MaxPool2D Forward + Backward

Implement max pooling — the standard downsampling operation in CNNs. A sliding window takes the maximum value in each non-overlapping region, reducing spatial dimensions while retaining the strongest activations.

Forward pass: For each pooling window of size pool_size × pool_size, output the maximum value across all spatial positions (per channel). Also track which position held the max (the mask) — needed for the backward pass.

Backward pass: Gradients flow only to the position that was the max in the forward pass; all other positions get 0. The mask encodes this routing.

Signature: def maxpool2d(x, pool_size=2, stride=2)

• x: (H, W, C) — input feature map, channels-last
• pool_size: int — pooling window size (default 2)
• stride: int — step between windows (default 2)
• Returns: (output, mask) where:
  • output: (H_out, W_out, C) — max values, where H_out = (H - pool_size) // stride + 1
  • mask: (H, W, C) boolean — True at the position that was max in each window

The test harness checks the pooled output values. Your mask must correctly mark exactly one True per window per channel.