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Bro googled the word vector and was waiting to use it.
No, they's referring to the internal workings of AI models, which are essentially a series of incredibly high-dimension matrices with extra bits around them to make them work. Individual concepts are embedded as vectors in the space that these models work in. That's why linear algebra is brought up so frequently in discussions of AI.
While it's true that linear algebra and vectors are used in learning models, they're not using the term correctly in a way that says they know something about the subject (at least, the modern subject). Concepts aren't embedded as vectors. In older models (before the craze), concepts were manually embedded as numbers or a collection of numbers, which could be a vector (but could be something else as well), and the machine would learn by modifying weights. However, in current models (and by current, I mean at least more than a couple years), concepts are learnt by the machine (weights are still modified by the machine as well) and the machine makes its own connections between features presented to it.
For example, you give it a dataset of 10x10 pixel images (with text descriptions) and it reads that as 100 pixels split into 3 numbers (RGB) and then looks for connections between those numbers and in which pixels. It's not identifying what a boob is, but knows that when an image has 'boob' in the text description then there's a very high likelihood that there will be a circular collection of pixels with lots of red somewhere in the image that are also connected to other pixels that are often also lots of red. That's me breaking down what a human would think given the same task/information, but the reality is the machine will come up with its own connections/concepts which are both often far better than humans (when the model works, at least) and far more ineffable to humans.
From my perspective as an algebraist, you seem to be splitting hairs when you're making a distinction between vectors and n-tuples of real numbers. Furthermore, he's referencing a specific 3blue1brown video. I'm not saying their conclusion is correct; they's dead wrong but that doesn't mean their understanding is so shallow that they're simply repeating a word they heard to sound smart.
Here is an alternative Piped link(s):
specific 3blue1brown video.
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I'm open-source; check me out at GitHub.