1 Introduction to Artificial Intelligence

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1.1 Just what is artificial intelligence?

Artificial intelligence is harder to describe infinite terms than it is to recreate many of the most popular algorithms that serve to represent it.

The definition, if we can say that such a thing exists, is a moving socio-cultural target and just as we get closer to it’s said definition, it again slips just outside of our grasp.

This is partly because AI has always been fundamentally tied up with some of our deepest philosophical queries and as we make further progress in AI and related sciences, we again are forced to redraw the line of what it means to be human.

“Nothing that we may know or learn about the functioning of the organism can give, without ‘microscopic,’ cytological work any clues regarding the further details of the neural mechanism.” - Von Neumann

Generation after generation, we’ve asked ourselves fundamental questions that AI, as a philosophical project, touches upon:

  • What does it mean to be human?
  • what is intelligence?
  • What is the difference between humans and other animals?
  • Is there another species that is more intelligent than we are ++(Übermensch)? +++references
  • Will humans be surpassed by a more intelligent species?

Neurobiologists like Sapolsky and others, have highlighted that many of the features we have held so dearly, empathy, politics, culture, tool usage, are not unique to the human species. It seems that is the only true advantage may be in the sheer number of neurons (86 billion) and synaptic connections (100 trillion+) between them that has allowed for more elaborate and subtle ways of those elements unfolding over time.

“We have the same nuts-and-bolts physiology, yet we’re using it in very novel ways. - Robert Sapolsky”

While scientific discoveries continue to redraw the line of what is truly unique to humans, so does progress in artificial intelligence. So while it is clear that there is much hype around artificial intelligence, it can not be argued that there shouldn’t be at least some concern over its possible futures.

Rather than focus on the takeover, we will focus here on intelligence and some of the major categorisations that have played a part in today’s AI.

We will primarily cover the first two subtypes of intelligence in this book and leave the reader to discover more about embodied cognition.

1.2 Intelligence as logic and reasoning

Logic and Reasoning - a type of intelligence that implies the ability of mental mechanisms to explicitly reason about a phenomenon in the world in a Pattern Recognition/Perception - ++a ty +++what is this?

Before we had anything like the first computer, Aristotle and others were already forming, what we call logic today. Aristotle concerned himself with what

  • what is thinking and reasoning?

  • what does it mean to think or reason?

  • what is it to think and reason well?

  • can correct reasoning be mechanized?

Perhaps there is a logic calculus than can mechanise reasoning

These are just some of the questions that the likes of Aristotle, Leibniz, Turing, Laplace, Wittgenstein, Gödel, and Boole and many others attempted to answer definitively. Aristotle and the Stoics gave us a framework for reasoning and propositional logic respectively. Leibniz gave us logical calculi and a glimpse into computers that could do the same. We also have George Boole’s Boolean algebra (1847) would catch up with Claude Shannon to begin the digital revolution and progress artificial intelligence.

Let us think about the context of such questions.

Rene Descartes stated “Cogito, ergo sum” which translated means, “I think therefore I am”. He arrived at this statement after trying to use pure “reason” to find what was fundamentally true without any doubt. Although he couldn’t complete his project, his value of “reason” was not unpopular and is gaining popularity in much of modern culture and can be heard in everyday conversations when we talk about the distinction between our thoughts and body.

Reasoning starts with logic.

++Aristotle. +++why is it here

So let us begin with reasoning.

The branch and discipline titled logic was originally focused on finding absolute truths from statements that could be found in everyday discourse. Logic is fundamentally tied up with questions around how one can reason correctly. How one is able to deduce the correct answer given a set of statements or propositions.

1.3 Logic and Philosophy +++not sure if it is a proper title I would suggest ‘From logic to biology’

1.4 Dealing with Uncertainty and Probability

While Boole was transforming the world of logic, the likes of Kolmogorov, Laplace, Jaynes and others were setting out to find a way for us to better reason when we didn’t have complete information and especially when we have data from several different places. After all, the incomplete knowledge is the only working material a scientist has and science itself is a way to help us make inference with partial information.

Jaynes even described probability as an extension of logic. But there were others who didn’t see them as connected at all.

1.4.1 Information Theory

While logic and probability were now firmly established, Claude Shannon combined probability, and logic, to create the mathematical theory of communication which we now call Information Theory.

While probability allows us to reason under uncertainty, Shannon’s information theory allowed us to quantify the uncertainty with a measure called \(entropy\). This has laid the foundation of many other important concepts including mutual information, KL divergence, and even a very popular deep learning loss function. (Encoder-decoder or data compression strategies)

1.5 The Rise of AI and Neuroscience

1.6 Neurobiology and Cognitive Science

1.6.1 Cortexes

1.6.2 Neurons

1.6.3 Perceptrons and Perception

The second set of questions were just as philosophically motivated, but differed in their approaches. Individuals from disciplines like biology, especially psychology, neurobiology, then called neurophysiology, began to see that the intelligence of humans and other species may be uncovered by emulating the central nervous system. As we began to understand an infinitesimally small amount about how a given number of neurons can give rise to intelligent behaviour. ++(Pitts, McCulloch) give rise to basic intelligence in simpler species like fruit flies to the advanced intelligence to that of the great apes. +++reference here

Pitts, McCulloch, Rosenblatt, Minsky, and others set out to combine the advances of logic, from Leibniz’s logical calculi to Bool’s Boolean algebra) and combine them with our growing knowledge in brain science which eventually leads to the creation of the first artificial neural network, named the perceptron. The first neural network which was based in the science of logic pushed forward by the likes of Leibniz and George Boole.

They too had similar questions, “Can machines think?”, “Can the brain be emulated?”. These questions moved away from deductive reasoning and towards emulating our senses and pereptions. Rosenblatt, Hebb, Minsky, and others were able to move towards learning from data as humans do by recognising patterns which birthed ++the first neural network, the perceptron. +++reference here

This dichotomy, between symbolism and perception, like all dichotomies don’t pin down the reality but we hope that it provides a way of thinking about our path towards today’s artificial intelligence. ++We are now at a stage where we are bringing what we have learned in symbolic. +++not sure if I can understand this sentence

1.7 The Limits of Logic

Though we don’t usually think of logic in neural networks, the perceptron was actually based on logic as you can see from the references to Pitts paper are all around logic.

Godel determined that logic couldn’t. Turing found a limit to such machines. Logic isn’t how biological neurons work and limit the capacity of a neural network.

1.8 Statistical Learning Theory

Vapnik, the learnable theorems PAC learning bounds

1.9 The modern wave of deep neural networks

Bengio, LeCunn Andrew Ng Hinton, Goodfellow

1.10 Deepmind, OpenAI, and so on

1.11 Why learn the mathematics of deep learning

1.12 The Mathematics Needed

  • Logic
  • Calculus
  • Probability
  • Geometry (?)
  • Information Theory – entropy – mutual information – bottleneck
  • Statistical Learning Theory – approximation theory – learnable
  • Representation Learning
  • Optimization

1.12.1 Final Thoughts

Whatever your motivations for wanting to read the Mathematics of Deep Learning and Artificial Intelligence, we wish you well on your journey.

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++ is the location where I think in question +++ is my comment

Overall I think I like the story and the storyline seems relatively complete. Somehow the transition from logic to biology is not very well illustrated. I am expecting to see more explanation about how biology or even philosophy changes the trajectory of AI in the last few decades.

You may also need to cover a little bit more about the following questions:

  • what framework or mental model we are following now?
  • what is the possible future direction of AI?

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