[quantadev]

In college (BSME) I wrote a computer program to generate cam profiles from Bezier curves. It's just a programming trick to generate curves from straight lines at any level of accuracy you want just by letting the computer take smaller and smaller steps.

It's an interesting concept to think of how NNs might be able to exploit this effect in some way based on straight lines in the weights, because a very small number of points can identify avery precise and smooth curves, where directions on the curve might equate to Semantic Space Vectors.

[quantadev]

In fact now that I think about it, for any 3 or more points in Semantic Space, there would necessarily be a "Bezier Path" which would have genuine meaning at every point as a good smooth differentiable path thru higher dimensional space to get from one point to another point while "visiting" all intermediate other points. This has to have a direct use in LLMs in terms of reasoning.