of [-threshold, +threshold] and is applied to the input of activations. No clip if not specified.

• direction: Specify if the RNN is forward, reverse, or bidirectional. Must be one of forward (default), reverse, or bidirectional. Default value is `'forward'`.

• hidden_size: Number of neurons in the hidden layer

• layout: The shape format of inputs X, initial_h and outputs Y, Y_h. If 0, the following shapes are expected: X.shape = [seq_length, batch_size, input_size], Y.shape = [seq_length, num_directions, batch_size, hidden_size], initial_h.shape = Y_h.shape = [num_directions, batch_size, hidden_size]. If 1, the following shapes are expected: X.shape = [batch_size, seq_length, input_size], Y.shape = [batch_size, seq_length, num_directions, hidden_size], initial_h.shape = Y_h.shape = [batch_size, num_directions, hidden_size]. Default value is `0`.

Inputs

Between 3 and 6 inputs.

• X (heterogeneous) - T: The input sequences packed (and potentially padded) into one 3-D tensor with the shape of [seq_length, batch_size, input_size].

• W (heterogeneous) - T: The weight tensor for input gate. Concatenation of Wi and WBi (if bidirectional). The tensor has shape [num_directions, hidden_size, input_size].

• R (heterogeneous) - T: The recurrence weight tensor. Concatenation of Ri and RBi (if bidirectional). The tensor has shape [num_directions, hidden_size, hidden_size].

• B (optional, heterogeneous) - T: The bias tensor for input gate. Concatenation of [Wbi, Rbi] and [WBbi, RBbi] (if bidirectional). The tensor has shape [num_directions, 2*hidden_size]. Optional: If not specified - assumed to be 0.

• sequence_lens (optional, heterogeneous) - T1: Optional tensor specifying lengths of the sequences in a batch. If not specified - assumed all sequences in the batch to have length seq_length. It has shape [batch_size].

• initial_h (optional, heterogeneous) - T: Optional initial value of the hidden. If not specified - assumed to be 0. It has shape [num_directions, batch_size, hidden_size].

Outputs

Between 0 and 2 outputs.

• Y (optional, heterogeneous) - T: A tensor that concats all the intermediate output values of the hidden. It has shape [seq_length, num_directions, batch_size, hidden_size].

• Y_h (optional, heterogeneous) - T: The last output value of the hidden. It has shape [num_directions, batch_size, hidden_size].

Type Constraints

• T in ( tensor(double), tensor(float), tensor(float16) ): Constrain input and output types to float tensors.

• T1 in ( tensor(int32) ): Constrain seq_lens to integer tensor.

Examples

_defaults

```input = np.array([[[1., 2.], [3., 4.], [5., 6.]]]).astype(np.float32)

input_size = 2
hidden_size = 4
weight_scale = 0.1

node = onnx.helper.make_node(
'RNN',
inputs=['X', 'W', 'R'],
outputs=['', 'Y_h'],
hidden_size=hidden_size
)

W = weight_scale * np.ones((1, hidden_size, input_size)).astype(np.float32)
R = weight_scale * np.ones((1, hidden_size, hidden_size)).astype(np.float32)

rnn = RNN_Helper(X=input, W=W, R=R)
_, Y_h = rnn.step()
expect(node, inputs=[input, W, R], outputs=[Y_h.astype(np.float32)], name='test_simple_rnn_defaults')
```

_initial_bias

```input = np.array([[[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]]]).astype(np.float32)

input_size = 3
hidden_size = 5
custom_bias = 0.1
weight_scale = 0.1

node = onnx.helper.make_node(
'RNN',
inputs=['X', 'W', 'R', 'B'],
outputs=['', 'Y_h'],
hidden_size=hidden_size
)

W = weight_scale * np.ones((1, hidden_size, input_size)).astype(np.float32)
R = weight_scale * np.ones((1, hidden_size, hidden_size)).astype(np.float32)

# Adding custom bias
W_B = custom_bias * np.ones((1, hidden_size)).astype(np.float32)
R_B = np.zeros((1, hidden_size)).astype(np.float32)
B = np.concatenate((W_B, R_B), axis=1)

rnn = RNN_Helper(X=input, W=W, R=R, B=B)
_, Y_h = rnn.step()
expect(node, inputs=[input, W, R, B], outputs=[Y_h.astype(np.float32)],
name='test_simple_rnn_with_initial_bias')
```

_seq_length

```input = np.array([[[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]],
[[10., 11., 12.], [13., 14., 15.], [16., 17., 18.]]]).astype(np.float32)

input_size = 3
hidden_size = 5

node = onnx.helper.make_node(
'RNN',
inputs=['X', 'W', 'R', 'B'],
outputs=['', 'Y_h'],
hidden_size=hidden_size
)

W = np.random.randn(1, hidden_size, input_size).astype(np.float32)
R = np.random.randn(1, hidden_size, hidden_size).astype(np.float32)

# Adding custom bias
W_B = np.random.randn(1, hidden_size).astype(np.float32)
R_B = np.random.randn(1, hidden_size).astype(np.float32)
B = np.concatenate((W_B, R_B), axis=1)

rnn = RNN_Helper(X=input, W=W, R=R, B=B)
_, Y_h = rnn.step()
expect(node, inputs=[input, W, R, B], outputs=[Y_h.astype(np.float32)], name='test_rnn_seq_length')
```

