Book review: A tutorial introduction to the mathematics of deep learning

Preamble

Artificial Intelligence Engines:
An introduction to the Mathematics
of Deep Learning by Dr James V. Stone
the book and Github repository.
(c) 2019 Sebtel Press

Deep learning and associated connectionist approaches are now applied routinely in industry and academic research from image analysis to natural language processing and areas as cool as reinforcement learning. As practitioners, we use these techniques and utilise them from well designed and tested reliable libraries like Tensorflow or Pytorch as shipped black-boxed algorithms. However, most practitioners lack mathematical foundational knowledge and core algorithmic understanding. Unfortunately, many academic books and papers try to make an impression of superiority show subliminally and avoid a simple pedagogical approach. In this post we review, a unique book trying to fill this gap with a pedagogical approach to the mathematics of deep learning avoiding showing of mathematical complexity but aiming at conveying the understanding of how things work from the ground up. Moreover, the book provides pseudo-codes that one can be used to implement things from scratch along with a supporting implementation in Github repo. Author Dr James V. Stone, a trained cognitive scientist and researcher in mathematical neuroscience provides such approaches with other books many years now, writing for students, not for his peers to show off. One important note that this is not a cookbook or practice tutorial but an upper-intermediate level academic book.

Building associations and classify with a network

The logical and conceptual separation of associations and classification tasks are introduced in the initial chapters. It is ideal to start with from learning one association with one connection to many via gentle introduction to Gradient descent in learning the weights before going to 2 associations and 2 connections. This reminds me of George Gamow's term 1, 2 and infinity as a pedagogical principle. Perceptron is introduced later on how classification rules can be generated via a network and the problems it encounters with XOR problem.

Backpropagation, Hopfield networks and Boltzmann machines

Detail implementation of backpropagation is provided from scratch without too many cluttering index notation in such clarity. Probably this is the best explanation I have ever encountered. Following chapters introduced Hopfield networks and Boltzmann machines from the ground up to applied level. Unfortunately, many modern deep learning books skip these two great models but Dr Stone makes these two models implementable for a practitioner by reading his chapters.  It is very impressive. Even though I am a bit biased in Hopfield networks as I see them as an extension to Ising models and its stochastic counterparts, but I have not seen anywhere else such explanations on how to use Hopfield networks in learning and in a pseudo-code algorithm to use in a real task.

Advanced topics

Personally, I see the remaining chapters as advanced topics: Deep Boltzmann machines, variational encoders, GANs and introduction to reinforcement learning. Probably exception of deep backpropagation in Chapter 9. I would say what is now known as deep learning now was the inception of the architectures mentioned in sections 9.1 till 9.7.

Glossary, basic linear algebra and statistics

Appendices provide a fantastic conceptual introduction to jargon and basics to main mathematical techniques. Of course, this isn't a replacement to fully-fledged linear algebra and statistics book but it provides immediate concise explanations.

Not a cookbook: Not import tensorflow as tf book

One other crucial advantage of this book is that it is definitely not a cookbook. Unfortunately, almost all books related to deep learning are written in a cookbook style. This book is not. However, it is supplemented by full implementation in a repository supporting each chapter, URL here.

Conclusion

This little book archives so much with down to earth approach with introducing basic concepts with a respectful attitude, assuming the reader is very smart but inexperience in the field. If you are a beginner or even experienced research scientist this is a must-have book.  I still see this book as an academic book and can be used in upper-undergraduate class as the main book in an elective such as
"Mathematics of Deep Learning".

Enjoy reading and learning from this book. Thank you, Dr Stone, for your efforts on making academic books more accessible.

Disclosure: I received a review copy of the book but I have bought another copy for a family member. 

Teaching to machines: What is learning in machine learning entails?

Preamble

Ebbinghaus (Wikipedia

Machine Learning (ML) is now a de-facto skill for every quantitative job and almost every industry embraced it, even though fundamentals of the field is not new at all. However, what does it mean to teach to a machine? Unfortunately, for even moderate technical people coming from different backgrounds, answer to this question is not apparent in the first instance. This sounds like a conceptual and jargon issue, but it lies in the very success of supervised learning algorithms.

What is a machine in machine learning

First of all here, machine does not mean a machine in conventional sense, but computational modules or set of instructions. It is called machine because of thermodynamics can be applied to analyse this computational modules, their algorithmic complexity can be map to an energy consumption and work production, recall Landauer Principle. Charles Bennett has an article on this principle, here.

Learning curve for machines

What about learning bit? Learning is a natural process for humans, specially for the younger ones. We learn new things naturally without explicitly thinking with instruction and some training, such as practised in University of Bologna a millennia ago. Usually,  it takes time for us to learn new thing, and the process is called learning curve, due to Hermann Ebinghauss. Essentially, learning in machine learning exactly roots in Ebinghauss approach.  But question remains, how this manifests quantitatively in machine learning. Answer to this question is going to be given here.

The concept of learning curve and  effect of sample size in training machine learning models for both experienced and novice practitioners. It is often this type of analysis is omitted in producing supervised learning solutions. In the advent of deep learning architecture, multi-layered neural networks, this concept becomes more pronounced.

Quantifying learning curve lies in measuring performance over increasing experience. If the performance of the machine, or human, increases over experience we denote that learning is achieved. We distinguish good learner.

On the misconception of unsupervised learning

Figure 2: Donald Webb,
father of unsupervised
learning.
(Source: Wikipedia)

A generic misconception appear on what unsupervised learning means. Clustering, or categorising unlabelled data, is not learning in Ebbinghaus sense. The goodness of fit or cluster validation exercise do not account an increase in experience, at least this is not established in the literature, judging from cluster validation techniques, see, Jain-Dubes's Algorithms for clustering data. Wikipedia defines unsupervised learning "inferring a function to describe hidden structure from "unlabeled" data", this is a function inference is not learning,.

Then, what is unsupervised learning? It originates from Hebbian Theory from neuroscience that "Cells that fire together wire together". This implies, unsupervised learning is about how information is encoded, not how it is labelled. One good practical model that could be classified as unsupervised learning, so called spiking network model.

Outlook

The concept of learning from Machine Learning perspective is summarised in this post. In data science, it is a good practice to differentiate what we call learning and function inference/optimisation. Being attentive to this details would help us.