Generally, each problem has an appropriate model configuration. I recommend that you test the model against the various configurations. I recommend reading the following article I wrote on how to set up neural networks.

Article Analysis of training techniques of ANN for classification of...

Thanks Stéfano Frizzo Stefenon

Hi

Please check the following link. I believe it will help you.

https://www.researchgate.net/post/How_to_decide_the_number_of_hidden_layers_and_nodes_in_a_hidden_layer

Regards

Dropout by N Srivastava

A simple way to reduce connectivity is to use early stopping. Each epoch plot your test and train error. When the test error starts to rise (overfitting) stop the training. This results in many connections with low weights which is reduced connectivity.

A similar question here: https://www.researchgate.net/post/How_to_decide_the_number_of_hidden_layers_and_nodes_in_a_hidden_layer

A genetic algorithm can be helpful in your case.

There is a tendency to build deeper and deeper networks because they can represent/learn more complex features but they also need a lot of data to be trained. You can start also from an already trained network. I don't think it is a good idea to remove layers.

Prunning connections (dropout) is a way to avoid overfitting. Removing half of them randomly is a standard procedure. Read

http://jmlr.org/papers/volume15/srivastava14a/srivastava14a.pdf