Problems
Loading...
Step 1 of 6
U-Net Encoder Block
Easy

Implement one numerical U-Net encoder block in NHWC layout. Apply two same-padded convolutions with ReLU, preserve the result as the skip tensor, then apply non-overlapping 2 by 2 max pooling.

S=ReLU⁡(Conv⁡K2(ReLU⁡(Conv⁡K1(X))))S = \operatorname{ReLU}\left(\operatorname{Conv}_{K_2}(\operatorname{ReLU}(\operatorname{Conv}_{K_1}(X)))\right) P=MaxPool⁡2×2(S)P = \operatorname{MaxPool}_{2\times2}(S)

Here, XX is the input, K1K_1 and K2K_2 are supplied odd-sized convolution kernels, SS is the skip tensor, and PP is the pooled tensor. Convolution uses zero padding so height and width are preserved before pooling. Return a Python dictionary with exactly pooled and skip, both float64 NumPy arrays.

Loading visualization...

Examples

Input: x = [[[[1],[-1]],[[2],[0.5]]]], kernel1 = [[[[2,-1]]]], bias1 = [0,0.5], kernel2 = [[[[0.5],[1]]]], bias2 = [0.1]

Output: {"pooled":[[[[2.1]]]],"skip":[[[[1.1],[1.6]],[[2.1],[0.6]]]]}

Explanation: The two convolution stages build the skip features before max pooling halves their spatial dimensions.

Input: x = [[[[1],[2]],[[3],[4]]]], kernel1 = [[[[1,-1]]]], bias1 = [0,1], kernel2 = [[[[0.5,0.2],[1,-0.5]]]], bias2 = [0,0.1]

Output: {"pooled":[[[[2,0.9]]]],"skip":[[[[0.5,0.3],[1,0.5]],[[1.5,0.7],[2,0.9]]]]}

Input: x = [[[[1],[0]],[[-1],[2]]],[[[0.5],[1.5]],[[2.5],[-0.5]]]], kernel1 = [[[[1]]]], bias1 = [0], kernel2 = [[[[2]]]], bias2 = [-0.5]

Output: {"pooled":[[[[3.5]]],[[[4.5]]]],"skip":[[[[1.5],[0]],[[0],[3.5]]],[[[0.5],[2.5]],[[4.5],[0]]]]}

Hint 1

Pad only the height and width axes by kernel_size // 2.

Hint 2

Use np.tensordot to contract a spatial patch with a convolution kernel.

Hint 3

Reshape paired spatial positions before reducing them with max.

Requirements

  • Use NumPy.
  • Apply each supplied convolution, bias, and ReLU in order.
  • Use same zero padding for every odd kernel size.
  • Apply non-overlapping 2 by 2 max pooling to the skip tensor.
  • Return exactly the documented float64 arrays.

Constraints

  • x has shape (B, H, W, C) and dtype float64.
  • H and W are positive even integers.
  • Both kernels are square with the same positive odd spatial size.
  • Kernel input and output channels match adjacent tensors and biases.
  • All kernels and biases have dtype float64.
Prev1 / 6Next