A stride is the number of pixels a convolutional filter jumps each time it moves across an input. A stride of 1 checks every neighboring position; a stride of 2 skips one pixel between positions. section 12.17
Halving a feature map
A downsampling layer uses a 4×4 filter with stride 2 on an 8×8 feature map. The filter jumps two pixels at a time, producing a 4×4 output and a more compressed summary of the image. Padding adds a border of blank values to help preserve edge information. section 12.17
Figure 12.35 How filters scan an image with padding
Trace how a padded filter scans an image and how stride changes the filter’s successive positions. section 12.17
def apply_padding_3d(tensor, padding): #A
return np.pad(tensor, ((0, 0), (padding, padding),
➥(padding, padding)), mode='constant', constant_values=0)
def downsample_convolution(feature_maps_in, num_output_channels):
input_channels = feature_maps_in.shape[0]
input_height = feature_maps_in.shape[1]
filter_size = 4
stride = 2
padding = 1
padded_maps = apply_padding_3d(feature_maps_in, padding)
output_height = (input_height + 2 * padding - filter_size)
➥// stride + 1 #B
output_width = output_height
filters = np.random.randn(num_output_channels,
➥input_channels, filter_size, filter_size) * 0.01 #C
biases = np.random.randn(num_output_channels) * 0.01
feature_maps_out = []
for k in range(num_output_channels):
current_bias = biases[k]
output_map = np.zeros((output_height, output_width))
for i in range(output_height):
for j in range(output_width):
accumulation_sum = 0
for c in range(input_channels):
current_filter = filters[k, c]
r_start, c_start = i * stride, j * stride
region = padded_maps[c, r_start : r_start +
➥filter_size, c_start : c_start + filter_size] #D
accumulation_sum += np.sum(region * current_filter)
output_map[i, j] =
➥accumulation_sum + current_bias #E
feature_maps_out.append(output_map)
h2 = np.stack(feature_maps_out, axis=0)
return h2
Inspect a NumPy-style downsampling convolution where stride, padding, filter size, and output dimensions are configured explicitly. section 12.17
