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> Andrew Ng's notation for machine learning sometimes uses superscripts as indices, and sometimes as exponents. In the same formula. I've never read Ng's work,
by bsilvereagle 11y ago
> Andrew Ng's notation for machine learning sometimes uses superscripts as indices, and sometimes as exponents. In the same formula.
I've never read Ng's work, but typically upper and lower indices is a sign of a summation. It's known as "Einstein Summation Notation". At first glance it seems obtuse, but when you start doing covariant/contravariant derivatives on tensors, the notation makes things much easier.
- OscarCunningham 11y agoIn a general relativity lecture I once saw an expression where indices were being used to mean three different things. As a power, to denote the components of a vector and as an index over some other indexing set. Of course it was perfectly readable because there are implicit conventions about what kind of letters you can use for each of these things, and because the formula would only make sense if you read it a certain way.
- Maken 11y agoMaybe it's me, but I've always find physics' mathematical notation highly inconsistent, like if every author felt the necessity of inventing his own notation and overloading every well-established operator. Mathematicians tend to be much more consistent in their use of symbols and their manipulation.
- IshKebab 11y agoYou can use Einstein's summation without superscripts though. Example: http://mathworld.wolfram.com/EinsteinSummation.html http://mathworld.wolfram.com/EinsteinSummation.html Anyway that doesn't invalidate the point that mathematics often has highly ambiguous and hand-wavy notation, whereas programming doesn't.