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Not just similarity. It also includes all other possible relationships if you want, such as order, connectivity, etc.

I'd say similarity, but any and all kinds of similarity you could ever think of - as long as you have enough dimensions and training data to feed it.

My current belief is that a hundred thousand+ dimensional latent space, as in SOTA LLMs, seems to have enough dimensions to reduce a large array of cognitive skills into a proximity search.

What is order/connectivity in R^n?

It's pretty arbitrary. For example, you can define order as the product of all order relationships along each single dimension (binary product). As for connectivity, they can also be defined as boolean functions under certain radius, like the persistent homology spectrum.

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