A new math : The power behind Deep Learning

 We all have seen, in the last few years, an explosion of a powerful new Computer Science. Born on the most brilliant computing minds, working at the excellence of tech research centres of the rich world, Deep Learning showed itself, in the beginning, as no more than a turbo evolution of statistics-powered machine learning algorithms, merged with the so promised wave of intelligent machines that might never come out of sci-fi movies and comics.

But, for those who have enough guts to read academic papers, or at least follow IT blogs,  mailing News and whatever else which broadcasts top advances on information technology, it has been shown too more than this.

I personally stayed away from the mathematical side of the Science of computers. Years of hard Work on software development, finance, project management, and then I suddenly had all the time I wanted to learn new things (those who know me, know what I’m talking about). An apparently aleatory (really not!) email advertising a MOOC on Machine Learning - - a really long course, but with a good price - - appeared on my inbox. Guys like @Kirill Eremenko and @Hadelin de Ponteves introduced me to a new world. Not the heavy-metal math I was accustomed to at college, several decades before : this time it was computer Science, there was coding, computer languages, operating systems, all of them with some kind of a new spirit: powerful mathematics, arising from simple concepts, and giving a new meaning to the world statistics. Suddenly I saw myself studying and analyzing linear and multilinear regression, choosing parametres, observing logistics calculation.

Great tools, being used to solve practical problems. Great math with great scientific calculation packages, all stable and the serious and mature result of the open source hype from the 90’s.

But wait, there was more than that. Inside that first course, there was a hard nucleum. It was like diving to the centre of the Earth and facing an atomic engine moving the most outstanding computing advances. Deep Learning. The name was like the sleeve of a book, of a portal, to some kind of different, very new and unbelievably powerful mathematical world. Of course, connected to machines whose computing strength surpasses by far the giants which we used to count with the fingers of one single hand, not a longa go.

It seem all the knowledge bodies of calculus, linear algebra, combinatorics, statistical analysis, and, among many others, even mathematical physics. All of them, summed up and reinforced with new concepts – all of them born on the needs of this decade’s world. No, it’s not the etereum math that used to become practical after centuries. Practical applications, complex Science, algorithms and turbo hardware, everyone running together. Yes, running, not walking. In several months trying to follow the allucinating speed of DL blogs and forums, and doing my best to read books, install the top packages at my computer (I even had to change my old one for a new with too much more RAM and HD, and proc speed, of course) and learn it all, I see how much new stuff is appearing on specialized media everyday. And not only there... DL gurus are becoming more and more like rock stars, great books are being released all around. And the math... Geez. Different departments inter-communicating, no more silos.

Although the actual structure and functioning of the human brain, as it really is, is yet to be properly understood. The neural networks, from the classic to most complex structures like Boltzmann Machines or autoencoders – not talking about stacked structures --, believe or not, are a over-simplified model of our biological neurons. Science paradigmas tell us that simplified models become more and more complex while they get closer to reality. What kind of mathematics would be the one that would model our brain the closest possible? DL learning, in a sense, could be regarded as a new age of computer math. Packages built on other packages help us using very complex structures that have filled academic papers. These structures are handled with algorithms which go far beyond limits that were, themselves, only crazy fiction talk – last decade.

Well, I love Science and, who know, my professional rebirth will take me to that land as a worker. Reading all this stuff – most of it i’m still struggling to understand – really makes me feel amazed, thrilled, alive. DL, as everything related to artificial intelligence, might deny or confirm some dark prophecies related to it. This will come in the future – not the far one. When the human brain can be modeled mathematically the best possible way, we will know whether this will be a limit or not : after all, models can evolve while there is intelligent life working on them. If this models is bigger, stronger than the real brain, and makes possible that artificial intelligence grows better then the biological, well... Some say it’s completely impossible. As electric light was stated as an impossibility 200 years ago.