RNN parameters — weight sharing across time

Background

An RNN reuses the same weights at every timestep, so its parameter count depends on the sizes, not the sequence length. For input size $D$ and hidden size $H$:

$$\underbrace{H \cdot D}_{W_{xh}} + \underbrace{H \cdot H}_{W_{hh}} + \underbrace{H}_{b_h} = H\,(D + H + 1)$$

Problem statement

Implement rnn_param_count(input_size, hidden_size) returning the number of parameters in a vanilla RNN cell.

Input

• input_size — int, $D$.
• hidden_size — int, $H$.

Output

Returns an int: $H(D + H + 1)$.

Examples

Example 1

Input:  input_size = 3, hidden_size = 4
Output: 32

Explanation: $4\times3 + 4\times4 + 4 = 12 + 16 + 4 = 32$.

Example 2

Input:  input_size = 10, hidden_size = 20
Output: 620

Constraints

• Count W_xh ($H\times D$), W_hh ($H\times H$), and bias ($H$).
• The answer must not depend on the sequence length.
• Return a plain int.

Notes

• This length-independence is exactly weight sharing: a 5-token and a 500-token sequence use the identical parameter budget, which is how RNNs handle variable-length inputs.