_batchwise

```input = np.array([[[1., 2.]], [[3., 4.]], [[5., 6.]]]).astype(np.float32)

input_size = 2
hidden_size = 4
weight_scale = 0.5
layout = 1

node = onnx.helper.make_node(
'RNN',
inputs=['X', 'W', 'R'],
outputs=['Y', 'Y_h'],
hidden_size=hidden_size,
layout=layout
)

W = weight_scale * np.ones((1, hidden_size, input_size)).astype(np.float32)
R = weight_scale * np.ones((1, hidden_size, hidden_size)).astype(np.float32)

rnn = RNN_Helper(X=input, W=W, R=R, layout=layout)
Y, Y_h = rnn.step()
expect(node, inputs=[input, W, R], outputs=[Y.astype(np.float32), Y_h.astype(np.float32)], name='test_simple_rnn_batchwise')
```

Differences

 `0` `0` `Computes an one-layer simple RNN. This operator is usually supported` `Computes an one-layer simple RNN. This operator is usually supported` `1` `1` `via some custom implementation such as CuDNN.` `via some custom implementation such as CuDNN.` `2` `2` `3` `3` `Notations:` `Notations:` `4` `4` `5` `5` `X - input tensor` `X - input tensor` `6` `6` `7` `7` `i - input gate` `i - input gate` `8` `8` `9` `9` `t - time step (t-1 means previous time step)` `t - time step (t-1 means previous time step)` `10` `10` `11` `11` `Wi - W parameter weight matrix for input gate` `Wi - W parameter weight matrix for input gate` `12` `12` `13` `13` `Ri - R recurrence weight matrix for input gate` `Ri - R recurrence weight matrix for input gate` `14` `14` `15` `15` `Wbi - W parameter bias vector for input gate` `Wbi - W parameter bias vector for input gate` `16` `16` `17` `17` `Rbi - R parameter bias vector for input gate` `Rbi - R parameter bias vector for input gate` `18` `18` `19` `19` `WBi - W parameter weight matrix for backward input gate` `WBi - W parameter weight matrix for backward input gate` `20` `20` `21` `21` `RBi - R recurrence weight matrix for backward input gate` `RBi - R recurrence weight matrix for backward input gate` `22` `22` `23` `23` `WBbi - WR bias vectors for backward input gate` `WBbi - WR bias vectors for backward input gate` `24` `24` `25` `25` `RBbi - RR bias vectors for backward input gate` `RBbi - RR bias vectors for backward input gate` `26` `26` `27` `27` `H - Hidden state` `H - Hidden state` `28` `28` `29` `29` `num_directions - 2 if direction == bidirectional else 1` `num_directions - 2 if direction == bidirectional else 1` `30` `30` `31` `31` `Activation functions:` `Activation functions:` `32` `32` `33` `33` ` Relu(x) - max(0, x)` ` Relu(x) - max(0, x)` `34` `34` `35` `35` ` Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})` ` Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})` `36` `36` `37` `37` ` Sigmoid(x) - 1/(1 + e^{-x})` ` Sigmoid(x) - 1/(1 + e^{-x})` `38` `38` `39` `39` ` (NOTE: Below are optional)` ` (NOTE: Below are optional)` `40` `40` `41` `41` ` Affine(x) - alpha*x + beta` ` Affine(x) - alpha*x + beta` `42` `42` `43` `43` ` LeakyRelu(x) - x if x >= 0 else alpha * x` ` LeakyRelu(x) - x if x >= 0 else alpha * x` `44` `44` `45` `45` ` ThresholdedRelu(x) - x if x >= alpha else 0` ` ThresholdedRelu(x) - x if x >= alpha else 0` `46` `46` `47` `47` ` ScaledTanh(x) - alpha*Tanh(beta*x)` ` ScaledTanh(x) - alpha*Tanh(beta*x)` `48` `48` `49` `49` ` HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)` ` HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)` `50` `50` `51` `51` ` Elu(x) - x if x >= 0 else alpha*(e^x - 1)` ` Elu(x) - x if x >= 0 else alpha*(e^x - 1)` `52` `52` `53` `53` ` Softsign(x) - x/(1 + |x|)` ` Softsign(x) - x/(1 + |x|)` `54` `54` `55` `55` ` Softplus(x) - log(1 + e^x)` ` Softplus(x) - log(1 + e^x)` `56` `56` `57` `57` `Equations (Default: f=Tanh):` `Equations (Default: f=Tanh):` `58` `58` `59` `59` ` - Ht = f(Xt*(Wi^T) + Ht-1*(Ri^T) + Wbi + Rbi)` ` - Ht = f(Xt*(Wi^T) + Ht-1*(Ri^T) + Wbi + Rbi)` `60` `60` `This operator has **optional** inputs/outputs. See ONNX _ for more details about the representation of optional arguments. An empty string may be used in the place of an actual argument's name to indicate a missing argument. Trailing optional arguments (those not followed by an argument that is present) may also be simply omitted.