2002/09/10 by Michal Rosen‐Zvi, Michal Rosen-Zvi, Einat Klein +2 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Physics and Astronomy · #Advanced Memory and Neural Computing #Neural Networks and Applications #Receptor Mechanisms and Signaling #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.66.066135
arxiv created 2002/09/10 · openalex publication_date 2002/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mutual learning of a pair of tree parity machines with continuous and discrete weight vectors is studied analytically. The analysis is based on a mapping procedure that maps the mutual learning in tree parity machines onto mutual learning in noisy perceptrons. The stationary solution of the mutual learning in the case of continuous tree parity machines depends on the learning rate where a phase transition from partial to full synchronization is observed. In the discrete case the learning process is based on a finite increment and a full synchronized state is achieved in a finite number of steps. The synchronization of discrete parity machines is introduced in order to construct an ephemeral key-exchange protocol. The dynamic learning of a third tree parity machine (an attacker) that tries to imitate one of the two machines while the two still update their weight vectors is also analyzed. In particular, the synchronization times of the naive attacker and the flipping attacker recently introduced in Ref. 9 are analyzed. All analytical results are found to be in good agreement with simulation results.