How does " Sparsity of connections" in CNNs causes the network to have less parameters? I am studying Andrew NG's lectures on Convolutional Neural Network and he had provided two reasons for CNNs having less parameters compared to Non-Convolutional networks . They are :

Parameter Sharing
Sparsity of connections .

While I can make sense of the first reason causing CNN to have less parameters . I don't understand why Sparsity of connections , that is , &quot; Each output in a layer comes from a small number of inputs &quot; cause the network to have less parameters .
Isn't the second reason a bit redundant ?
Can someone please explain ?
In fact these involve different aspects of parameters in a CNN.

Parameter sharing, means one parameter may be shared by more than one input/connection. So this reduces total amount of independent parameters. Parameters shared are non-zero.
Sparsity of connections means that some parameters are simply missing (ie are zero), nothing to do with sharing same non-zero parameter. Parameters in this case are zero, ignored. That means that not necessarily all (potential) inputs to a layer are actually connected to that layer, only some of them, rest are ignored. Thus sparsity of connections.