` `This operator has **optional** inputs/outputs. See ONNX _ for more details about the representation of optional arguments. An empty string may be used in the place of an actual argument's name to indicate a missing argument. Trailing optional arguments (those not followed by an argument that is present) may also be simply omitted.` `61` `61` `62` `62` `**Attributes**` `**Attributes**` `63` `63` `64` `64` `* **activation_alpha**:` `* **activation_alpha**:` `65` `65` ` Optional scaling values used by some activation functions. The` ` Optional scaling values used by some activation functions. The` `66` `66` ` values are consumed in the order of activation functions, for` ` values are consumed in the order of activation functions, for` `67` `67` ` example (f, g, h) in LSTM. Default values are the same as of` ` example (f, g, h) in LSTM. Default values are the same as of` `68` `68` ` corresponding ONNX operators.For example with LeakyRelu, the default` ` corresponding ONNX operators.For example with LeakyRelu, the default` `69` `69` ` alpha is 0.01.` ` alpha is 0.01.` `70` `70` `* **activation_beta**:` `* **activation_beta**:` `71` `71` ` Optional scaling values used by some activation functions. The` ` Optional scaling values used by some activation functions. The` `72` `72` ` values are consumed in the order of activation functions, for` ` values are consumed in the order of activation functions, for` `73` `73` ` example (f, g, h) in LSTM. Default values are the same as of` ` example (f, g, h) in LSTM. Default values are the same as of` `74` `74` ` corresponding ONNX operators.` ` corresponding ONNX operators.` `75` `75` `* **activations**:` `* **activations**:` `76` `76` ` One (or two if bidirectional) activation function for input gate.` ` One (or two if bidirectional) activation function for input gate.` `77` `77` ` The activation function must be one of the activation functions` ` The activation function must be one of the activation functions` `78` `78` ` specified above. Optional: Default Tanh if not specified. Default value is [b'Tanh' b'Tanh'].` ` specified above. Optional: Default Tanh if not specified. Default value is [b'Tanh' b'Tanh'].` `79` `79` `* **clip**:` `* **clip**:` `80` `80` ` Cell clip threshold. Clipping bounds the elements of a tensor in the` ` Cell clip threshold. Clipping bounds the elements of a tensor in the` `81` `81` ` range of [-threshold, +threshold] and is applied to the input of` ` range of [-threshold, +threshold] and is applied to the input of` `82` `82` ` activations. No clip if not specified.` ` activations. No clip if not specified.` `83` `83` `* **direction**:` `* **direction**:` `84` `84` ` Specify if the RNN is forward, reverse, or bidirectional. Must be` ` Specify if the RNN is forward, reverse, or bidirectional. Must be` `85` `85` ` one of forward (default), reverse, or bidirectional. Default value is 'forward'.` ` one of forward (default), reverse, or bidirectional. Default value is 'forward'.` `86` `86` `* **hidden_size**:` `* **hidden_size**:` `87` `87` ` Number of neurons in the hidden layer` ` Number of neurons in the hidden layer` `88` `* **layout**:` `89` ` The shape format of inputs X, initial_h and outputs Y, Y_h. If 0,` `90` ` the following shapes are expected: X.shape = [seq_length,` `91` ` batch_size, input_size], Y.shape = [seq_length, num_directions,` `92` ` batch_size, hidden_size], initial_h.shape = Y_h.shape =` `93` ` [num_directions, batch_size, hidden_size]. If 1, the following` `94` ` shapes are expected: X.shape = [batch_size, seq_length, input_size],` `95` ` Y.shape = [batch_size, seq_length, num_directions, hidden_size],` `96` ` initial_h.shape = Y_h.shape = [batch_size, num_directions,` `97` ` hidden_size]. Default value is 0.` `88` `98` `89` `99` `**Inputs**` `**Inputs**` `90` `100` `91` `101` `Between 3 and 6 inputs.` `Between 3 and 6 inputs.` `92` `102` `93` `103` `* **X** (heterogeneous) - **T**:` `* **X** (heterogeneous) - **T**:` `94` `104` ` The input sequences packed (and potentially padded) into one 3-D` ` The input sequences packed (and potentially padded) into one 3-D` `95` `105` ` tensor with the shape of [seq_length, batch_size, input_size].