Pranesh

“How do we learn? Is there a better way? What can we predict? Can we trust what we’ve learned? Rival schools of thought within machine learning have very different answers to these questions. The main ones are five in number, and we’ll devote a chapter to each. Symbolists view learning as the inverse of deduction and take ideas from philosophy, psychology, and logic. Connectionists reverse engineer the brain and are inspired by neuroscience and physics. Evolutionaries simulate evolution on the computer and draw on genetics and evolutionary biology. Bayesians believe learning is a form of probabilistic inference and have their roots in statistics. Analogizers learn by extrapolating from similarity judgments and are influenced by psychology and mathematical optimization.”
― Pedro Domingos, The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World

“Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..."
Klapaucius thought, and thought some more. Finally he nodded and said:
"Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit."
"Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming:

Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!

Come, every frustum longs to be a cone,
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.

In Reimann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.

I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in bound partition never part.

For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?

Cancel me not--for what then shall remain?
Abscissas, some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.

Ellipse of bliss, converge, O lips divine!
The product of our scalars is defined!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.

I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a^2 cos 2 phi!”
― Stanisław Lem, The Cyberiad

“In a different direction, the necessity to model the analysis of noisy incomplete sensory data not by logic but by Bayesian inference first came to the forefront in the robotics community with their use of Kalman filters.”
― Ulf Grenander, Calculus Of Ideas, A: A Mathematical Study Of Human Thought

“The second simplest algorithm is: combine two bits. Claude Shannon, better known as the father of information theory, was the first to realize that what transistors are doing, as they switch on and off in response to other transistors, is reasoning. (That was his master’s thesis at MIT—the most important master’s thesis of all time.)”
― Pedro Domingos, The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World