To validate the programmatic implementation of a two-dimensional pooling layer, one can evaluate the pool2d function using a known input tensor. For instance, consider a $3 imes 3$ input tensor X populated with sequential values from $0$ to $8$. Applying a $2 imes 2$ max-pooling layer (the default mode in the implementation) slides the window across the tensor, outputting the maximum value in each $2 imes 2$ region. This results in a $2 imes 2$ output tensor with elements $4$, $5$, $7$, and $8$. Conversely, passing the 'avg' mode argument to the same function calculates the average for each region, producing a $2 imes 2$ tensor with elements $2$, $3$, $5$, and $6$. This practical evaluation confirms that the custom function correctly computes both max and average deterministic aggregations across the input subtensors.