Is it possible to do feature selection within the Keras deep learning framework?

I know most people perform feature selection running RFE on a linear regression model, for example, BEFORE training the model with Keras.

However is it possible to do it within the training procedure of the deep neural network? If so how? Are there any downsides to it?

I think a deep neural network does feature selection by default during training and searches for the most important information, but it can lead to overfitting and/or make convergence slower.