Hi Khaled,

Particularly 'Notes on Convolutional Neural Networks ' article is found mathematically comprehend and easy to understand CNN. It can be accessed in following link.

http://www.cogprints.org/5869/1/cnn_tutorial.pdf

Bests

M M Manjurul Islam

The difference between statistical learning theory (which has a mathematical model) and deep learning is neatly summarised here: https://www.quora.com/What-are-the-advantages-and-disadvantages-of-deep-learning-Can-you-compare-it-with-the-statistical-learning-theory

Dear Sir,

U can read this article

Article Understanding Convolutional Neural Networks with A Mathematical Model

http://www.wildml.com/2015/11/understanding-convolutional-neural-networks-for-nlp/

Although deep learning often outperforms classical pattern recognition methods experimentally, a mathematical theory to explain its behavior and performance is nevertheless lacking. Without a solid understanding of deep learning, we can only have a set of empirical rules and intuitions, which is not sufficient to advance the scientific knowledge profoundly. There has been a large amount of efforts devoted to the understanding of CNNs from various angles. Examples include scattering networks [2, 3, 4], tensor analysis [5], generative modeling [6], relevance propagation [7], Taylor decomposition [8], etc. Another popular topic along this line is on the visualization of filter responses at various layers [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. 

Kindly have a look onto the following URL for further details;

https://www.linkedin.com/pulse/deep-convolutional-neural-networks-mathematical-model-fernandes

Thanks