Network — total trainable parameters

Background

A feedforward network is a list of layer sizes, e.g. [i, h, o]. The input layer holds no weights — parameters live between consecutive layers. So the total is the sum of each dense layer's parameter count:

$$\text{total} = \sum_{\ell} \bigl(s_{\ell}\,s_{\ell+1} + s_{\ell+1}\bigr)$$

where $s_\ell$ are the layer sizes in order.

Problem statement

Implement network_params(sizes) returning the total number of trainable parameters for a fully connected network described by the list sizes.

Input

• sizes — list of int layer sizes, input first, output last (length $\ge 1$).

Output

Returns an int: the summed parameters over all consecutive layer pairs.

Examples

Example 1 — the lesson's i=3, h=4, o=2 net

Input:  sizes = [3, 4, 2]
Output: 26

Explanation: $(3\cdot4+4) + (4\cdot2+2) = 16 + 10 = 26$.

Example 2 — a single layer

Input:  sizes = [5, 3]
Output: 18

Explanation: one dense layer, $5\cdot3+3 = 18$.

Constraints

• The input layer contributes no parameters; only count between consecutive sizes.
• A list with one element (just an input) has 0 parameters.
• Return a plain int.

Notes

• This is the network's capacity in raw scalar count. More/wider layers grow it fast — more flexible, but easier to overfit.