Perceptron Convergence Theorem Research Articles

Multilayered artificial neural network for performance prediction of an adiabatic solar liquid desiccant dehumidifier

Abstract In this study, a multi-layered artificial neural network (ANN) algorithm was developed and trained to predict the performance of a solar powered liquid desiccant air conditioning (LDAC) system particularly the adiabatic packed tower dehumidifier using Lithium Bromide (LiBr) desiccant. A reinforced technique of supervised learning based on error correction principle rule coupled with perceptron convergence theorem was applied to create the algorithm. The parameters such as temperature, flow rates and humidity ratio of both air and desiccant fluid were fed as inputs to the ANN algorithm and their respective outputs used to determine dehumidifier effectiveness and moisture removal rate (MRR). The ANN model when subjected to validity tests using vapour pressure of LiBr desiccant solution at specific random temperatures and concentrations, gave astounding outcomes with precise estimation to R2 values of 0.9999 for all desiccant concentration levels. Due to the variation in solar radiation, the MRR and effectiveness fluctuated with the change in desiccant and air temperatures, giving maximum differences of 0.2 g/s and 1.8% respectively between the predicted and measured values depicting a perfect match. With respect to humidity ratio, MRR was accurately predicted by ANN algorithm with maximum difference of 3.4969% while the mean variation was −0.5957%. With respect to air temperature, the dehumidifier effectiveness was perfectly predicted by the ANN algorithm to an average accuracy of 0.53% and extreme positive deviation of 4.14%. The MRR was replicated to a mean variation of 0.013% and highest point difference of 0.08%. In all the above cases, the mean and maximum differences between the ANN model and experimental values were far below the allowable limit of ± 5%, hence the algorithm was deemed to be successful and could find use in air conditioning scenarios. The ANN algorithm’s capability and flexibility test of processing unforeseen inputs was accurate with negligible deviations and prospects of predicting the desiccant’s vapour pressure, dehumidifier effectiveness and MRR within all ranges of temperature and concentration which then eliminates the need for use of charts.

What Can a Neuron Learn with Spike-Timing-Dependent Plasticity?

Spiking neurons are very flexible computational modules, which can implement with different values of their adjustable synaptic parameters an enormous variety of different transformations F from input spike trains to output spike trains. We examine in this letter the question to what extent a spiking neuron with biologically realistic models for dynamic synapses can be taught via spike-timing-dependent plasticity (STDP) to implement a given transformation F. We consider a supervised learning paradigm where during training, the output of the neuron is clamped to the target signal (teacher forcing). The well-known perceptron convergence theorem asserts the convergence of a simple supervised learning algorithm for drastically simplified neuron models (McCulloch-Pitts neurons). We show that in contrast to the perceptron convergence theorem, no theoretical guarantee can be given for the convergence of STDP with teacher forcing that holds for arbitrary input spike patterns. On the other hand, we prove that average case versions of the perceptron convergence theorem hold for STDP in the case of uncorrelated and correlated Poisson input spike trains and simple models for spiking neurons. For a wide class of cross-correlation functions of the input spike trains, the resulting necessary and sufficient condition can be formulated in terms of linear separability, analogously as the well-known condition of learnability by perceptrons. However, the linear separability criterion has to be applied here to the columns of the correlation matrix of the Poisson input. We demonstrate through extensive computer simulations that the theoretically predicted convergence of STDP with teacher forcing also holds for more realistic models for neurons, dynamic synapses, and more general input distributions. In addition, we show through computer simulations that these positive learning results hold not only for the common interpretation of STDP, where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.

Learning Only When Necessary: Better Memories of Correlated Patterns in Networks with Bounded Synapses

Learning in a neuronal network is often thought of as a linear superposition of synaptic modifications induced by individual stimuli. However, since biological synapses are naturally bounded, a linear superposition would cause fast forgetting of previously acquired memories. Here we show that this forgetting can be avoided by introducing additional constraints on the synaptic and neural dynamics. We consider Hebbian plasticity of excitatory synapses. A synapse is modified only if the postsynaptic response does not match the desired output. With this learning rule, the original memory performances with unbounded weights are regained, provided that (1) there is some global inhibition, (2) the learning rate is small, and (3) the neurons can discriminate small differences in the total synaptic input (e.g., by making the neuronal threshold small compared to the total postsynaptic input). We prove in the form of a generalized perceptron convergence theorem that under these constraints, a neuron learns to classify any linearly separable set of patterns, including a wide class of highly correlated random patterns. During the learning process, excitation becomes roughly balanced by inhibition, and the neuron classifies the patterns on the basis of small differences around this balance. The fact that synapses saturate has the additional benefit that nonlinearly separable patterns, such as similar patterns with contradicting outputs, eventually generate a subthreshold response, and therefore silence neurons that cannot provide any information.

Multilinear perceptron convergence theorem.

An adaptive perceptron with multilinear couplings is introduced. While an adaptive perceptron exhibits severe shortcomings if it is applied to complex tasks, this is not so for the adaptive multilinear perceptron.

Cone algorithm: an extension of the perceptron algorithm

The perceptron convergence theorem played an important role in the early development of machine learning. Mathematically, the perceptron learning algorithm is an iterative procedure for finding a separating hyperplane for a finite set of linearly separable vectors, or equivalently, for finding a separating hyperplane for a finite set of linearly contained vectors. In this paper, the author shows that the perceptron algorithm can be extended to a more general algorithm, called the cone algorithm, for finding a covering cone for a finite set of linearly contained vectors. A proof of the convergence of the cone algorithm is given. The relationship between the cone algorithm and other related algorithms is discussed. The equivalence of the problem of finding a covering cone for a set of linearly contained vectors and the problem of finding a solution cone for a system of homogeneous linear inequalities is established. >

A Convergence Theorem for Hierarchies of Model Neurones

The threshold logic unit (T.L.U.) has been proposed as a model for a single neurone; other substantially cognate terms are “perceptron” and “adaline”. Networks of these elements have been advanced as tentative models of some aspects of brain functioning. In particular, hierarchical nets appear to exhibit a sufficient flexibility to make them interesting both as plausible models of learning in the central nervous system and also as general objects of study in connection with pattern recognition and artificial intelligence.In this paper, we discuss the well-known “perceptron convergence theorem” in a fairly general setting, and consider variations appropriate to nets of such units. A certain familiarity with the relevant chapters of Nilsson’s Learning Machines [1] and also with current mathematical formalism is presupposed.