> The advantage of this approach is that it generalizes efficiently to any number of dimensions.
I am unsure about whether this is true. The ratio of a ball’s volume to its enclosing hypercube’s volume should decrease to 0 as dimensionality increases. Thus, the approach should actually generalize very poorly.
Let S = {S_i} be any set of cubes that covers a d-sphere. Choose a point in a cube and an integer i in [0, |S|). Now you have a random point in S. With a judicious choice of S you obtain a uniformly random point in the unit sphere with high probability.
I find it difficult to think of examples that aren't just based on niche information (what did we talk about on this day? what analogy does the teacher make repeatedly?). Maybe multimodal stuff?
Even multimodal stuff is something is advancing pretty quickly. And with the more widespread incorporation of things like this, the information will be fed back into AI systems as training data making finding new things more difficult.
reply