Conv2D Forward Pass

Implement the forward pass of a 2-D convolution over a single channel image.

Zero pad the input by padding pixels on all four sides, then slide the kernel with the given stride, and at each position take the elementwise product with the window and sum it.

out_h = (H + 2 * padding - kH) // stride + 1
out_w = (W + 2 * padding - kW) // stride + 1

Two things to get right:

• This is cross correlation, not textbook convolution. Do not flip the kernel. Every deep learning framework calls this operation convolution, and since the kernel is learned the flip would make no difference to what the network can express.
• Pad with zeros, and pad before striding, not after.

Return an array of shape (out_h, out_w). If the padded input is smaller than the kernel, return an empty (0, 0) array.

Function signature

def conv2d(x, kernel, stride=1, padding=0):

Example

Input

x      = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
kernel = np.array([[1, 0], [0, 1]])
conv2d(x, kernel, stride=1, padding=0)

Output

array([[ 6.,  8.],
       [12., 14.]])

Reasoning

The kernel adds the top left and bottom right of each 2 by 2 window: 1 + 5 = 6, 2 + 6 = 8, 4 + 8 = 12 and 5 + 9 = 14.

Constraints and notes

• Do not flip the kernel.
• Pad with zeros before you apply the stride.
• If the padded input is smaller than the kernel, return an empty (0, 0) array.