` ` tensor with the shape of [seq_length, batch_size, input_size].` `96` `106` `* **W** (heterogeneous) - **T**:` `* **W** (heterogeneous) - **T**:` `97` `107` ` The weight tensor for input gate. Concatenation of Wi and WBi` ` The weight tensor for input gate. Concatenation of Wi and WBi` `98` `108` ` (if bidirectional). The tensor has shape [num_directions,` ` (if bidirectional). The tensor has shape [num_directions,` `99` `109` ` hidden_size, input_size].` ` hidden_size, input_size].` `100` `110` `* **R** (heterogeneous) - **T**:` `* **R** (heterogeneous) - **T**:` `101` `111` ` The recurrence weight tensor. Concatenation of Ri and RBi (if` ` The recurrence weight tensor. Concatenation of Ri and RBi (if` `102` `112` ` bidirectional). The tensor has shape [num_directions, hidden_size,` ` bidirectional). The tensor has shape [num_directions, hidden_size,` `103` `113` ` hidden_size].` ` hidden_size].` `104` `114` `* **B** (optional, heterogeneous) - **T**:` `* **B** (optional, heterogeneous) - **T**:` `105` `115` ` The bias tensor for input gate. Concatenation of [Wbi, Rbi] and` ` The bias tensor for input gate. Concatenation of [Wbi, Rbi] and` `106` `116` ` [WBbi, RBbi] (if bidirectional). The tensor has shape` ` [WBbi, RBbi] (if bidirectional). The tensor has shape` `107` `117` ` [num_directions, 2*hidden_size]. Optional: If not specified -` ` [num_directions, 2*hidden_size]. Optional: If not specified -` `108` `118` ` assumed to be 0.` ` assumed to be 0.` `109` `119` `* **sequence_lens** (optional, heterogeneous) - **T1**:` `* **sequence_lens** (optional, heterogeneous) - **T1**:` `110` `120` ` Optional tensor specifying lengths of the sequences in a batch. If` ` Optional tensor specifying lengths of the sequences in a batch. If` `111` `121` ` not specified - assumed all sequences in the batch to have length` ` not specified - assumed all sequences in the batch to have length` `112` `122` ` seq_length. It has shape [batch_size].` ` seq_length. It has shape [batch_size].` `113` `123` `* **initial_h** (optional, heterogeneous) - **T**:` `* **initial_h** (optional, heterogeneous) - **T**:` `114` `124` ` Optional initial value of the hidden. If not specified - assumed to` ` Optional initial value of the hidden. If not specified - assumed to` `115` `125` ` be 0. It has shape [num_directions, batch_size, hidden_size].` ` be 0. It has shape [num_directions, batch_size, hidden_size].` `116` `126` `117` `127` `**Outputs**` `**Outputs**` `118` `128` `119` `129` `Between 0 and 2 outputs.` `Between 0 and 2 outputs.` `120` `130` `121` `131` `* **Y** (optional, heterogeneous) - **T**:` `* **Y** (optional, heterogeneous) - **T**:` `122` `132` ` A tensor that concats all the intermediate output values of the` ` A tensor that concats all the intermediate output values of the` `123` `133` ` hidden. It has shape [seq_length, num_directions, batch_size,` ` hidden. It has shape [seq_length, num_directions, batch_size,` `124` `134` ` hidden_size].` ` hidden_size].` `125` `135` `* **Y_h** (optional, heterogeneous) - **T**:` `* **Y_h** (optional, heterogeneous) - **T**:` `126` `136` ` The last output value of the hidden. It has shape [num_directions,` ` The last output value of the hidden. It has shape [num_directions,` `127` `137` ` batch_size, hidden_size].` ` batch_size, hidden_size].` `128` `138` `129` `139` `**Type Constraints**` `**Type Constraints**` `130` `140` `131` `141` `* **T** in (` `* **T** in (` `132` `142` ` tensor(double),` ` tensor(double),` `133` `143` ` tensor(float),` ` tensor(float),` `134` `144` ` tensor(float16)` ` tensor(float16)` `135` `145` ` ):` ` ):` `136` `146` ` Constrain input and output types to float tensors.` ` Constrain input and output types to float tensors.` `137` `147` `* **T1** in (` `* **T1** in (` `138` `148` ` tensor(int32)` ` tensor(int32)` `139` `149` ` ):` ` ):` `140` `150` ` Constrain seq_lens to integer tensor.` ` Constrain seq_lens to integer tensor.`

