Hacker News Reader

Hacker News

Comment by brrrrrm | Hacker News Reader

Parent Full thread

brrrrrm

Newton method: find an error and attempt to fix it by approximation

Convex objective: a bowl-like function, we want inputs that put us at the bottom of it

Lipschitz: a space that isn’t too stretchy

Hessians: second partial derivatives of the terms we’re optimizing (inputs we want)

Regularization: make the “fix by approx” procedure a bit more well behaved

Levenberg–Marquardt: another adaptation to make the fix procedure better

View on HN

It's funny how many complex ideas are "just" simpler ideas mapped to the right sequence of steps. The jargon and naming conventions can obscure the idea from outsiders, but allows for brief and accurate communication. If they'd explained the idea Barney-style, they'd have needed twice as many pages.

Thanks for the breakdown, it makes the paper more accessible.

Math is about formalizing "simple ideas" so that they can be reasoned about exactly.

Every idea in math is like that, because the rules of math are to do everything in little steps.

Well a simpler idea is in way like the initial guess for Newton-Raphson. Sometimes you get convergence and sometimes you don't

Would be great to have a resource written like this that covers the rest of maths, (or in fact jargon in general).

The problem would be the resource would be too sloppy to be useful. For example, the phrase "Lipschitz: a space that isn’t too stretchy" doesn't tell you about the precise definition of Lipschitz, which is absolutely essential, and there are tons of names in math that would all be sloppified to "a space that isn’t too stretchy".

Not knowing precisely which definition you need for an application or which one you need for a proof to hold is essential for progress.

Math doesn't make up "jargon" for no reason. The names are to denote to professionals the least needed elements to make something true.

I always thought biology would be easier to learn if instead of entity names based on old languages they were instead verbose descriptions

i.e. Mitochondria->PowerHouseOfTheCell

Wow, it'd make the textbooks look enterprise-y. On the other hand, if you didn't capitalise every word in the compound it'd look like German.

Reply on news.ycombinator.com