LSTM Cell

Compute one LSTM cell update. The single weight matrix W has shape (4H, d + H) and acts on the concatenation [x, h]; the four resulting gate blocks, each of length $HH$, are in the order input, forget, output, candidate ($i,f,o,gi,f,o,g$). The bias b has length $4H4H$.

Implement solve(x, h, c, W, b).

Returns. Return a tuple (h_new, c_new) with $c_{new}=\sigma (f)\odot c+\sigma (i)\odot \tanh (g)c\_\{new\}=\backslash sigma(f)\backslash odot\; c+\backslash sigma(i)\backslash odot\backslash tanh(g)$ and $h_{new}=\sigma (o)\odot \tanh (c_{new})h\_\{new\}=\backslash sigma(o)\backslash odot\backslash tanh(c\_\{new\})$.

Examples

Example 1

Input:

solve([1.0], [0.0], [0.0], np.zeros((4, 2)), np.zeros(4))

Output:

([0.0], [0.0])

Example 2

Input:

solve([0.0], [0.0], [2.0], np.zeros((4, 2)), [0.0, 4.0, 4.0, 0.0])

Output:

([0.944104], [1.964028])