Vectors are arrays of numbers that can represent any type of data (video, documents, audio) by passing it through machine learning models, where the distance between vectors in vector space represents the similarity in meaning of the original data, measured using Euclidean distance (the Pythagorean theorem extended to multiple dimensions).
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Totally lost on AI?Added:
[Music] all I hear is how vectors of the future of everything and AI is taking over the world etc etc I don't even know what these term I don't even I don't even know what these terms of veter mayic tensor even mean is there any AI for dummies content out there maybe there is but I'm unaware of any but I thought I would do a a little bit of a sort of thing here I'm not sure if this is going to work so here we go so I wanted to help you out with vectors so what is a vector very simple it's an array of numbers it sounds super cool sounds much better and that's what we do in the IT industry we never say oh by the way vectors are just a list of numbers that you've had for 50 years because that doesn't sound cool does it we have to say it's something new vectors tensils Etc all this stuff is just an array of numbers what's the magic why why is just an array of numbers so good because you know my commodor 64 had arrays and I wouldn't say it's the equivalent of chat GPT the thing that makes vectors special is you can take for example video you can take documents who knows what the thing for audio is I draw the music there we go anything you have you can put through some sort of magic function and create a vector out of it this is the magic of vectors now even this is not something you call particularly spectacular because for example think about the monitor I'm you know broadcasting on if it already has this magic in terms of mapping something that's tangible to humans for example color to numbers RGB we know that the color purple for example is a little bit of red little bit of green a little bit of blue so the ability to map something like color to a list of numbers is also something that's been around for decades so why are vectors so special the thing that makes vectors so special is the fact that the mapping system we use the concept of taking some arbitrary data and putting it into vectors go through a big machine learning model and that model grunts away for literally millions of dollars of GPU time that's why these companies are buying you know hundreds of thousands of gpus they crank away and and they're building nuclear reactors to do this compute work cranking away such that the vectors come out preserve the meaning of that data you can think of it as like windzip for human understanding I could take a video put it through this magic model and out comes a list of vectors which preserves the meaning of that model now the best way to describe that let me use a very simple metaphor which hopefully will um help you describe why these vectors might be something like magic so I'm going to do some very bad drawing here I'll do my best so I'm going to go back to the RGB model okay so if I draw for example let's draw there we go three dimensions that's hopefully three dimensions there's my red there's my green and that's a g and and there's my blue so let's draw some colors now let me take a color so if I took something which is mainly red then it might have a little bit of green a little bit of blue but mainly red so if I plot it in three dimensions it would look somewhere up there so the vector for that in terms of for red might be uh 5% green 5% blue and 90% red that's the top one up there now let's get another color let's get some a a color like um sort of a Bluey green color so now it's going to have not much red so just a little bit up a little bit of a lot of green and a good chunk of blue so it might sit about there so if I plot that one it's was it not much red lots of green lots of blue and we sort of get some color out here and if I get another color which is closer but just a little bit more green in it so it might come uh same distance up as red a little bit more green about the same amount of blue it sits there so let's assume that was I can't remember which one was which now but let's say that's 60 green 50 blue and 5 red as well so there's my very beautifully drawn three-dimensional diagram so the thing that makes vectors spectacular and it's even applies in this simple example with RGB is these two colors as best as I could pick colors from the palette are similar one's a Bluey green one's a greeny blue and on the diagram they're also close together the red is totally different red looks very different from those two colors and on the diagram it's far away and this is the key thing with vectors is the distance between these vectors represents the similarity in meaning of these things so for this very simple RGB thing we're saying that these two colors are relatively similar and they're not very similar to to this color now for RGB that's trivial but we can do this with the machine learning models for vectors to do it with anything I can take for example a picture of my dog Bailey and the word Greyhound put it through an appropriate model and the vectors that come out of those two models will be closely in distance to each other because they are both related to Greyhounds now in terms of distance yeah how do we measure these distance well it's just the old high school geometry if I was doing this in terms of high school how would I do the distance between two things well I would draw a triangle like that let's go back to black I'll draw a triangle like that a right angle triangle and you got the standard X2 you know y^2 z s Etc that's why the terminology you'll often see in these Vector diagrams is they say oh yes we worked out the ukian distance between two vectors all that is is this concept the old Pythagoras rule extended to many many dimensions this RGB is three dimensions a typical Vector might be 384 512 or 1,000 Dimensions but these vectors even though there are a lot more elements in them obey the same principles if two vectors the ukian distance between them is small then the meaning of the original data behind those vectors is similar one might be two things about dogs there might be a picture of a tree that's nothing like a dog and therefore its Vector will be a long way away in terms of distance so I hopefully that makes and hopefully it helps answer the question [Music]
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