LSTM#

LSTM - 14 #

Version

name: LSTM (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 LSTM. This operator is usually supported via some custom implementation such as CuDNN.

Notations:

X - input tensor

i - input gate

o - output gate

f - forget gate

c - cell gate

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

W[iofc] - W parameter weight matrix for input, output, forget, and cell gates

R[iofc] - R recurrence weight matrix for input, output, forget, and cell gates

Wb[iofc] - W bias vectors for input, output, forget, and cell gates

Rb[iofc] - R bias vectors for input, output, forget, and cell gates

P[iof] - P peephole weight vector for input, output, and forget gates

WB[iofc] - W parameter weight matrix for backward input, output, forget, and cell gates

RB[iofc] - R recurrence weight matrix for backward input, output, forget, and cell gates

WBb[iofc] - W bias vectors for backward input, output, forget, and cell gates

RBb[iofc] - R bias vectors for backward input, output, forget, and cell gates

PB[iof] - P peephole weight vector for backward input, output, and forget gates

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=Sigmoid, g=Tanh, h=Tanh):

it = f(Xt*(Wi^T) + Ht-1*(Ri^T) + Pi (.) Ct-1 + Wbi + Rbi)

ft = f(Xt*(Wf^T) + Ht-1*(Rf^T) + Pf (.) Ct-1 + Wbf + Rbf)

ct = g(Xt*(Wc^T) + Ht-1*(Rc^T) + Wbc + Rbc)

Ct = ft (.) Ct-1 + it (.) ct

ot = f(Xt*(Wo^T) + Ht-1*(Ro^T) + Po (.) Ct + Wbo + Rbo)

Ht = ot (.) h(Ct)

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: A list of 3 (or 6 if bidirectional) activation functions for input, output, forget, cell, and hidden. The activation functions must be one of the activation functions specified above. Optional: See the equations for default if not specified.
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.
hidden_size: Number of neurons in the hidden layer
input_forget: Couple the input and forget gates if 1.
layout: The shape format of inputs X, initial_h, initial_c and outputs Y, Y_h, Y_c. 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 = initial_c.shape = Y_c.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 = initial_c.shape = Y_c.shape = [batch_size, num_directions, hidden_size].

Inputs

Between 3 and 8 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 the gates. Concatenation of W[iofc] and WB[iofc] (if bidirectional) along dimension 0. The tensor has shape [num_directions, 4*hidden_size, input_size].
R (heterogeneous) - T: The recurrence weight tensor. Concatenation of R[iofc] and RB[iofc] (if bidirectional) along dimension 0. This tensor has shape [num_directions, 4*hidden_size, hidden_size].
B (optional, heterogeneous) - T: The bias tensor for input gate. Concatenation of [Wb[iofc], Rb[iofc]], and [WBb[iofc], RBb[iofc]] (if bidirectional) along dimension 0. This tensor has shape [num_directions, 8*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].
initial_c (optional, heterogeneous) - T: Optional initial value of the cell. If not specified - assumed to be 0. It has shape [num_directions, batch_size, hidden_size].
P (optional, heterogeneous) - T: The weight tensor for peepholes. Concatenation of P[iof] and PB[iof] (if bidirectional) along dimension 0. It has shape [num_directions, 3*hidde_size]. Optional: If not specified - assumed to be 0.

Outputs

Between 0 and 3 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].
Y_c (optional, heterogeneous) - T: The last output value of the cell. 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

import numpy as np
import onnx

input = np.array([[[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]]).astype(np.float32)

input_size = 2
hidden_size = 3
weight_scale = 0.1
number_of_gates = 4

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

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

lstm = LSTM_Helper(X=input, W=W, R=R)
_, Y_h = lstm.step()
expect(
    node,
    inputs=[input, W, R],
    outputs=[Y_h.astype(np.float32)],
    name="test_lstm_defaults",
)

_initial_bias

import numpy as np
import onnx

input = np.array([[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]]]).astype(
    np.float32
)

input_size = 3
hidden_size = 4
weight_scale = 0.1
custom_bias = 0.1
number_of_gates = 4

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

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

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

lstm = LSTM_Helper(X=input, W=W, R=R, B=B)
_, Y_h = lstm.step()
expect(
    node,
    inputs=[input, W, R, B],
    outputs=[Y_h.astype(np.float32)],
    name="test_lstm_with_initial_bias",
)

_peepholes

import numpy as np
import onnx

input = np.array([[[1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0]]]).astype(
    np.float32
)

input_size = 4
hidden_size = 3
weight_scale = 0.1
number_of_gates = 4
number_of_peepholes = 3

node = onnx.helper.make_node(
    "LSTM",
    inputs=["X", "W", "R", "B", "sequence_lens", "initial_h", "initial_c", "P"],
    outputs=["", "Y_h"],
    hidden_size=hidden_size,
)

# Initializing Inputs
W = weight_scale * np.ones(
    (1, number_of_gates * hidden_size, input_size)
).astype(np.float32)
R = weight_scale * np.ones(
    (1, number_of_gates * hidden_size, hidden_size)
).astype(np.float32)
B = np.zeros((1, 2 * number_of_gates * hidden_size)).astype(np.float32)
seq_lens = np.repeat(input.shape[0], input.shape[1]).astype(np.int32)
init_h = np.zeros((1, input.shape[1], hidden_size)).astype(np.float32)
init_c = np.zeros((1, input.shape[1], hidden_size)).astype(np.float32)
P = weight_scale * np.ones((1, number_of_peepholes * hidden_size)).astype(
    np.float32
)

lstm = LSTM_Helper(
    X=input, W=W, R=R, B=B, P=P, initial_c=init_c, initial_h=init_h
)
_, Y_h = lstm.step()
expect(
    node,
    inputs=[input, W, R, B, seq_lens, init_h, init_c, P],
    outputs=[Y_h.astype(np.float32)],
    name="test_lstm_with_peepholes",
)

_batchwise

import numpy as np
import onnx

input = np.array([[[1.0, 2.0]], [[3.0, 4.0]], [[5.0, 6.0]]]).astype(np.float32)

input_size = 2
hidden_size = 7
weight_scale = 0.3
number_of_gates = 4
layout = 1

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

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

lstm = LSTM_Helper(X=input, W=W, R=R, layout=layout)
Y, Y_h = lstm.step()
expect(
    node,
    inputs=[input, W, R],
    outputs=[Y.astype(np.float32), Y_h.astype(np.float32)],
    name="test_lstm_batchwise",
)

LSTM - 7 vs 14

LSTM - 7 #

Version

name: LSTM (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.