Machine learning could need, and probably has needed, some unified math notation for the past 15 years IMO. With that said, it was worse back in the day - when ML papers were the products of researchers from all over, you'd see some wild notation.

Many will likely disagree with me, but inconsistent notation (across papers!) is to me friction. At least in this article the author explicitly explains the notation at the very start...that is not always the case. Rarely, even.

EDIT: Didn't even notice the notation switch, much appreciated.

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olalonde 33 minutes ago | parent [-]

I never understood people who preferred traditional math notation (e.g. single letter symbols, weird characters like ∣q⟩ instead of writing down an explicit type, etc.). I guess the main advantage is terseness? To me, the mathematical expressions would be so much easier to understand if they were just written in pseudo code or an actual programming language like Python.

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aeternum 23 minutes ago | parent | next [-]

Math notation ultimately is pseudo code just with mostly single letter variables and many operators that are encoded purely by position thus not even requiring a symbol.

Remember that the oft-used e^x is actually an infinite series, even writing it out in summation form would be quite verbose given its frequency in many equations.

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SkyBelow 8 minutes ago | parent | next [-]

I feel the magic in math is that the notation is to a more universal sort of language, and the e^x captures that. e^x means that infinite series, but it means a few other things at the same time. That those different things are sometimes related, that e^2 means e*e, a simple enough operation most can understand, but that it also means that infinite series with 2 in place of x, is part of the complexity of math that makes it quite different than a classical programming language. With most programming languages, someone assigned those equivalent meaning, and while it might be important to understand why, it shows you the mind of the who designed the language. But, in math (and in true Computer Science), when you see an equivalence of this sort, whose mind are you now glimpsing into?

But, for someone just starting out (or even an expert who just wandered into a new area), this becomes a barrier to understanding. Sometimes we need the mathematical summary, what tells us the immediately answer we are interested in, perhaps even if it loses the deeper nuances that are beneficial for the experts more fluent in the language.

(And yes, all math notation is human created, so it makes my point quite a bit messier in practice.)

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crubier 15 minutes ago | parent | prev [-]

exp(x)

	▲	kurthr 7 minutes ago \| parent [-]
		Longer to write and generally a numerical rather than symbolic representation.

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crubier 15 minutes ago | parent | prev | next [-]

This 1,000%

Trying to read any math paper is basically like trying to read CodeGolf.

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dboreham 9 minutes ago | parent | prev | next [-]

Well, humanity struggled for 2000 years trying to do mathematics without notation, so its benefit is not to be sniffed at. But really it's just an APL-vs-Fortran type debate. They're not fundamentally different. Remember also that Ramanujan had to re-use paper it was so costly/hard to find.

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htrp 29 minutes ago | parent | prev [-]

math notation doesn't bias towards English language understanding like pseudocode

	▲	dfee 15 minutes ago \| parent [-]
		but it biases towards the latin alphabet. so your point is diminished.