increase in number of filters in convolutional neural nets

Question

I am self-studying CNNs, and have noticed that in many implementations the number of feature maps / filters increase as we get deeper in the network (closer to the output layer). What is the intuition / reason for this? How does this help learning? (example from a typical CNN below, with an increase from 32 to 64 to 128)

net2 = NeuralNet(
    layers=[
        ('input', layers.InputLayer),
        ('conv1', layers.Conv2DLayer),
        ('pool1', layers.MaxPool2DLayer),
        ('conv2', layers.Conv2DLayer),
        ('pool2', layers.MaxPool2DLayer),
        ('conv3', layers.Conv2DLayer),
        ('pool3', layers.MaxPool2DLayer),
        ('hidden4', layers.DenseLayer),
        ('hidden5', layers.DenseLayer),
        ('output', layers.DenseLayer),
        ],
    input_shape=(None, 1, 96, 96),
    conv1_num_filters=32, conv1_filter_size=(3, 3), pool1_pool_size=(2, 2),
    conv2_num_filters=64, conv2_filter_size=(2, 2), pool2_pool_size=(2, 2),
    conv3_num_filters=128, conv3_filter_size=(2, 2), pool3_pool_size=(2, 2),
    hidden4_num_units=500, hidden5_num_units=500,
    output_num_units=30, output_nonlinearity=None,

    update_learning_rate=0.01,
    update_momentum=0.9,

    regression=True,
    max_epochs=1000,
    verbose=1,
    )

Answer 1

Here is an example of what a convolutional network might be looking for, layer by layer.

Layer 1: simple edges at various orientations

Layer 2: combinations of simple edges that form more complex edges and textures such as rounded edges or multiple edges touching

Layer 3: combinations of complex edges that form parts of objects, such as circles or grid like patterns

Layer 4: combinations of object parts that form whole objects, such as faces, cars, or trees

Each layer has a much wider scope of different things it can look for. The first layer doesn't have a wide variety of things to look for because it is so general. There are vertical edges, horizontal edges, diagonal edges, and some angles in between. But the final layer has a huge variety of things it could be looking for, so a larger number of filters is beneficial.

This image may also make it clearer. A technique is used to visualize the learned filters of the first, 2nd, and 3rd layers.