Problems
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Step 5 of 6
U-Net Output Layer
Easy

Implement U-Net's final 1 by 1 convolution as a per-pixel linear projection.

Yb,h,w,:=Xb,h,w,:Wout+boutY_{b,h,w,:} = X_{b,h,w,:}W_{\mathrm{out}} + b_{\mathrm{out}}

Here, XX has CC feature channels, WoutW_{\mathrm{out}} has shape (C,K)(C,K), and KK is the number of segmentation classes. Do not apply an activation. Return raw logits as a float64 NumPy array with shape (B,H,W,K)(B,H,W,K).

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Examples

Input: features = [[[[1,-1],[0.5,2]]]], W_out = [[0.3,-0.2],[0.5,0.1]], b_out = [0.1,-0.1]

Output: [[[[-0.1,-0.4],[1.25,0]]]]

Explanation: The same channel-to-class projection is applied independently at each pixel.

Input: features = [[[[1],[2]],[[3],[4]]]], W_out = [[0.25]], b_out = [-0.5]

Output: [[[[-0.25],[0]],[[0.25],[0.5]]]]

Input: features = [[[[0,1,-1]]],[[[2,-0.5,1]]]], W_out = [[1,0],[0,1],[0.5,-0.5]], b_out = [0.2,0.3]

Output: [[[[-0.3,1.8]]],[[[2.7,-0.7]]]]

Hint 1

The final feature axis aligns with the first axis of W_out.

Hint 2

NumPy broadcasts b_out across batch and spatial axes.

Requirements

  • Use NumPy.
  • Apply the supplied channel projection independently at every pixel.
  • Add the supplied class bias.
  • Do not apply sigmoid or softmax.
  • Return a float64 NumPy array.

Constraints

  • features has shape (B, H, W, C) and dtype float64.
  • W_out has shape (C, K) and dtype float64.
  • b_out has shape (K) and dtype float64.
  • All dimensions are positive.
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