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In the paper Wrist-worn blood pressure tracking in healthy free-living individuals using neural networks, the authors talk about a combination of feed-forward and recurrent layers, as if FC layers cannot be part of the RNN.

So, must all Convolutional Neural Networks and Recurrent Neural Networks not have a fully connected layer in order to be considered CNNs and RNNs, respectively? If yes, should we consider CNNs and RNNs with an FC layer "hybrid models"?

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Not quite sure about RNN & LSTM (and it always depends on the task), but for CNN the answer is clearly no; CNN routinely include FC layers. Quoting from the highly popular (and recommended) Stanford course CS231n: Convolutional Neural Networks for Visual Recognition:

ConvNet Architectures

We have seen that Convolutional Networks are commonly made up of only three layer types: CONV, POOL (we assume Max pool unless stated otherwise) and FC (short for fully-connected).

You can easily verify that this is the case for practically all popular CNN models for computer vision in any relevant exposition (e.g. Illustrated: 10 CNN Architectures).

In fact, the all-convolutional NN (i.e. without FC layers) is considered a special case: see Striving for Simplicity: The All Convolutional Net.

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