## RNN - 7#

Version

• name: RNN (GitHub)

• domain: main

• since_version: 7

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 7.

Summary

Computes an one-layer simple RNN. This operator is usually supported via some custom implementation such as CuDNN.

Notations:

X - input tensor

i - input gate

t - time step (t-1 means previous time step)

Wi - W parameter weight matrix for input gate

Ri - R recurrence weight matrix for input gate

Wbi - W parameter bias vector for input gate

Rbi - R parameter bias vector for input gate

WBi - W parameter weight matrix for backward input gate

RBi - R recurrence weight matrix for backward input gate

WBbi - WR bias vectors for backward input gate

RBbi - RR bias vectors for backward input gate

H - Hidden state

num_directions - 2 if direction == bidirectional else 1

Activation functions:

Relu(x) - max(0, x)

Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})

Sigmoid(x) - 1/(1 + e^{-x})

(NOTE: Below are optional)

Affine(x) - alpha*x + beta

LeakyRelu(x) - x if x >= 0 else alpha * x

ThresholdedRelu(x) - x if x >= alpha else 0

ScaledTanh(x) - alpha*Tanh(beta*x)

HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)

Elu(x) - x if x >= 0 else alpha*(e^x - 1)

Softsign(x) - x/(1 + |x|)

Softplus(x) - log(1 + e^x)

Equations (Default: f=Tanh):

• Ht = f(Xt*(Wi^T) + Ht-1*(Ri^T) + Wbi + Rbi)

This operator has optional inputs/outputs. See ONNX for more details about the representation of optional arguments. An empty string may be used in the place of an actual argument’s name to indicate a missing argument. Trailing optional arguments (those not followed by an argument that is present) may also be simply omitted.

Attributes

• activation_alpha: Optional scaling values used by some activation functions. The values are consumed in the order of activation functions, for example (f, g, h) in LSTM. Default values are the same as of corresponding ONNX operators.For example with LeakyRelu, the default alpha is 0.01.

• activation_beta: Optional scaling values used by some activation functions. The values are consumed in the order of activation functions, for example (f, g, h) in LSTM. Default values are the same as of corresponding ONNX operators.

• activations: One (or two if bidirectional) activation function for input gate. The activation function must be one of the activation functions specified above. Optional: Default Tanh if not specified. Default value is `[b'Tanh' b'Tanh']`.

• clip: Cell clip threshold. Clipping bounds the elements of a tensor in the range of [-threshold, +threshold] and is applied to the input of activations. No clip if not specified.

• direction: Specify if the RNN is forward, reverse, or bidirectional. Must be one of forward (default), reverse, or bidirectional. Default value is `'forward'`.

• hidden_size: Number of neurons in the hidden layer

Inputs

Between 3 and 6 inputs.

• X (heterogeneous) - T: The input sequences packed (and potentially padded) into one 3-D tensor with the shape of [seq_length, batch_size, input_size].

• W (heterogeneous) - T: The weight tensor for input gate. Concatenation of Wi and WBi (if bidirectional). The tensor has shape [num_directions, hidden_size, input_size].

• R (heterogeneous) - T: The recurrence weight tensor. Concatenation of Ri and RBi (if bidirectional). The tensor has shape [num_directions, hidden_size, hidden_size].

• B (optional, heterogeneous) - T: The bias tensor for input gate. Concatenation of [Wbi, Rbi] and [WBbi, RBbi] (if bidirectional). The tensor has shape [num_directions, 2*hidden_size]. Optional: If not specified - assumed to be 0.

• sequence_lens (optional, heterogeneous) - T1: Optional tensor specifying lengths of the sequences in a batch. If not specified - assumed all sequences in the batch to have length seq_length. It has shape [batch_size].

• initial_h (optional, heterogeneous) - T: Optional initial value of the hidden. If not specified - assumed to be 0. It has shape [num_directions, batch_size, hidden_size].

Outputs

Between 0 and 2 outputs.

• Y (optional, heterogeneous) - T: A tensor that concats all the intermediate output values of the hidden. It has shape [seq_length, num_directions, batch_size, hidden_size].

• Y_h (optional, heterogeneous) - T: The last output value of the hidden. It has shape [num_directions, batch_size, hidden_size].

Type Constraints

• T in ( tensor(double), tensor(float), tensor(float16) ): Constrain input and output types to float tensors.

• T1 in ( tensor(int32) ): Constrain seq_lens to integer tensor.

