The upsampling operation of bilinear interpolation can be implemented using a transposed convolutional layer by initializing its weights with a specially constructed bilinear kernel. A programmatic implementation of this kernel calculates weights based on relative distances from the center. For example, the bilinear_kernel function constructs a kernel tensor where the values decrease linearly from the center, effectively mimicking the distance-weighted averaging of bilinear interpolation.

def bilinear_kernel(in_channels, out_channels, kernel_size):
    factor = (kernel_size + 1) // 2
    if kernel_size % 2 == 1:
        center = factor - 1
    else:
        center = factor - 0.5
    og = (torch.arange(kernel_size).reshape(-1, 1),
          torch.arange(kernel_size).reshape(1, -1))
    filt = (1 - torch.abs(og[0] - center) / factor) * \
           (1 - torch.abs(og[1] - center) / factor)
    weight = torch.zeros((in_channels, out_channels,
                          kernel_size, kernel_size))
    weight[range(in_channels), range(out_channels), :, :] = filt
    return weight