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GRUBlockCellGrad

public final class GRUBlockCellGrad

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 *

Additional notes for clarity:

`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
 
Mathematics behind the Gradients below:
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 <T extends Number> 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.
Output<T>
dCBar()
Output<T>
dHPrev()
Output<T>
Output<T>
dX()

Inherited Methods

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> dCBar ()

public Output<T> dHPrev ()

public Output<T> dRBarUBar ()

public Output<T> dX ()