Differences

 `0` `0` `Computes an one-layer simple RNN. This operator is usually supported` `Computes an one-layer simple RNN. This operator is usually supported` `1` `1` `via some custom implementation such as CuDNN.` `via some custom implementation such as CuDNN.` `2` `2` `3` `3` `Notations:` `Notations:` `4` `4` `5` `5` `X - input tensor` `X - input tensor` `6` `6` `7` `7` `i - input gate` `i - input gate` `8` `8` `9` `9` `t - time step (t-1 means previous time step)` `t - time step (t-1 means previous time step)` `10` `10` `11` `11` `Wi - W parameter weight matrix for input gate` `Wi - W parameter weight matrix for input gate` `12` `12` `13` `13` `Ri - R recurrence weight matrix for input gate` `Ri - R recurrence weight matrix for input gate` `14` `14` `15` `15` `Wbi - W parameter bias vector for input gate` `Wbi - W parameter bias vector for input gate` `16` `16` `17` `17` `Rbi - R parameter bias vector for input gate` `Rbi - R parameter bias vector for input gate` `18` `18` `19` `19` `WBi - W parameter weight matrix for backward input gate` `WBi - W parameter weight matrix for backward input gate` `20` `20` `21` `21` `RBi - R recurrence weight matrix for backward input gate` `RBi - R recurrence weight matrix for backward input gate` `22` `22` `23` `23` `WBbi - WR bias vectors for backward input gate` `WBbi - WR bias vectors for backward input gate` `24` `24` `25` `25` `RBbi - RR bias vectors for backward input gate` `RBbi - RR bias vectors for backward input gate` `26` `26` `27` `27` `H - Hidden state` `H - Hidden state` `28` `28` `29` `29` `num_directions - 2 if direction == bidirectional else 1` `num_directions - 2 if direction == bidirectional else 1` `30` `30` `31` `31` `Activation functions:` `Activation functions:` `32` `32` `33` `33` ` Relu(x) - max(0, x)` ` Relu(x) - max(0, x)` `34` `34` `35` `35` ` Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})` ` Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})` `36` `36` `37` `37` ` Sigmoid(x) - 1/(1 + e^{-x})` ` Sigmoid(x) - 1/(1 + e^{-x})` `38` `38` `39` `39` ` (NOTE: Below are optional)` ` (NOTE: Below are optional)` `40` `40` `41` `41` ` Affine(x) - alpha*x + beta` ` Affine(x) - alpha*x + beta` `42` `42` `43` `43` ` LeakyRelu(x) - x if x >= 0 else alpha * x` ` LeakyRelu(x) - x if x >= 0 else alpha * x` `44` `44` `45` `45` ` ThresholdedRelu(x) - x if x >= alpha else 0` ` ThresholdedRelu(x) - x if x >= alpha else 0` `46` `46` `47` `47` ` ScaledTanh(x) - alpha*Tanh(beta*x)` ` ScaledTanh(x) - alpha*Tanh(beta*x)` `48` `48` `49` `49` ` HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)` ` HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)` `50` `50` `51` `51` ` Elu(x) - x if x >= 0 else alpha*(e^x - 1)` ` Elu(x) - x if x >= 0 else alpha*(e^x - 1)` `52` `52` `53` `53` ` Softsign(x) - x/(1 + |x|)` ` Softsign(x) - x/(1 + |x|)` `54` `54` `55` `55` ` Softplus(x) - log(1 + e^x)` ` Softplus(x) - log(1 + e^x)` `56` `56` `57` `57` `Equations (Default: f=Tanh):` `Equations (Default: f=Tanh):` `58` `58` `59` ` - Ht = f(Xt*(Wi^T) + Ht-1*(Ri^T) + Wbi + Rbi)` `59` `60` ` - Ht = f(Xt*(Wi^T) + Ht-1*Ri + Wbi + Rbi)` `This operator has **optional** inputs/outputs. See ONNX _ for more details about the representation of optional arguments. An empty string may be used in the place of an actual argument's name to indicate a missing argument. Trailing optional arguments (those not followed by an argument that is present) may also be simply omitted.` `60` `61` `61` `62` `**Attributes**` `**Attributes**` `62` `63` `63` `64` `* **activation_alpha**:` `* **activation_alpha**:` `64` `65` ` Optional scaling values used by some activation functions. The` ` Optional scaling values used by some activation functions. The` `65` `66` ` values are consumed in the order of activation functions, for` ` values are consumed in the order of activation functions, for` `66` `67` ` example (f, g, h) in LSTM. Default values are the same as of` ` example (f, g, h) in LSTM. Default values are the same as of` `67` `68` ` corresponding ONNX operators.For example with LeakyRelu, the default` ` corresponding ONNX operators.For example with LeakyRelu, the default` `68` `69` ` alpha is 0.01.` ` alpha is 0.01.` `69` `70` `* **activation_beta**:` `* **activation_beta**:` `70` `71` ` Optional scaling values used by some activation functions. The` ` Optional scaling values used by some activation functions. The` `71` `72` ` values are consumed in the order of activation functions, for` ` values are consumed in the order of activation functions, for` `72` `73` ` example (f, g, h) in LSTM. Default values are the same as of` ` example (f, g, h) in LSTM. Default values are the same as of` `73` `74` ` corresponding ONNX operators.` ` corresponding ONNX operators.` `74` `75` `* **activations**:` `* **activations**:` `75` `76` ` One (or two if bidirectional) activation function for input gate.` ` One (or two if bidirectional) activation function for input gate.` `76` `77` ` The activation function must be one of the activation functions` ` The activation function must be one of the activation functions` `77` `78` ` specified above. Optional: Default Tanh if not specified. Default value is [b'Tanh' b'Tanh'].` ` specified above. Optional: Default Tanh if not specified. Default value is [b'Tanh' b'Tanh'].