GRU Cell

Compute one GRU update. W has shape (2H, d + H) and produces the reset and update gates (in that order) from [x, h] plus the bias b; Wh has shape (H, d + H) and, together with the bias bh, produces the candidate state from [x, r ⊙ h]. The new state is $(1-z)\odot h+z\odot \tilde{h}(1-z)\backslash odot\; h+z\backslash odot\backslash tilde\; h$.

Implement solve(x, h, W, b, Wh, bh).

Returns. Return the new hidden state as a NumPy vector of length $HH$.

Examples

Example 1

Input:

solve([1.0], [2.0], np.zeros((2, 2)), [0.0, 0.0], np.zeros((1, 2)), [0.0])

Output:

[1.0]

Example 2

Input:

solve([0.0], [0.0], np.zeros((2, 2)), [0.0, 0.0], np.zeros((1, 2)), [0.0])

Output:

[0.0]