4 ms·
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 Lip
by brrrrrm 5y ago
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
- robbedpeter 5y agoIt'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.
- sorokod 5y agoWell a simpler idea is in way like the initial guess for Newton-Raphson. Sometimes you get convergence and sometimes you don't
- whatshisface 5y agoEvery idea in math is like that, because the rules of math are to do everything in little steps.
- tubby12345 5y agoMath is about formalizing "simple ideas" so that they can be reasoned about exactly.
- montebicyclelo 5y agoWould be great to have a resource written like this that covers the rest of maths, (or in fact jargon in general).
- adampk 5y agoI 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
- syockit 5y agoWow, 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.
- ChrisLomont 5y agoThe 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.