Calculate Parameter Count for Grouped Convolutions

Implement a function to calculate the parameter count ratio between grouped convolutions and standard convolutions. Grouped convolutions are a technique used in ConvNext architectures to reduce computational costs by splitting input and output channels into $G$ groups, where each group operates on a subset of the channels.

This process can be broken down into the following steps:

Determine the number of parameters in a standard convolution, given by $K_W \times K_H \times C_{in} \times C_{out}$ .
Calculate the number of parameters in a grouped convolution, where each of the $G$ groups operates on $C_{in}/G$ input channels producing $C_{out}/G$ output channels. The key formula for the ratio of parameters is

\text{Ratio} = \frac{\text{Params}_G}{\text{Params}_S}

This technique is widely used in deep learning models for image classification tasks.

Example:

Input:

K_W=3, K_H=3, C_in=256, C_out=256, G=4

Output:

0.25

Reasoning:

Standard: 3×3×256×256 = 589,824. Grouped (G=4): 4×(3×3×64×64) = 147,456. Ratio = 147,456/589,824 = 0.25 = 1/G

Constraints:

$K_W = K_H = 3$ (kernel size)
$C_{in} = C_{out} = 256$ (channels)
$G$ is a divisor of $C_{in}$ : $1 \leq G \leq C_{in}$

Example:

Constraints:

Test Results