Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9306039

Neural networks with high order connections

J. J. Arenzon·R. M. C. de Almeida
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical simulations. An optimal learning algorithm for fourth order connections is given that improves the storage capacity without increasing the weight of the higher order term. While the behavior of one of the models qualitatively resembles the original Hopfield one, the other presents a new and very rich behavior: depending on the strength of the fourth order connections and the temperature, the system presents two distinct retrieval regions separated by a gap, as well as several phase transitions. Also, the spin glass states seems to disappear above a certain value of the load parameter $α$, $α_g$.

Explore related subjects

cond-matq-bio.NC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. J. Arenzon, R. M. C. de Almeida. 1993-06-17. Neural networks with high order connections. https://doi.org/10.1103/physreve.48.4060

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2017

Random-Matrix Theory of Quantum Size Effects on Nuclear Magnetic Resonance in Metal Particles

The distribution function of the local density of states is computed exactly for the Wigner-Dyson ensemble of random Hamiltonians. In the absence of time-reversal symmetry, precise agreement is obtained with the "supersymmetry" theory by Efetov and Prigodin of the NMR lineshape in disordered metal particles. Upon breaking time-reversal symmetry, the variance of the Knight shift in the smallest particles is reduced by a universal factor of 2/3. ***To be published in Physical Review B.****

cond-mat↗
arXiv2017

Andreev Reflection In Ferromagnet-Superconductor Junctions

The transport properties of a ferromagnet-superconductor (FS) junction are studied in a scattering formulation. Andreev reflection at the FS interface is strongly affected by the exchange interaction in the ferromagnet. The conductance G_FS of a ballistic point contact between F and S can be both larger or smaller than the value G_FN with the superconductor in the normal state, depending on the ratio of the exchange and Fermi energies. If the ferromagnet contains a tunnel barrier (I), the conductance G_FIFS exhibits resonances which do not vanish in linear response -- in contrast to the Tomasch oscillations for non-ferromagnetic materials.

cond-mat↗
arXiv2017

Long-Range Energy-Level Interaction in Small Metallic Particles

We consider the energy level statistics of non-interacting electrons which diffuse in a $ d $-dimensional disordered metallic conductor of characteristic Thouless energy $ E_c. $ We assume that the level distribution can be written as the Gibbs distribution of a classical one-dimensional gas of fictitious particles with a pairwise additive interaction potential $ f(\varepsilon ). $ We show that the interaction which is consistent with the known correlation function of pairs of energy levels is a logarithmic repulsion for level separations $ \varepsilon E_c, $ $ f(\varepsilon ) $ vanishes as a power law in $ \varepsilon /E_c $ with exponents $ -{1 \over 2},-2, $ and $ -{3 \over 2} $ for $ d=1,2, $ and 3, respectively. While for $ d=1,2 $ the energy-level interaction is always repulsive, in three dimensions there is long-range level attraction after the short-range logarithmic repulsion.

cond-mat↗