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

tf.raw_ops.GRUBlockCellGrad( x, h_prev, w_ru, w_c, b_ru, b_c, r, u, c, d_h, name=None )

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

Args | |
---|---|

`x` | A `Tensor` . Must be one of the following types: `float32` . |

`h_prev` | A `Tensor` . Must have the same type as `x` . |

`w_ru` | A `Tensor` . Must have the same type as `x` . |

`w_c` | A `Tensor` . Must have the same type as `x` . |

`b_ru` | A `Tensor` . Must have the same type as `x` . |

`b_c` | A `Tensor` . Must have the same type as `x` . |

`r` | A `Tensor` . Must have the same type as `x` . |

`u` | A `Tensor` . Must have the same type as `x` . |

`c` | A `Tensor` . Must have the same type as `x` . |

`d_h` | A `Tensor` . Must have the same type as `x` . |

`name` | A name for the operation (optional). |

Returns | |
---|---|

A tuple of `Tensor` objects (d_x, d_h_prev, d_c_bar, d_r_bar_u_bar). | |

`d_x` | A `Tensor` . Has the same type as `x` . |

`d_h_prev` | A `Tensor` . Has the same type as `x` . |

`d_c_bar` | A `Tensor` . Has the same type as `x` . |

`d_r_bar_u_bar` | A `Tensor` . Has the same type as `x` . |

© 2020 The TensorFlow Authors. All rights reserved.

Licensed under the Creative Commons Attribution License 3.0.

Code samples licensed under the Apache 2.0 License.

https://www.tensorflow.org/versions/r2.4/api_docs/python/tf/raw_ops/GRUBlockCellGrad