2,090 research outputs found

### Learning and generation of long-range correlated sequences

We study the capability to learn and to generate long-range, power-law
correlated sequences by a fully connected asymmetric network. The focus is set
on the ability of neural networks to extract statistical features from a
sequence. We demonstrate that the average power-law behavior is learnable,
namely, the sequence generated by the trained network obeys the same
statistical behavior. The interplay between a correlated weight matrix and the
sequence generated by such a network is explored. A weight matrix with a
power-law correlation function along the vertical direction, gives rise to a
sequence with a similar statistical behavior.Comment: 5 pages, 3 figures, accepted for publication in Physical Review

### Robust chaos generation by a perceptron

The properties of time series generated by a perceptron with monotonic and
non-monotonic transfer function, where the next input vector is determined from
past output values, are examined. Analysis of the parameter space reveals the
following main finding: a perceptron with a monotonic function can produce
fragile chaos only whereas a non-monotonic function can generate robust chaos
as well. For non-monotonic functions, the dimension of the attractor can be
controlled monotonically by tuning a natural parameter in the model.Comment: 7 pages, 5 figures (reduced quality), accepted for publication in
EuroPhysics Letter

### Dynamics of Interacting Neural Networks

The dynamics of interacting perceptrons is solved analytically. For a
directed flow of information the system runs into a state which has a higher
symmetry than the topology of the model. A symmetry breaking phase transition
is found with increasing learning rate. In addition it is shown that a system
of interacting perceptrons which is trained on the history of its minority
decisions develops a good strategy for the problem of adaptive competition
known as the Bar Problem or Minority Game.Comment: 9 pages, 3 figures; typos corrected, content reorganize

### Secure and linear cryptosystems using error-correcting codes

A public-key cryptosystem, digital signature and authentication procedures
based on a Gallager-type parity-check error-correcting code are presented. The
complexity of the encryption and the decryption processes scale linearly with
the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted
by Bob, whereas a private-noise added by Alice to a given fraction of the
ciphertext of each encrypted plaintext serves to increase the secure channel
and is the cornerstone for digital signatures and authentication. Various
scenarios are discussed including the possible actions of the opponent Oscar as
an eavesdropper or as a disruptor

### The Entropy of a Binary Hidden Markov Process

The entropy of a binary symmetric Hidden Markov Process is calculated as an
expansion in the noise parameter epsilon. We map the problem onto a
one-dimensional Ising model in a large field of random signs and calculate the
expansion coefficients up to second order in epsilon. Using a conjecture we
extend the calculation to 11th order and discuss the convergence of the
resulting series

### Secure exchange of information by synchronization of neural networks

A connection between the theory of neural networks and cryptography is
presented. A new phenomenon, namely synchronization of neural networks is
leading to a new method of exchange of secret messages. Numerical simulations
show that two artificial networks being trained by Hebbian learning rule on
their mutual outputs develop an antiparallel state of their synaptic weights.
The synchronized weights are used to construct an ephemeral key exchange
protocol for a secure transmission of secret data. It is shown that an opponent
who knows the protocol and all details of any transmission of the data has no
chance to decrypt the secret message, since tracking the weights is a hard
problem compared to synchronization. The complexity of the generation of the
secure channel is linear with the size of the network.Comment: 11 pages, 5 figure

### Statistical mechanical aspects of joint source-channel coding

An MN-Gallager Code over Galois fields, $q$, based on the Dynamical Block
Posterior probabilities (DBP) for messages with a given set of autocorrelations
is presented with the following main results: (a) for a binary symmetric
channel the threshold, $f_c$, is extrapolated for infinite messages using the
scaling relation for the median convergence time, $t_{med} \propto 1/(f_c-f)$;
(b) a degradation in the threshold is observed as the correlations are
enhanced; (c) for a given set of autocorrelations the performance is enhanced
as $q$ is increased; (d) the efficiency of the DBP joint source-channel coding
is slightly better than the standard gzip compression method; (e) for a given
entropy, the performance of the DBP algorithm is a function of the decay of the
correlation function over large distances.Comment: 6 page

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