` `78` `79` `* **clip**:` `* **clip**:` `79` `80` ` Cell clip threshold. Clipping bounds the elements of a tensor in the` ` Cell clip threshold. Clipping bounds the elements of a tensor in the` `80` `81` ` range of [-threshold, +threshold] and is applied to the input of` ` range of [-threshold, +threshold] and is applied to the input of` `81` `82` ` activations. No clip if not specified.` ` activations. No clip if not specified.` `82` `83` `* **direction**:` `* **direction**:` `83` `84` ` Specify if the RNN is forward, reverse, or bidirectional. Must be` ` Specify if the RNN is forward, reverse, or bidirectional. Must be` `84` `85` ` one of forward (default), reverse, or bidirectional. Default value is 'forward'.` ` one of forward (default), reverse, or bidirectional. Default value is 'forward'.` `85` `86` `* **hidden_size**:` `* **hidden_size**:` `86` `87` ` Number of neurons in the hidden layer` ` Number of neurons in the hidden layer` `87` `* **output_sequence**:` `88` ` The sequence output for the hidden is optional if 0. Default 0. Default value is 0.` `89` `88` `90` `89` `**Inputs**` `**Inputs**` `91` `90` `92` `91` `Between 3 and 6 inputs.` `Between 3 and 6 inputs.` `93` `92` `94` `93` `* **X** (heterogeneous) - **T**:` `* **X** (heterogeneous) - **T**:` `95` `94` ` The input sequences packed (and potentially padded) into one 3-D` ` The input sequences packed (and potentially padded) into one 3-D` `96` `95` ` tensor with the shape of [seq_length, batch_size, input_size].` ` tensor with the shape of [seq_length, batch_size, input_size].` `97` `96` `* **W** (heterogeneous) - **T**:` `* **W** (heterogeneous) - **T**:` `98` `97` ` The weight tensor for input gate. Concatenation of Wi and WBi` ` The weight tensor for input gate. Concatenation of Wi and WBi` `99` `98` ` (if bidirectional). The tensor has shape [num_directions,` ` (if bidirectional). The tensor has shape [num_directions,` `100` `99` ` hidden_size, input_size].` ` hidden_size, input_size].` `101` `100` `* **R** (heterogeneous) - **T**:` `* **R** (heterogeneous) - **T**:` `102` `101` ` The recurrence weight tensor. Concatenation of Ri and RBi (if` ` The recurrence weight tensor. Concatenation of Ri and RBi (if` `103` `102` ` bidirectional). The tensor has shape [num_directions, hidden_size,` ` bidirectional). The tensor has shape [num_directions, hidden_size,` `104` `103` ` hidden_size].` ` hidden_size].` `105` `104` `* **B** (optional, heterogeneous) - **T**:` `* **B** (optional, heterogeneous) - **T**:` `106` `105` ` The bias tensor for input gate. Concatenation of [Wbi, Rbi] and` ` The bias tensor for input gate. Concatenation of [Wbi, Rbi] and` `107` `106` ` [WBbi, RBbi] (if bidirectional). The tensor has shape` ` [WBbi, RBbi] (if bidirectional). The tensor has shape` `108` `107` ` [num_directions, 2*hidden_size]. Optional: If not specified -` ` [num_directions, 2*hidden_size]. Optional: If not specified -` `109` `108` ` assumed to be 0.` ` assumed to be 0.` `110` `109` `* **sequence_lens** (optional, heterogeneous) - **T1**:` `* **sequence_lens** (optional, heterogeneous) - **T1**:` `111` `110` ` Optional tensor specifying lengths of the sequences in a batch. If` ` Optional tensor specifying lengths of the sequences in a batch. If` `112` `111` ` not specified - assumed all sequences in the batch to have length` ` not specified - assumed all sequences in the batch to have length` `113` `112` ` seq_length. It has shape [batch_size].` ` seq_length. It has shape [batch_size].` `114` `113` `* **initial_h** (optional, heterogeneous) - **T**:` `* **initial_h** (optional, heterogeneous) - **T**:` `115` `114` ` Optional initial value of the hidden. If not specified - assumed to` ` Optional initial value of the hidden. If not specified - assumed to` `116` `115` ` be 0. It has shape [num_directions, batch_size, hidden_size].` ` be 0. It has shape [num_directions, batch_size, hidden_size].` `117` `116` `118` `117` `**Outputs**` `**Outputs**` `119` `118` `120` `119` `Between 0 and 2 outputs.` `Between 0 and 2 outputs.` `121` `120` `122` `121` `* **Y** (optional, heterogeneous) - **T**:` `* **Y** (optional, heterogeneous) - **T**:` `123` `122` ` A tensor that concats all the intermediate output values of the` ` A tensor that concats all the intermediate output values of the` `124` `123` ` hidden. It has shape [seq_length, num_directions, batch_size,` ` hidden. It has shape [seq_length, num_directions, batch_size,` `125` `124` ` hidden_size]. It is optional if output_sequence is 0.` ` hidden_size].` `126` `125` `* **Y_h** (optional, heterogeneous) - **T**:` `* **Y_h** (optional, heterogeneous) - **T**:` `127` `126` ` The last output value of the hidden. It has shape [num_directions,` ` The last output value of the hidden. It has shape [num_directions,` `128` `127` ` batch_size, hidden_size].` ` batch_size, hidden_size].` `129` `128` `130` `129` `**Type Constraints**` `**Type Constraints**` `131` `130` `132` `131` `* **T** in (` `* **T** in (` `133` `132` ` tensor(double),` ` tensor(double),` `134` `133` ` tensor(float),` ` tensor(float),` `135` `134` ` tensor(float16)` ` tensor(float16)` `136` `135` ` ):` ` ):` `137` `136` ` Constrain input and output types to float tensors.` ` Constrain input and output types to float tensors.` `138` `137` `* **T1** in (` `* **T1** in (` `139` `138` ` tensor(int32)` ` tensor(int32)` `140` `139` ` ):` ` ):` `141` `140` ` Constrain seq_lens to integer tensor.` ` Constrain seq_lens to integer tensor.`

