Perceptron: Learning, Generalization, Model Selection, Fault Tolerance, and Role in the Deep Learning Era

Abstract

The single-layer perceptron, introduced by Rosenblatt in 1958, is one of the earliest and simplest neural network models. However, it is incapable of classifying linearly inseparable patterns. A new era of neural network research started in 1986, when the backpropagation (BP) algorithm was rediscovered for training the multilayer perceptron (MLP) model. An MLP with a large number of hidden nodes can function as a universal approximator. To date, the MLP model is the most fundamental and important neural network model. It is also the most investigated neural network model. Even in this AI or deep learning era, the MLP is still among the few most investigated and used neural network models. Numerous new results have been obtained in the past three decades. This survey paper gives a comprehensive and state-of-the-art introduction to the perceptron model, with emphasis on learning, generalization, model selection and fault tolerance. The role of the perceptron model in the deep learning era is also described. This paper provides a concluding survey of perceptron learning, and it covers all the major achievements in the past seven decades. It also serves a tutorial for perceptron learning.

Inclined Curved Crack Composite Beam: Experimental and Computational Analysis with Recycled Aluminum Composite Materials and Comparison with an Artificial Neural Network

“…Desire and Shengzhi reported that the hidden layer is a squeeze-and-excitation one. a = italice n − italice − n italice n − italice n where n is the input function and a is the output function; the transfer function is the output, which is a pure linear function a = n . Ke et al derived a scaled conjugate gradient algorithm to train the architecture for precaution of the output, as shown in eq . There are totally six sets (one undamaged and five damaged).…”

“…With the generalized differential quadrature method (GDQ), the r th order derivative of a function f ( x ) with n discrete grid points can be expressed as higher-order derivatives with any number and distribution of grid points, as shown in eq . Shu’s method provided a great deal of versatility in how the method can be applied to tackle different engineering challenges. , true( ∂ f T ( x ) ∂ x T true) x i = ∑ j = 1 n c i j true( r true) f j where x i represents different points in the variable region, and f j and C ij ( r ) are the function values and related weighting coefficients, respectively.…”

A bacteriorhodopsin multisensor system for qualitative and quantitative monitoring of methanol, ethanol, propanol, and butanol under extreme conditions

“…The multi-layer perceptron model is important in the sensors/biosensors field due to: the learning of complex, non-linear models (problems), handling large amounts of input data (if necessary), making quick predictions after training and achieving the same accuracy with smaller samples, and, additionally, it can be trained in real time. 33…”

“…The multi-layer perceptron model is important in the sensors/biosensors eld due to: the learning of complex, non-linear models (problems), handling large amounts of input data (if necessary), making quick predictions aer training and achieving the same accuracy with smaller samples, and, additionally, it can be trained in real time. 33 The procedures of ANN performances were as follows: for training, 14 concentrations from 0 to 800 mM for combinations of three pHs and three temperatures were used (126 total samples). Independently, 5 concentrations were prepared for the above combination of pHs and temperatures as test samples (45 total samples).…”

“…Particularly useful for researchers in the field are some comparative studies in which different methods may be contrasted to see which one shows better performance. 32 For example, in the review article published in 2022: “Perceptron: Learning, Generalization, Model Selection, Fault Tolerance, and Role in the Deep Learning Era”, Du et al 33 present the multilayer perceptron (MLP) model of ANN and references to other models. To date, the MLP is the most fundamental and important neural network model.…”