1,964 research outputs found
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
Cryptography based on neural networks - analytical results
Mutual learning process between two parity feed-forward networks with
discrete and continuous weights is studied analytically, and we find that the
number of steps required to achieve full synchronization between the two
networks in the case of discrete weights is finite. The synchronization process
is shown to be non-self-averaging and the analytical solution is based on
random auxiliary variables. The learning time of an attacker that is trying to
imitate one of the networks is examined analytically and is found to be much
longer than the synchronization time. Analytical results are found to be in
agreement with simulations
Phase Transitions of Neural Networks
The cooperative behaviour of interacting neurons and synapses is studied
using models and methods from statistical physics. The competition between
training error and entropy may lead to discontinuous properties of the neural
network. This is demonstrated for a few examples: Perceptron, associative
memory, learning from examples, generalization, multilayer networks, structure
recognition, Bayesian estimate, on-line training, noise estimation and time
series generation.Comment: Plenary talk for MINERVA workshop on mesoscopics, fractals and neural
networks, Eilat, March 1997 Postscript Fil
Replica Symmetry Breaking and the Kuhn-Tucker Cavity Method in simple and multilayer Perceptrons
Within a Kuhn-Tucker cavity method introduced in a former paper, we study
optimal stability learning for situations, where in the replica formalism the
replica symmetry may be broken, namely
(i) the case of a simple perceptron above the critical loading, and
(ii) the case of two-layer AND-perceptrons, if one learns with maximal
stability.
We find that the deviation of our cavity solution from the replica symmetric
one in these cases is a clear indication of the necessity of replica symmetry
breaking. In any case the cavity solution tends to underestimate the storage
capabilities of the networks.Comment: 32 pages, LaTex Source with 9 .eps-files enclosed, accepted by J.
Phys I (France
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