Recently uploaded paper in [Arxiv (1512.06293)][1]. This paper formalize concepts and proves them. And few others that you might check out:

 1. J. Bruna and S. Mallat, “[Invariant Scattering Convolution
Networks][2],” 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][3],” 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][4],” 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
  [2]: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6522407&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6522407
  [3]: http://arxiv.org/abs/1412.0233
  [4]: http://arxiv.org/abs/1410.3831