It is more helpful to describe the convolution and recurrent layers first.
Convolution layer:
Includes input, one or more filters (as well as subsampling).
The input can be one-dimensional or n-dimensional (n>1), for example, it can be a two-dimensional image. One or more filters are also defined in each layer. Inputs are convolving with each filter. The method of convolution is almost similar to the convolution of filters in image processing. In general, the purpose of this section is to extract the features of each filter from the input. The output of each convolution is called a feature map.
For example, a filter is considered for horizontal edges, and the result of its convolution with the input is the extraction of the horizontal edges of the input image. Usually, in practice and especially in the first layers, a large number of filters (for example, 60 filters in one layer) are defined. Also, after convolution, the subsampling operation is usually performed, for example, their maximum or average of each of the two neighborhood values is selected.
The convolution layer allows important features and patterns to be extracted from the input. And delete input data dependencies (linear and nonlinear).
[The following figure shows an example of the use of convolutional layers and pattern extraction for classification.][1]
[1]: https://i.stack.imgur.com/HS4U0.png [Kalhor, A. (2020). Classification and Regression NNs. Lecture.]
Advantages of convolutional layers:
Able to remove correlations and reduce input dimensions
Network generalization is increasing
Network robustness increases against changes because it extracts key features
Very powerful and widely used in supervised learning
...
Recurrent layers:
In these layers, the output of the current layer or the output of the next layers can also be used as the input of the layer. It also can receive time series as input.
The output without using the recurrent layer is as follows (a simple example):
y = f(W * x)
Where x is input, W is weight and f is the activator function.
But in recurrent networks it can be as follows:
y = f(W * x)
y = f(W * y)
y = f(W * y)
... until convergence
This means that in these networks the generated output can be used as an input and thus have memory networks. Some types of recurrent networks are Discrete Hopfield Net and Recurrent Auto-Associative NET, which are simple networks or complex networks such as LSTM.
An example is shown in the image below.
Advantages of Recurrent Layers:
They have memory capability
They can use time series as input.
They can use the generated output for later use.
Very used in machine translation, voice recognition, image description
...
Networks that use convolutional layers are called convolutional networks (CNN). Similarly, networks that use recurrent layers are called recurrent networks. It is also possible to use both layers in a network according to the desired application!