def _GRUBlockCellGrad(op, *grad):
r"""Gradient for GRUBlockCell.
Args:
op: Op for which the gradient is defined.
*grad: Gradients of the optimization function wrt output
for the Op.
Returns:
d_x: Gradients wrt to x
d_h: Gradients wrt to h
d_w_ru: Gradients wrt to w_ru
d_w_c: Gradients wrt to w_c
d_b_ru: Gradients wrt to b_ru
d_b_c: Gradients wrt to b_c
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
```
"""
x, h_prev, w_ru, w_c, b_ru, b_c = op.inputs
r, u, c, _ = op.outputs
_, _, _, d_h = grad
d_x, d_h_prev, d_c_bar, d_r_bar_u_bar = gen_gru_ops.gru_block_cell_grad(
x, h_prev, w_ru, w_c, b_ru, b_c, r, u, c, d_h)
x_h_prev = array_ops.concat([x, h_prev], 1)
d_w_ru = math_ops.matmul(x_h_prev, d_r_bar_u_bar, transpose_a=True)
d_b_ru = nn_ops.bias_add_grad(d_r_bar_u_bar)
x_h_prevr = array_ops.concat([x, h_prev * r], 1)
d_w_c = math_ops.matmul(x_h_prevr, d_c_bar, transpose_a=True)
d_b_c = nn_ops.bias_add_grad(d_c_bar)
return d_x, d_h_prev, d_w_ru, d_w_c, d_b_ru, d_b_c
def _GRUBlockCellGrad(op, *grad):
r"""Gradient for GRUBlockCell.
Args:
op: Op for which the gradient is defined.
*grad: Gradients of the optimization function wrt output
for the Op.
Returns:
d_x: Gradients wrt to x
d_h: Gradients wrt to h
d_w_ru: Gradients wrt to w_ru
d_w_c: Gradients wrt to w_c
d_b_ru: Gradients wrt to b_ru
d_b_c: Gradients wrt to b_c
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
```
"""
x, h_prev, w_ru, w_c, b_ru, b_c = op.inputs
r, u, c, _ = op.outputs
_, _, _, d_h = grad
d_x, d_h_prev, d_c_bar, d_r_bar_u_bar = gen_gru_ops.gru_block_cell_grad(
x, h_prev, w_ru, w_c, b_ru, b_c, r, u, c, d_h)
x_h_prev = array_ops.concat([x, h_prev], 1)
d_w_ru = math_ops.matmul(x_h_prev, d_r_bar_u_bar, transpose_a=True)
d_b_ru = nn_ops.bias_add_grad(d_r_bar_u_bar)
x_h_prevr = array_ops.concat([x, h_prev * r], 1)
d_w_c = math_ops.matmul(x_h_prevr, d_c_bar, transpose_a=True)
d_b_c = nn_ops.bias_add_grad(d_c_bar)
return d_x, d_h_prev, d_w_ru, d_w_c, d_b_ru, d_b_c