## RNN - 1#

Version

• name: RNN (GitHub)

• domain: main

• since_version: 1

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 1.

Summary

Computes an one-layer simple RNN. This operator is usually supported via some custom implementation such as CuDNN.

Notations:

X - input tensor

i - input gate

t - time step (t-1 means previous time step)

Wi - W parameter weight matrix for input gate

Ri - R recurrence weight matrix for input gate

Wbi - W parameter bias vector for input gate

Rbi - R parameter bias vector for input gate

WBi - W parameter weight matrix for backward input gate

RBi - R recurrence weight matrix for backward input gate

WBbi - WR bias vectors for backward input gate

RBbi - RR bias vectors for backward input gate

H - Hidden state

num_directions - 2 if direction == bidirectional else 1

Activation functions:

Relu(x) - max(0, x)

Tanh(x) - (1 - e^{-2x})/(1 + e^{-2x})

Sigmoid(x) - 1/(1 + e^{-x})

(NOTE: Below are optional)

Affine(x) - alpha*x + beta

LeakyRelu(x) - x if x >= 0 else alpha * x

ThresholdedRelu(x) - x if x >= alpha else 0

ScaledTanh(x) - alpha*Tanh(beta*x)

HardSigmoid(x) - min(max(alpha*x + beta, 0), 1)

Elu(x) - x if x >= 0 else alpha*(e^x - 1)

Softsign(x) - x/(1 + |x|)

Softplus(x) - log(1 + e^x)

Equations (Default: f=Tanh):

• Ht = f(Xt*(Wi^T) + Ht-1*Ri + Wbi + Rbi)

Attributes

• activation_alpha: Optional scaling values used by some activation functions. The values are consumed in the order of activation functions, for example (f, g, h) in LSTM. Default values are the same as of corresponding ONNX operators.For example with LeakyRelu, the default alpha is 0.01.

• activation_beta: Optional scaling values used by some activation functions. The values are consumed in the order of activation functions, for example (f, g, h) in LSTM. Default values are the same as of corresponding ONNX operators.

• activations: One (or two if bidirectional) activation function for input gate. The activation function must be one of the activation functions specified above. Optional: Default Tanh if not specified. Default value is `[b'Tanh' b'Tanh']`.

• clip: Cell clip threshold. Clipping bounds the elements of a tensor in the range of [-threshold, +threshold] and is applied to the input of activations. No clip if not specified.

• direction: Specify if the RNN is forward, reverse, or bidirectional. Must be one of forward (default), reverse, or bidirectional. Default value is `'forward'`.

• hidden_size: Number of neurons in the hidden layer

• output_sequence: The sequence output for the hidden is optional if 0. Default 0. Default value is `0`.

Inputs

Between 3 and 6 inputs.

• X (heterogeneous) - T: The input sequences packed (and potentially padded) into one 3-D tensor with the shape of [seq_length, batch_size, input_size].

• W (heterogeneous) - T: The weight tensor for input gate. Concatenation of Wi and WBi (if bidirectional). The tensor has shape [num_directions, hidden_size, input_size].

• R (heterogeneous) - T: The recurrence weight tensor. Concatenation of Ri and RBi (if bidirectional). The tensor has shape [num_directions, hidden_size, hidden_size].

• B (optional, heterogeneous) - T: The bias tensor for input gate. Concatenation of [Wbi, Rbi] and [WBbi, RBbi] (if bidirectional). The tensor has shape [num_directions, 2*hidden_size]. Optional: If not specified - assumed to be 0.

• sequence_lens (optional, heterogeneous) - T1: Optional tensor specifying lengths of the sequences in a batch. If not specified - assumed all sequences in the batch to have length seq_length. It has shape [batch_size].

• initial_h (optional, heterogeneous) - T: Optional initial value of the hidden. If not specified - assumed to be 0. It has shape [num_directions, batch_size, hidden_size].

Outputs

Between 0 and 2 outputs.

• Y (optional, heterogeneous) - T: A tensor that concats all the intermediate output values of the hidden. It has shape [seq_length, num_directions, batch_size, hidden_size]. It is optional if output_sequence is 0.

• Y_h (optional, heterogeneous) - T: The last output value of the hidden. It has shape [num_directions, batch_size, hidden_size].

Type Constraints

• T in ( tensor(double), tensor(float), tensor(float16) ): Constrain input and output types to float tensors.

• T1 in ( tensor(int32) ): Constrain seq_lens to integer tensor.