Dense layer — count the parameters

Background

A fully connected (dense) layer from $n_{\text{in}}$ inputs to $n_{\text{out}}$ outputs has a weight matrix plus one bias per output neuron:

$$\text{params} = n_{\text{in}} \times n_{\text{out}} + n_{\text{out}}$$

Every input connects to every output ($n_{\text{in}}\,n_{\text{out}}$ weights), and each output neuron adds a bias ($n_{\text{out}}$ more).

Problem statement

Implement dense_params(n_in, n_out) returning the number of trainable parameters in one dense layer.

Input

• n_in — int, number of input neurons.
• n_out — int, number of output neurons.

Output

Returns an int: $n_{\text{in}}\,n_{\text{out}} + n_{\text{out}}$.

Examples

Example 1

Input:  n_in = 5, n_out = 3
Output: 18

Explanation: $5\times3 + 3 = 15 + 3 = 18$.

Example 2 — the lesson's first layer

Input:  n_in = 3, n_out = 4
Output: 16

Explanation: $3\times4 + 4 = 16$.

Constraints

• Count weights and biases: $n_{\text{in}}\,n_{\text{out}} + n_{\text{out}}$.
• Return a plain int.

Notes

• A handy refactor is $n_{\text{out}}\,(n_{\text{in}} + 1)$ — the "+1" is the bias folded in as an extra input that is always 1.