Fully Connected Layers

Each feature in the final spatial layer is connected to each hidden state in the first fully connected layer. This layer functions in exactly the same way as a traditional feed-forward network. In most cases, one might use more than one fully connected layer to increase the power of the computations towards the end. The connections among these layers are exactly structured like a traditional feed-forward network. Since the fully connected layers are densely connected, the vast majority of parameters lie in the fully connected layers. For example, if each of two fully connected layers has 4096 hidden units, then the connections between them have more than 16 million weights. Similarly, the connections from the last spatial layer to the first fully connected layer will have a large number of parameters.Even though the convolutional layers have a larger number of activations (and a larger memory footprint), the fully connected layers often have a larger number of connections (and parameter footprint). The reason that activations contribute to the memory footprint more significantly is that the number of activations are multiplied by mini-batch size while tracking variables in the forward and backward passes of backpropagation. These trade-offs are useful to keep in mind while choosing neural-network design based on specific types of resource constraints (e.g., data versus memory availability). It is noteworthy that the nature of the fully-connected layer can be sensitive to the application at hand. 

For example,the nature of the fully-connected layer for a classification application would be somewhatdifferent from the case of a segmentation application. The aforementioned discussion is for the most common use-case of a classification application.The output layer of a convolutional neural network is designed in an application-specific way. In the following, we will consider the representative application of classification. In such a case, the output layer is fully connected to every neuron in the penultimate layer, and has a weight associated with it. One might use the logistic, softmax, or linear activation depending on the nature of the application (e.g., classification or regression).

One alternative to using fully connected layers is to use average pooling across the whole spatial area of the final set of activation maps to create a single value. Therefore, the number of features created in the final spatial layer will be exactly equal to the number of filters. In this scenario, if the final activation maps are of size 7 × 7 × 256, then 256 features will be created. Each feature will be the result of aggregating 49 values. This type of approach greatly reduces the parameter footprint of the fully connected layers, and it has some advantages in terms of generalizability. This approach was used in GoogLeNet. In some applications like image segmentation, each pixel is associated with a class label, and one does not use fully connected layers. Fully convolutional networks with 1×1 convolutions are used in order to create an output spatial map.

The Interleaving Between Layers

The convolution, pooling, and ReLU layers are typically interleaved in a neural network in order to increase the expressive power of the network. The ReLU layers often follow the convolutional layers, just as a nonlinear activation function typically follows the linear dot product in traditional neural networks. Therefore, the convolutional and ReLU layers are typically stuck together one after the other. Some pictorial illustrations of neural architectures like AlexNet  do not explicitly show the ReLU layers because they are assumed to be always stuck to the end of the linear convolutional layers. After two or three sets of convolutional-ReLU combinations, one might have a max-pooling layer. Examples of this

basic pattern are as follows:

CRCRP

CRCRCRP

Here, the convolutional layer is denoted by C, the ReLU layer is denoted by R, and the max-pooling layer is denoted by P. This entire pattern (including the max-pooling layer) might be repeated a few times in order to create a deep neural network. For example, if the first pattern above is repeated three times and followed by a fully connected layer (denoted by F), then we have the following neural network:

CRCRPCRCRPCRCRPF

The description above is not complete because one needs to specify the number/size/padding of filters/pooling layers. The pooling layer is the key step that tends to reduce the spatial footprint of the activation maps because it uses strides that are larger than 1. It is also possible to reduce the spatial footprints with strided convolutions instead of max-pooling. These networks are often quite deep, and it is not uncommon to have convolutional networks with more than 15 layers. Recent architectures also use skip connections between layers, which become increasingly important as the depth of the network increases.

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