Absolutely! This is actually the original reason I began exploration into quasirandom numbers. I wanted to see if I could replace some of the stochastic process in current machine learning architectures with quasirandom processes.
In principle, the curse of dimensionality kicks in after a dozen or so dimensions, as convergence is O( log(N)^D / N). But in practice I have found that in a surprising number of applications and circumstances, quasirandom sequences can have offer a substantial improvement even when the number of dimensions are in the hundreds or even thousands. (Some authors have suggested this works because the solution space is of low dimensions but embedded in a much higher dimensional space...)
However, to get the full benefit I needed to find a low discrepancy quasirandom sequence that did not suffer the many of the parameter degeneracy problems that many of the conventional ones exhibit for very large D. For me, the new R-sequence nicely solves this parameter selection problem by not having any parameters to optimize!
Can you explain how you figured out that these were the right generalization of the golden ratio? Were you doing a literature search? Just experimenting?
BTW, in the past couple months I have directed several people who were interested in spiral phyllotaxis and the like at your page. I think your sequences could make for some interesting art projects.
Personally I plan to try them out for dithering, picking well-spaced colors for diagrams, picking points in a region when trying to optimize a map projection, etc.
Thanks for the kind words and promotion! ;)
These findings were a combination of a lot of literature searching, perseverance, decades of mathematical intuition and computer modelling of various hypotheses.
I had a problem to solve so I was determined to find a solution. And then combine this with my obsession with simplicity, it meant I didn’t just want to tweak a million parameters to get a result.
In principle, the curse of dimensionality kicks in after a dozen or so dimensions, as convergence is O( log(N)^D / N). But in practice I have found that in a surprising number of applications and circumstances, quasirandom sequences can have offer a substantial improvement even when the number of dimensions are in the hundreds or even thousands. (Some authors have suggested this works because the solution space is of low dimensions but embedded in a much higher dimensional space...)
However, to get the full benefit I needed to find a low discrepancy quasirandom sequence that did not suffer the many of the parameter degeneracy problems that many of the conventional ones exhibit for very large D. For me, the new R-sequence nicely solves this parameter selection problem by not having any parameters to optimize!