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There are convolution layers, pooling layers, and possibly a classifier layer (e.g. softmax layer) in a convolutional neural network (CNN).

I heard that there is also a fully-connected layer. What is that?

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Every neuron from the previous layer is connected to every neuron on the next layer1.

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The convolutional and the Pooling layers create a feature space, and the flatten FUlly connected layer can be thought as a cheap way of learning a linear function out of the feature space. For the convenience of understanding think of it as a PCA that selects the good features among the feature space created by the Conv and POOL layer.

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