9 research outputs found
On the center of mass of Ising vectors
We show that the center of mass of Ising vectors that obey some simple
constraints, is again an Ising vector.Comment: 8 pages, 3 figures, LaTeX; Claims in connection with disordered
systems have been withdrawn; More detailed description of the simulations;
Inset added to figure
Mutual learning in a tree parity machine and its application to cryptography
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 [1] are analyzed. All analytical results are found to be in good
agreement with simulation results
Training a perceptron in a discrete weight space
On-line and batch learning of a perceptron in a discrete weight space, where
each weight can take different values, are examined analytically and
numerically. The learning algorithm is based on the training of the continuous
perceptron and prediction following the clipped weights. The learning is
described by a new set of order parameters, composed of the overlaps between
the teacher and the continuous/clipped students. Different scenarios are
examined among them on-line learning with discrete/continuous transfer
functions and off-line Hebb learning. The generalization error of the clipped
weights decays asymptotically as / in the case of on-line learning with binary/continuous activation
functions, respectively, where is the number of examples divided by N,
the size of the input vector and is a positive constant that decays
linearly with 1/L. For finite and , a perfect agreement between the
discrete student and the teacher is obtained for . A crossover to the generalization error ,
characterized continuous weights with binary output, is obtained for synaptic
depth .Comment: 10 pages, 5 figs., submitted to PR