Maths 4.7Lesson outlineLesson 7 of 9 in Module 4
Convexity, Local Minima and Saddle Points
Tell a convex function from a non-convex one, and know what a zero gradient does and does not guarantee.
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In this lesson10 parts
- 01One answer, or several?
- 02The chord test
- 03Why convex means one answer
- 04Saddle points
- 05Checkpoint: convexity so far
- 06The full ward: nine starts, one answer
- 07When the data separate
- 08A loss with two minimums
- 09Convexity in Python
- 10Recap, challenge, and next: the backward pass
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- chord
- a straight line between two points of a curve |
x²from−2to1 - convex function
- every chord lies on or above the curve |
x²,log(1 + eˣ) - strictly convex
- every chord lies strictly above the curve; at most one minimiser |
x²(one),log(1 + eˣ)(none) - saddle point
- a point with zero gradient that is neither a minimum nor a maximum | the origin of
x² − y²
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.