according to my knowledge
1 neuron and 1 layer -> known as a perceptron
2 or more neurons, 1 layer, 1 input --> as an equation of a line y = w*x + w0
2 or more neurons, 1 layer, multiple input instances --> hyper plane
when you add the sigmoid functionality to the output of these neurons activations and combine these in another perceptron or multiple neurons you get a non-linear combination of hyper-planes.
the thing that make CNN to be called CNN instead of a simple Deep Neural Network is that you learn local neighborhood weights that can be in any part of the image. So there is a weight sharing process between neuron activations.
- suppose you had N different 20x20 gray scale images and 5 hidden units in 1 layer,
- if you were to implement a fully connected deep neural network, you would try learning a weight matrix of 400x5 - hence 2000 parameters - for the first hidden layer. and as the output you would have 5 dimensional vectors for each N image.
- but in a cnn structure, you decide on a reasonable patch size in these 20x20 images, lets say 4x4, and learn 5 different 4x4 weights - hence 80 parameters. And as the output of this first hidden layer you would have 5 different 17x17 images for each N image. In other way of looking at the output of first layer is 1445 dimensional vectors for each N image. So it is like you learn less parameters but as the output you have more dimensions to learn from.
So when I look at your questions,
If there was only 1 layer and the classification/regression was made after that 1 single layer it wouldn't be called DBN. But it could still be called CNN because there is the concept of 'convolution' and 'neural network'. And of course with 1 single layer there would be no 'backpropogation'.
Backpropogation is needed when there is more than 1 layer present. Because the concept is to be able to backpropogate some error without having a 'real/expected output' which we can see in the middle layers. We only have ground truth for the last layer where we have our regression/classification. Hence, if I understood your question correctly, backprop here falls under deep network category.
We can not say 'CNNs do not follow same pattern as DBN'. Because they certainly are DBNs with weight sharing functionalities.
I hope this answers your questions. And additionally I think it would be nice to point out the difference between DBN and DNN here.
Quoting from another website (https://www.quora.com/Deep-Learning/What-are-the-difference-and-relevance-between-DNN-and-DBN)
“Deep Belief Networks construct beliefs (probablilistical relationships between instances) based on unsupervised data, and then apply those relationships to a problem when presented with supervised data.
Basically, learn on unsupervised, where there is more data to learn from, then use on a problem.
Deep neural networks are simply large multilayer neural networks.”</p>