Neural Networks - Difference between one dimensional layer vs multi-dimensional layer

Question

Please take a look at these Neural Network architectures:

I can understand the architecture of Hidden Layer in Net-2 : you add 12 Neurons to your hidden layer...

What I can't understand is the 2-dimensional hidden layers in Net-3, Net-4 and Net-5.

What exactly is a multi-dimensional hidden layer and how can it be implemented? is it an array of 1-dimensional hidden layers? or something else?

Thank you...

Answer 1

The 2D layer is what called the convolutional layer.
In some sense it is an array of 1-dimensional hidden layers that performs discrete convolution to the input, often with properties like local connectivity and shared weights (as shown in the figure).

Here's a good introduction to convolutional neural networks http://cs231n.github.io/convolutional-networks/