Threshold-induced phase transitions in perceptrons

Error rates of a Boolean perceptron with threshold and either spherical or Ising constraint on the weight vector are calculated for storing patterns from biased input and output distributions derived within a one-step replica symmetry breaking (RSB) treatment. For unbiased output distribution and non-zero stability of the patterns, we find a critical load, α p, above which two solutions to the saddlepoint equations appear; one with higher free energy and zero threshold and a dominant solution with non-zero threshold. We examine this second-order phase transition and the dependence of α p on the required pattern stability, κ, for both one-step RSB and replica symmetry (RS) in the spherical case and for one-step RSB in the Ising case.

Finite-size effects in on-line learning of multilayer neural networks

We complement recent advances in thermodynamic limit analyses of mean on-line gradient descent learning dynamics in multi-layer networks by calculating fluctuations possessed by finite dimensional systems. Fluctuations from the mean dynamics are largest at the onset of specialisation as student hidden unit weight vectors begin to imitate specific teacher vectors, increasing with the degree of symmetry of the initial conditions. In light of this, we include a term to stimulate asymmetry in the learning process, which typically also leads to a significant decrease in training time.

Learning with regularizers in multilayer neural networks

We study the effect of regularization in an on-line gradient-descent learning scenario for a general two-layer student network with an arbitrary number of hidden units. Training examples are randomly drawn input vectors labelled by a two-layer teacher network with an arbitrary number of hidden units which may be corrupted by Gaussian output noise. We examine the effect of weight decay regularization on the dynamical evolution of the order parameters and generalization error in various phases of the learning process, in both noiseless and noisy scenarios.

Globally optimal parameters for on-line learning in multilayer neural networks

We present a framework for calculating globally optimal parameters, within a given time frame, for on-line learning in multilayer neural networks. We demonstrate the capability of this method by computing optimal learning rates in typical learning scenarios. A similar treatment allows one to determine the relevance of related training algorithms based on modifications to the basic gradient descent rule as well as to compare different training methods.

Globally optimal learning rates in multilayer neural networks

A method for calculating the globally optimal learning rate in on-line gradient-descent training of multilayer neural networks is presented. The method is based on a variational approach which maximizes the decrease in generalization error over a given time frame. We demonstrate the method by computing optimal learning rates in typical learning scenarios. The method can also be employed when different learning rates are allowed for different parameter vectors as well as to determine the relevance of related training algorithms based on modifications to the basic gradient descent rule.

Enterprise networking:multilayer switching and applications

Primarily targeted toward the network or MIS manager who wants to stay abreast of the latest networking technology, Enterprise Networking: Multilayer Switching and Applications offers up to date information relevant for the design of modern corporate networks and for the evaluation of new networking equipment. The book describes the architectures and standards of switching across the various protocol layers and will also address issues such as multicast quality of service, high-availability and network policies that are requirements of modern switched networks.

Exploitation of multilayer coatings for infrared surface plasmon resonance fiber sensors

We demonstrate surface plasmon resonance (SPR) fiber devices based upon ultraviolet inscription of a grating-type structure into both single-layered and multilayered thin films deposited on the flat side of a lapped D-shaped fiber. The single-layered devices were fabricated from germanium, while the multilayered ones comprised layers of germanium, silica, and silver. Some of the devices operated in air with high coupling efficiency in excess of 40 dB and an estimated index sensitivity of Delta lambda/Delta n = 90 mn from 1 to 1.15 index range, while others provided an index sensitivity of Delta lambda/Delta n = 6790 mn for refractive indices from 1.33 to 1.37. (C) 2009 Optical Society of America

Parallel strategy for optimal learning in perceptrons

We developed a parallel strategy for learning optimally specific realizable rules by perceptrons, in an online learning scenario. Our result is a generalization of the Caticha–Kinouchi (CK) algorithm developed for learning a perceptron with a synaptic vector drawn from a uniform distribution over the N-dimensional sphere, so called the typical case. Our method outperforms the CK algorithm in almost all possible situations, failing only in a denumerable set of cases. The algorithm is optimal in the sense that it saturates Bayesian bounds when it succeeds.

Computational capabilities of multilayer committee machines

We obtained an analytical expression for the computational complexity of many layered committee machines with a finite number of hidden layers (L < 8) using the generalization complexity measure introduced by Franco et al (2006) IEEE Trans. Neural Netw. 17 578. Although our result is valid in the large-size limit and for an overlap synaptic matrix that is ultrametric, it provides a useful tool for inferring the appropriate architecture a network must have to reproduce an arbitrary realizable Boolean function.

Large extraordinary Hall effect in [Pt/Co]5/Ru/[Co/Pt]5 multilayer

This Brief Report presents giant extraordinary Hall effect (EHE) in the Ru-mediated antiferromagnetically coupled [Pt/Co]5/Ru/[Co/Pt]5 multilayers (MLs) compared with those MLs without the Ru spacer. The enhancement of the EHE is attributed to the strong Ru/Co interface scattering. Through the variation in the Pt layer thickness and the temperature, we determine the relation between the Hall voltage and the longitudinal resistivity. It is found that the conventional scaling analysis has difficulties in consistently interpreting our data.

Numerical modelling of multilayer semiconductor devices

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A 20-Mb/s VLC link with a polymer LED and a multilayer perceptron equalizer

This letter experimentally demonstrates a visible light communication system using a 350-kHz polymer lightemitting diode operating at a total bit rate of 19 Mb/s with a bit error rate (BER) of 10-6and 20 Mb/s at the forward error correction limit for the first time. This represents a remarkable net data rate gain of ~55 times. The modulation format adopted is ON-OFF keying in conjunction with an artificial neural network classifier implemented as an equalizer. The number of neurons used in the experiment is varied from the set N = {5, 10, 20, 30, 40} with 40 neurons offering the best performance at 19 Mb/s and the BER of 10-6.

A facile spin-cast route for cation exchange of multilayer perpendicularly-aligned nanorod assemblies

A facile spin cast route was developed to convert perpendicularly aligned nanorod assemblies of cadmium chalcogenides into their silver and copper analogues. The assemblies are rapidly cation exchanged without affecting either the individual rod dimensions or collective superlattice order extending over several multilayers.

Supercapattery based on binder-free Co3 (PO4)2·8H2O multilayer nano/microflakes on nickel foam

A binder-free cobalt phosphate hydrate (Co3(PO4)2·8H2O) multilayer nano/microflake structure is synthesized on nickel foam (NF) via a facile hydrothermal process. Four different concentrations (2.5, 5, 10, and 20 mM) of Co2+ and PO4–3 were used to obtain different mass loading of cobalt phosphate on the nickel foam. The Co3(PO4)2·8H2O modified NF electrode (2.5 mM) shows a maximum specific capacity of 868.3 C g–1 (capacitance of 1578.7 F g–1) at a current density of 5 mA cm–2 and remains as high as 566.3 C g–1 (1029.5 F g–1) at 50 mA cm–2 in 1 M NaOH. A supercapattery assembled using Co3(PO4)2·8H2O/NF as the positive electrode and activated carbon/NF as the negative electrode delivers a gravimetric capacitance of 111.2 F g–1 (volumetric capacitance of 4.44 F cm–3). Furthermore, the device offers a high specific energy of 29.29 Wh kg–1 (energy density of 1.17 mWh cm–3) and a specific power of 4687 W kg–1 (power density of 187.5 mW cm–3).