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Biomedical subjects

I Kanter

Publications and source records attributed to I Kanter.

At least 19 recordsLinked to original sources
PubMed2002

Secure key-exchange protocol with an absence of injective functions.

The security of neural cryptography is investigated. A key-exchange protocol over a public channel is studied where the parties exchanging secret messages use multilayer neural networks which are trained by their mutual output bits and synchronize to a time dependent secret key. The weights of the networks have integer values between +/-L. Recently an algorithm for an eavesdropper which could break the key was introduced by [A. Shamir, A. Mityagin, and A. Klimov, Ramp Session (Eurocrypt, Amsterdam, 2002)]. We show that the synchronization time increases with L2 while the probability to find a successful attacker decreases exponentially with L. Hence for large L we find a secure key-exchange protocol which depends neither on number theory nor on injective trapdoor functions used in conventional cryptography.

Journal Article↗
PubMed2002

Statistical properties of contact vectors.

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n(i), representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three-dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.

Computational Biology↗
PubMed2001

Training a perceptron in a discrete weight space.

Learning in a perceptron having a discrete weight space, where each weight can take 2L+1 different values, is 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 and continuous transfer functions. The generalization error of the clipped weights decays asymptotically as exp(-Kalpha(2)) in the case of on-line learning with binary activation functions and exp(-e(|lambda|alpha)) in the case of on-line learning with continuous one, where alpha is the number of examples divided by N, the size of the input vector and K is a positive constant. For finite N and L, perfect agreement between the discrete student and the teacher is obtained for alpha~Lsqrt[ln(NL)]. A crossover to the generalization error approximately 1/alpha, characterizing continuous weights with binary output, is obtained for synaptic depth L>O(sqrt[N]).

Journal Article↗
PubMed2001

Multilayer neural networks with extensively many hidden units.

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions, whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter, the storage capacity is found to scale with the logarithm of the number of implementable Boolean functions. The generalization behavior is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.

Models, Statistical↗
PubMed2001

Multichoice minority game.

The generalization of the problem of adaptive competition, known as the minority game, to the case of K possible choices for each player, is addressed, and applied to a system of interacting perceptrons with input and output units of a type of K-state Potts spins. An optimal solution of this minority game, as well as the dynamic evolution of the adaptive strategies of the players, are solved analytically for a general K and compared with numerical simulations.

Journal Article↗
PubMed2001

Generation of unpredictable time series by a neural network.

A perceptron that "learns" the opposite of its own output is used to generate a time series. We analyze properties of the weight vector and the generated sequence, such as the cycle length and the probability distribution of generated sequences. A remarkable suppression of the autocorrelation function is explained, and connections to the Bernasconi model are discussed. If a continuous transfer function is used, the system displays chaotic and intermittent behavior, with the product of the learning rate and amplification as a control parameter.

Journal Article↗
PubMed2000

Cascading parity-check error-correcting codes

A method for improving the performance of sparse-matrix based parity check codes is proposed, based on insight gained from methods of statistical physics. The advantages of this approach are demonstrated on an existing encoding/decoding paradigm suggested by Sourlas. We also discuss the application of the same method to more advanced codes of a similar type.

Journal Article↗
PubMed2000

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.

Journal Article↗
PubMed2000

Interacting neural networks.

Several scenarios of interacting neural networks which are trained either in an identical or in a competitive way are solved analytically. In the case of identical training each perceptron receives the output of its neighbor. The symmetry of the stationary state as well as the sensitivity to the used training algorithm are investigated. Two competitive perceptrons trained on mutually exclusive learning aims and a perceptron which is trained on the opposite of its own output are examined analytically. An ensemble of competitive perceptrons is used as decision-making algorithms in a model of a closed market (El Farol Bar problem or the Minority Game. In this game, a set of agents who have to make a binary decision is considered.); each network is trained on the history of minority decisions. This ensemble of perceptrons relaxes to a stationary state whose performance can be better than random.

Algorithms↗
PubMed1999

Confidence in prediction by neural networks.

The idea that a trained network can assign a confidence number to its prediction, indicating the level of its reliability, is addressed and exemplified by an analytical examination of a perceptron with discrete and continuous output units. Results are derived for both Gibbs and Bayes scenarios. The information gain by the confidence number is estimated by various entropy measurements.

Entropy↗
PubMed1995

On the equivalence of two-layered perceptrons with binary neurons.

We consider two-layered perceptions consisting of N binary input units, K binary hidden units and one binary output unit, in the limit N >> K > or = 1. We prove that the weights of a regular irreducible network are uniquely determined by its input-output map up to some obvious global symmetries. A network is regular if its K weight vectors from the input layer to the K hidden units are linearly independent. A (single layered) perceptron is said to be irreducible if its output depends on every one of its input units; and a two-layered perceptron is irreducible if the K + 1 perceptrons that constitute such network are irreducible. By global symmetries we mean, for instance, permuting the labels of the hidden units. Hence, two irreducible regular two-layered perceptrons that implement the same Boolean function must have the same number of hidden units, and must be composed of equivalent perceptrons.

Computer Simulation↗