RNN Sequence Forward

Run a vanilla RNN over a whole sequence. X has one input vector per row; starting from the hidden state h0, apply $h_t=\tanh (W_x{x}_t+W_h{h}_{t-1}+b)h\_t=\backslash tanh(W\_xx\_t+W\_hh\_\{t-1\}+b)$ for each row in order.

Implement solve(X, h0, Wx, Wh, b).

Returns. Return an array of shape (T, hidden) whose row $tt$ is the hidden state after reading input $tt$ (the initial state h0 is not included).

Examples

Example 1

Input:

solve([[1.0], [2.0]], [0.0], [[1.0]], [[0.5]], [0.0])

Output:

[[0.761594], [0.983041]]

Example 2

Input:

solve([[0.0], [0.0], [0.0]], [1.0], [[1.0]], [[1.0]], [0.0])

Output:

[[0.761594], [0.642015], [0.56627]]