Skip to content
AI Atlas

Math & Statistics Foundations

Vectors, matrices, probability and gradients — the language of AI

OVERVIEW

All Concepts
6
Beginner
3
Intermediate
2
Expert
1

Every model ultimately reduces to operations on vectors and matrices, and every act of “learning” is ultimately the reduction of a loss along a gradient. This domain does not aim for a mathematician’s completeness; it selects only what is needed to understand AI: linear algebra gives data and weights their shape, probability gives uncertainty its measure, and calculus gives improvement its direction.

Questions this domain answers

  • Q1

    Why can data be written as a matrix?

  • Q2

    Which direction does the gradient actually point?

  • Q3

    Why can softmax be used as a probability?

Concepts in this domain

  1. 01Vectors & Vector SpacesBeginnerAI turns everything — words, images, sounds, users — into one thing: a list of numbers
  2. 02Gradients & Gradient DescentBeginnerAll of deep learning comes down to one thing: take a small step downhill
  3. 03Matrix Operations & Linear MapsIntermediateMatrix multiplication is not a pile of multiply-and-adds; it rewrites an entire space in one stroke
  4. 04Probability & DistributionsBeginnerA model never hands you an answer; it hands you a degree of belief over every possible answer
  5. 05Bayes’ TheoremIntermediateBelieve a little, see the evidence, revise a little — that is Bayes
  6. 06Entropy & Information TheoryExpertThe more surprising a sentence, the more information it carries — and a language model’s loss measures exactly that surprise