On measuring similarity between different two-layered networks

Abstract

In this paper we present a method for calculating g , the generalization error of two-layered networks. g is the fraction of the input space for which two networks yield di erent answers therefore it is a good index to measure the similarity between them. The method presented here is an extension of work reported previously. It is applied here to the case of a single-layer perceptron (which can be regarded as a particular two-layered perceptron) that tries to imitate a two-layered network. The particular realizations of such two-layered network that are analyzed here are the parity-machine, the and-machine and the committeemachine. We have also compared the input{output mapping of a committee and a parity machine.

Two-layer tree-connected feed-forward neural network model for neural cryptography

“…With the random input vectors, the generation error ε is the probability of the event that two corresponding hidden units have different σ . It can be computed from the overlap ρ [27,28],…”

“…According to Property 4, feasible conditions (19), (20), (24), and (28) are equivalent to each other, among which (28) will be most frequently used in the following.…”

“…(R 1 ) For the constructed protocol, it is preferable to let H 3. If we let H = 2, the feasibility should be further checked by applying (28).…”

“…In the same manner, from the classification of TPM (K = 3), TPCM (K = 3), and ( 1 ) 2 (+1,−1,+1) (+1,+1,−1) (+1,+1,+1) TCPM (K = 3), it can be found that H = 2. Therefore, their feasibilities should be further checked by applying (28).…”