I don't think that's right. I think "two times faster" would mean "twice as fast", not "three times as fast".
I don't see how that's the case. What is "50% bigger"? I understand it as 150% of the size. Similarly, I would understand "90% bigger" to mean "190% of the size" and "100% bigger" to mean "200% of the size", and I'm sure that is how they are used in practice.
So then surely "200% bigger" means "300% of the size"? And "two times bigger" - which is mathematically identical to "200% bigger" - would be three times the size. I acknowledge that the phrase is often used like you say but I don't think that is its literal meaning, and if you used that in a contract I think it would legally be interpretted in the way I've said (I'm thinking of consumer law in a situation where something is "n times bigger for the same price").
All this applies analagously to speed and x times faster. I gave the examples above with size because I think it's a bit more of a common thing to talk about this way and speed is a bit more subtle because what we're measuring here is the time which is something / "speed" and here the numerator isn't clear (number of training runs perhaps).
Interestingly, in Russian "100% bigger" and "two times bigger" will have different prepositions, so it's more clear that in the first case you do sum (x + 100%x = 2x), and in the second case you do multiplication (2 x = 2x).
I'm quite sure it's the same in English (sum with % and multiplication with times), but I'm not a native English speaker.
So I agree with the article, "3.5 times faster (1 hour vs. 3.5 hours)" is perfectly correct, and it is OK to abbreviate "3.5 times" as "3.5x".
but really, relative to something else, i guess it would be 0.33x as fast, because it would take two times more time, or 3 times as long
The meaning of "two times faster" as "twice as fast" is certainly the way such a statement would generally be interpreted everywhere I've worked.
It is of course possible that the meaning suggested by quietbritishjim is archaic British, but I certainly don't believe it's current: I've worked in various places Cambridge and London for the past 18 years and, as I say, have never encountered it.
If even that.
I think "3.5x faster" to mean "3.5x as fast" is fairly common, pretty clear, and very understandable to anyone but daft grammar prescriptivists.
> A personal note: I know the disparagement of Times-er from long ago, from my grade school years, I think; I was taught that two times more than X really means 'three times as many as X'. Since authority figures insisted on this interpretation, I avoided the construction entirely (as, as far as I know, I still do). Yet I've never stopped asking, "Why don't you understand the clear meaning of what people are saying?"
I absolutely agree with that, and in practice if I ever see that turn of phrase with anything more than 100% then I assume that they are using it the way that you're thinking of. But I maintain this is not the literal meaning. At the same time, I'm not saying people should be subtracting 100% to make the number mathematically correct, that would definitely be bizarre. Instead, I'm saying they shouldn't be using such a weird turn of phrase in the first place, so the headline should simply be "Deep learning on CPU 3.5x as fast as on GPU"
> I've worked in various places Cambridge and London for the past 18 years and, as I say, have never encountered it.
You have really never encountered an item in a supermarket saying "now 20% bigger!"? Thinking about it now, they're usually charging the same amount as the old size (otherwise it's not much to brag about really) in which case they use the vastly clearer phrase "20% extra free", but I'm sure I've seen the former phrase.
>> That last reaction incorporates one criticism of Times-er, namely that it is "illogical" or "irrational": X times more than Y MUST MEAN 'Y plus X-times-Y (that is, 'X+1 times Y'), not 'X times as many/great as Y' (that is, 'X times Y'). (In the most common variant of this reaction, X times more than Y is disparaged because it is said to be ambiguous, with both the 'X times Y' and 'X+1 times Y' interpretations.)
>> The appeal here is to the idea that ordinary-language expressions are simply realizations of logical (or arithmetical) formulas. This is just backwards. The formulas are there to represent the meanings of expressions; they are not the prior reality, merely cloaked in (those devilishly vague) words of actual languages.
For example you also wouldn’t say -0.5 times faster, it just doesn’t make sense.