Recently uploaded paper in [Arxiv][1]. This paper formalize concepts and proves them. And few other thinks that you might check out:

[1] J. Bruna and S. Mallat, “Invariant Scattering Convolution
Networks,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 35, no. 8, pp. 1872–1886, Aug. 2013.
- for Covnet

[2] A. Choromanska, M. Henaff, M. Mathieu, G. B. Arous, and Y. LeCun,
“The Loss Surfaces of Multilayer Networks,” arXiv:1412.0233 [cs], Nov.
2014.
- Spin Glasses Theory
- for Deep MLP and Convnet

[3] P. Mehta and D. J. Schwab, “An exact mapping between the
Variational Renormalization Group and Deep Learning,” arXiv:1410.3831
[cond-mat, stat], Oct. 2014.
- for Restricted Boltzmann Machine, Deep Belief Network and Deep
Boltzmann Machine.


  [1]: http://arxiv.org/abs/1512.06293