An introduction to Artificial Intelligence and Deep Learning Fabio Grazioso * 1) Microfiltration Processes Laboratory, WCRC “Advanced Digital Technologies”, Tyumen State University, Volodarskogo 6, Tyumen, 625003, Russia; 2) Photonics and Microfluidics Lab, Tyumen State University, Volodarskogo 6, Tyumen, 625003, Russia; 3) Tyumen State Medical University, Odesskaya 54, Tyumen, 625023, Russia. (Dated: November 20, 2022) The present work introduces the main concepts from the research on Artificial Neural Networks (ANNs) which represent the most promising model to realize artificial intelligence. We will see how historically the main ideas have been developed, the periods of great development of the neural computational paradigm and its long period of oblivion. We will describe the main features of an ANN discussing in some detail an example of an application to optical characters recognition. We will follow how the technique of backpropagation, although a mere technical tool, has made possible the use of more powerful networks, bringing the times of computation down to acceptable values for practical applications. We will also describe in some details the more advanced and recent model of ANN, the Convolutional Neural Network. CONTENTS I. Introduction 1 A. Machine Learning 2 B. The recognition/classification problems 2 C. Deep Learning 2 II. Artificial Neural Networks 2 A. The perceptron - the neuron 2 B. The XOR gate and the network 3 III. Optical Characters Recognition (OCR) 4 IV. The training 4 A. The Cost Function 5 B. Minimization and gradient descent 5 1. Gradient descent 6 V. Backpropagation 6 A. Details of backpropagation 7 VI. Convolutional Neural Networks 7 A. Feature maps and pooling layers 8 VII. Conclusions 8 References 9 I. INTRODUCTION Since the term Artificial Intelligence (AI), has become part of popular culture, it may have become too wide to be used in a scientific context. In general we may say that AI refers to the study of cog- nitive capabilities shown by man-made artifacts. Those capabilities can be divided in the following categories: * f.grazioso@utmn.ru (a) the ability to learn new behaviours, not previously programmed in its design, (b) the ability for proactive interaction with an unknown environment, (c) the abil- ity to infer and deduce new information. A very limited list of the application fields can be: com- puter vision, speech recognition, problem solving, knowl- edge representation. The implicit definition of AI on which the above state- ments are made is the Strong AI, as defined by Searle [1, 2]. In extreme summary, this definition of AI says that the artificial device that shows cognitive capabilities, is therefore assumed to have cognitive states, intelligence, self-awareness, or consciousness. This can be related to the Turing test [3]. Among several authors who wrote critically on the sub- ject of strong AI we can mention Roger Penrose [4] The quest for an “intelligent artificial device” can be traced very far back in time, as back as the mentions to intelligent machines found in the bible, or in the greek mythology. In the modern development of this scientific endeavour, there has been a time, between the two world wars, when two approaches have been compared to each other. On one side, there was the idea of mimicking the struc- tures that the research in biology and anatomy was dis- covering inside the brain and the nervous systems. This approach may dated back 1943, with the seminal article by Mc Culloch and Pitts [5]. At the same time, another approach was being devel- oped, relying on a much more abstract model, and on the idea of algorithm. A powerful thrust to this idea of the algorithmic approach to intelligence was coming from the famous entscheidungsproblem, the “decision prob- lem” formalized by Hilbert in 1928 [6]. This problem can be loosely described as whether it is possible or not to decide automatically about the truth or falseness of any possible statement of formal logic. Turing, and Church, independently tackled the problem, by first giving a pre- cise definition of “automatic decision”, i.e. a precise def- inition of algorithm [7, 8].