Theory of Interacting Neural Networks

In this contribution we give an overview over recent work on the theory of interacting neural networks. The model is defined in Section 2. The typical teacher/student scenario is considered in Section 3. A static teacher network is presenting training examples for an adaptive student network. In the case of multilayer networks, the student shows a transition from a symmetric state to specialisation. Neural networks can also generate a time series. Training on time series and predicting it are studied in Section 4. When a network is trained on its own output, it is interacting with itself. Such a scenario has implications on the theory of prediction algorithms, as discussed in Section 5. When a system of networks is trained on its minority decisions, it may be considered as a model for competition in closed markets, see Section 6. In Section 7 we consider two mutually interacting networks. A novel phenomenon is observed: synchronisation by mutual learning. In Section 8 it is shown, how this phenomenon can be applied to cryptography: Generation of a secret key over a public channel.Comment: Contribution to Networks, ed. by H.G. Schuster and S. Bornholdt, to be published by Wiley VC

Synchronization of random walks with reflecting boundaries

Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are found to increase proportional to the square of the system size. Additionally, the probability of synchronization in a given step is analyzed, which converges to a geometric distribution for long synchronization times. From this asymptotic behavior the number of steps required to synchronize an ensemble of independent random walk pairs is deduced. Here the synchronization time increases with the logarithm of the ensemble size. The results of this model are compared to those observed in neural synchronization.Comment: 10 pages, 7 figures; introduction changed, typos correcte

Pulses of chaos synchronization in coupled map chains with delayed transmission

Pulses of synchronization in chaotic coupled map lattices are discussed in the context of transmission of information. Synchronization and desynchronization propagate along the chain with different velocities which are calculated analytically from the spectrum of convective Lyapunov exponents. Since the front of synchronization travels slower than the front of desynchronization, the maximal possible chain length for which information can be transmitted by modulating the first unit of the chain is bounded.Comment: 4 pages, 6 figures, updated version as published in PR

Neural Cryptography

Two neural networks which are trained on their mutual output bits show a novel phenomenon: The networks synchronize to a state with identical time dependent weights. It is shown how synchronization by mutual learning can be applied to cryptography: secret key exchange over a public channel.Comment: 9th International Conference on Neural Information Processing, Singapore, Nov. 200

Interacting neural networks and cryptography

Two neural networks which are trained on their mutual output bits are analysed using methods of statistical physics. The exact solution of the dynamics of the two weight vectors shows a novel phenomenon: The networks synchronize to a state with identical time dependent weights. Extending the models to multilayer networks with discrete weights, it is shown how synchronization by mutual learning can be applied to secret key exchange over a public channel.Comment: Invited talk for the meeting of the German Physical Societ

Limit cycles of a perceptron

An artificial neural network can be used to generate a series of numbers. A boolean perceptron generates bit sequences with a periodic structure. The corresponding spectrum of cycle lengths is investigated analytically and numerically; it has similarities with properties of rational numbers.Comment: LaTeX and 4 postscript pages of figure