Analytical and Numerical Study of Internal Representations in Multilayer   Neural Networks with Binary Weights
  We study the weight space structure of the parity machine with binary weights by deriving the distribution of volumes associated to the internal representations of the learning examples. The learning behaviour and the symmetry breaking transition are analyzed and the results are found to be in very good agreement with extended numerical simulations. 
Simona Cocco, Remi Monasson and Riccardo Zecchina