Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.

Gradient-based learning applied to document recognition

Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

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Reinforcement Learning: An Introduction

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. >

ANFIS: adaptive-network-based fuzzy inference system

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

: The ordinary differential equation dx/dt = -P(t)x where P(t) is symmetric positive semi-definite time-varying matrix arises often in mathematical control theory. In this paper the authors consider the stability properties (in the sense of Lyapunov) of the equilibrium state x(t) identically equal to 0. It is a relatively trivial exercise to show that the origin is stable but (uniform) asymptotic stability does not generally hold unless P(t) is positive definite. The semi-definite case arises much more frequently in practice than the definite one and the main effort in this paper is directed towards finding conditions implying uniform asymptotic stability in such a case.

On the uniform asymptotic stability of certain linear nonautonomous differential equations

Stability of a Class of Differential Equations with a Single Monotone Nonlinearity

Adaptive, learning, and pattern recognition systems: Theory and applications

A new approach to model reference adaptive control, based on a combination of direct and indirect control methods, is introduced in this paper. The controller structure is identical to that used in the direct method, but the algorithm used to update the controller parameters depends both on the output error as in direct control and on the plant parameter estimates as in indirect control. The global stability of the overall system is assured by the existence of a Lyapunov function. In the ideal case discussed here, the combined approach results in improved transient response with smaller amplitude of the control input as compared to the constituent methods.

Kumpati S. Narendra

Papers

On the uniform asymptotic stability of certain linear nonautonomous differential equations

Stability of a Class of Differential Equations with a Single Monotone Nonlinearity

Adaptive, learning, and pattern recognition systems: Theory and applications

A new approach to model reference adaptive control

Stability Regions for the Damped Mathieu Equation