丘城桐:基础数学和AI, Big Data

AI and Big Data are Twins, their Mother is Math.

“AI 3.0“ today, although impressive in “DeepLearning“, is still using “primitive” high school Math, namely:

AI has not taken advantage of the power of post-Modern Math invented since WW II, esp. IT related, ie :

That is the argument of the Harvard Math Dean Prof ST Yau 丘城桐 (First Chinese Fields Medalist), who predicts the future “AI 4.0“ can be smarter and more powerful.

https://www.toutiao.com/group/6751615620304863755/?app=news_article_lite&timestamp=1572193294&req_id=2019102800213401000804710406682570&group_id=6751615620304863755

… Current AI deals with Big Data:

  1. Purely Statistical approach and experience-oriented, not from Big Data’s inherent Mathematical structures (eg. Homology or Homotopy).
  2. The Data analytical result is environment specific, lacks portability to other environments.

3. Lack effective Algorithms, esp. Algebraic Topology computes Homology or Co-homology using Linear Algebra (Matrices).

4. Limited by Hardware Speed (eg. GPU), reduced to layered-structure problem solving approach. It is a simple math analysis, not the REAL Boltzmann Machine which finds the most Optimum solution.

Notes:

AI 1.0 : 1950s by Alan Turing, MIT John McCarthy (coined the term “AI”, Lisp Language inventor).

AI 2.0 : 1970s/80s. “Rule-Based Expert Systems” using Fuzzy Logic.

[AI Winter : 1990s / 2000s. Failed ambitious Japanese “5th Generation Computer” based on Prolog-based “Predicate” Logic]

AI 3.0 : 2010s – now. “DeepLearning” by Prof Geoffry Hinton using primitive Math (Statistics, Probability, Calculus Gradient Descent)

AI 4.0 : Future. Using “Propositional Type” Logic, Topology (Homology, Homotopy) , Linear Algebra, Category.

Math for AI : Gradient Descent

Simplest explanation by Cheh Wu:

(4 Parts Video : auto-play after each part)

The Math Theory behind Gradient Descent: “Multi-Variable Calculus” invented by Augustin-Louis Cauchy (19 CE, France)

1. Revision: Dot Product of Vectors

https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length

2. Directional Derivative

3. Gradient Descent (opposite = Ascent)

https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/gradient-and-directional-derivatives/v/why-the-gradient-is-the-direction-of-steepest-ascent

Deeplearning with Gradient Descent: