Problems

Overlapping Max Pooling

Easy

Implement two-dimensional max pooling for an NHWC tensor. A square window of width $K$ moves by stride $s$ , and each output keeps the largest value independently in every batch item and channel.

Y_{n,i,j,c}=\max_{0\le u,v<K}X_{n,is+u,js+v,c}.

Here, $n$ is the batch index, $(i,j)$ is the output location, and $c$ is the channel. AlexNet used windows larger than their stride, so neighboring windows overlap. Return the pooled values as a float64 NumPy array with shape $(B,H_{out},W_{out},C)$ .

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Examples

Input: x = [[[[1],[2],[3],[4]],[[5],[6],[7],[8]],[[9],[10],[11],[12]],[[13],[14],[15],[16]]]], kernel_size = 3, stride = 1

Output: [[[[11],[12]],[[15],[16]]]]

Explanation: Each three-by-three window contributes its maximum value, and stride one makes adjacent windows overlap.

Input: x = [[[[1,8],[2,7]],[[3,6],[4,5]]]], kernel_size = 2, stride = 1

Output: [[[[4,8]]]]

Input: x = [[[[1],[5],[2],[4]],[[3],[0],[7],[6]],[[8],[2],[9],[1]],[[4],[3],[5],[0]]]], kernel_size = 2, stride = 2

Output: [[[[5],[7]],[[8],[9]]]]

Hint 1

Slice each window with row * stride and column * stride as its top-left corner.

Hint 2

np.max(window, axis=(1, 2)) preserves the batch and channel axes.

Requirements

Compute the maximum value in every valid spatial window.
Pool each batch item and channel independently.
Do not pad the input.
Return a new float64 NumPy array.

Constraints

x has shape $(B,H,W,C)$ .
kernel_size and stride are positive integers.
kernel_size is no larger than the input height or width.
Output sizes are $H_{out}=\lfloor(H-K)/s\rfloor+1$ and $W_{out}=\lfloor(W-K)/s\rfloor+1$ .

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