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Computes the GRU cell back-propagation for 1 time step.

Args x: Input to the GRU cell. h_prev: State input from the previous GRU cell. w_ru: Weight matrix for the reset and update gate. w_c: Weight matrix for the cell connection gate. b_ru: Bias vector for the reset and update gate. b_c: Bias vector for the cell connection gate. r: Output of the reset gate. u: Output of the update gate. c: Output of the cell connection gate. d_h: Gradients of the h_new wrt to objective function.

Returns d_x: Gradients of the x wrt to objective function. d_h_prev: Gradients of the h wrt to objective function. d_c_bar Gradients of the c_bar wrt to objective function. d_r_bar_u_bar Gradients of the r_bar & u_bar wrt to objective function.

This kernel op implements the following mathematical equations:

Note on notation of the variables:

Concatenation of a and b is represented by a_b Element-wise dot product of a and b is represented by ab Element-wise dot product is represented by \circ Matrix multiplication is represented by *

`w_ru` can be segmented into 4 different matrices.

w_ru = [w_r_x w_u_x
w_r_h_prev w_u_h_prev]

Similarly, `w_c` can be segmented into 2 different matrices.
w_c = [w_c_x w_c_h_prevr]

Same goes for biases.
b_ru = [b_ru_x b_ru_h]
b_c = [b_c_x b_c_h]

Another note on notation:
d_x = d_x_component_1 + d_x_component_2

where d_x_component_1 = d_r_bar * w_r_x^T + d_u_bar * w_r_x^T
and d_x_component_2 = d_c_bar * w_c_x^T

d_h_prev = d_h_prev_component_1 + d_h_prevr \circ r + d_h \circ u
where d_h_prev_componenet_1 = d_r_bar * w_r_h_prev^T + d_u_bar * w_r_h_prev^T

d_c_bar = d_h \circ (1-u) \circ (1-c \circ c)
d_u_bar = d_h \circ (h-c) \circ u \circ (1-u)

d_r_bar_u_bar = [d_r_bar d_u_bar]

[d_x_component_1 d_h_prev_component_1] = d_r_bar_u_bar * w_ru^T

[d_x_component_2 d_h_prevr] = d_c_bar * w_c^T

d_x = d_x_component_1 + d_x_component_2

d_h_prev = d_h_prev_component_1 + d_h_prevr \circ r + u

Below calculation is performed in the python wrapper for the Gradients (not in the gradient kernel.)
d_w_ru = x_h_prevr^T * d_c_bar

d_w_c = x_h_prev^T * d_r_bar_u_bar

d_b_ru = sum of d_r_bar_u_bar along axis = 0

d_b_c = sum of d_c_bar along axis = 0

Public Methods

 static GRUBlockCellGrad ( Scope scope, Operand x, Operand hPrev, Operand wRu, Operand wC, Operand bRu, Operand bC, Operand r, Operand u, Operand c, Operand dH) Factory method to create a class wrapping a new GRUBlockCellGrad operation. Output () Output () Output Output ()

Public Methods

public static GRUBlockCellGrad <T> create ( Scope scope, Operand <T> x, Operand <T> hPrev, Operand <T> wRu, Operand <T> wC, Operand <T> bRu, Operand <T> bC, Operand <T> r, Operand <T> u, Operand <T> c, Operand <T> dH)

Factory method to create a class wrapping a new GRUBlockCellGrad operation.

Parameters
 scope current scope
Returns
• a new instance of GRUBlockCellGrad

public Output <T> dX ()

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