We study the problem of supervised learning in a scenario with a student, a teacher and a book. The student and teacher learn using the Hebbian learning rule, but while the teacher’s training set comes exclusively from the book, the student receives examples from the book and from the teacher....

We study the problem of determining the Hamiltonian of a fully connected Ising spin glass of N units from a set of measurements, whose sizes needs to be O(N2) bits. The student–teacher scenario, used to study learning in feed-forward neural networks, is here extended to spin systems with...

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. A large...

We introduce a neural network with the ability of recalling p non-random patterns displaying a hierarchical distribution of activities for all p⩽N − 1, N being the number of neurons. The stability of the retrieval states is studied as a function of temperature T and α = p/N. The temperature...

A fully connected set of formal neurons that has not been subject to any training algorithm is studied. The thresholds and couplings are random variables chosen from Gaussian distributions. The dynamics of the model can be studied within a mean field approximation. Our results show a change of...

The small-world phenomenon, popularly known as six degrees of separation, has been mathematically formalized by Watts and Strogatz in a study of the topological properties of a network. Small-world networks are defined in terms of two quantities: they have a high clustering coefficient C like...

The aim of this work is to examine how neural networks can be used for solving the problem of the forecast of large financial crashes due to the presence of speculative bubbles. Some microeconomic theories have been developed for the explanation of a bubble due to a cooperation among the...

We present a training algorithm for multilayer perceptrons which relates to the technique of principal component analysis. The latter is performed with respect to a correlation matrix which is computed from the example inputs and their target outputs. For large networks the novel procedure...

A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type is extended and analyzed here for a symmetrically diluted network with finite connectivity near saturation. Equations for the dynamics and the stationary states are obtained for the...

We examine a simple biologically motivated neural network, the three-layer version of the Chialvo–Bak ‘minibrain’ (Neurosci. 90 (1999) 1137), and present numerical results which indicate that a non-equilibrium phase transition between ordered and disordered phases occurs subject to the...