Let be a finite field, with algebraic closure , and let be an (affine) algebraic variety defined over , by which I mean a set of the form for some ambient dimension , and some finite number of polynomials . In order to reduce the number of subscripts later on, let us say that has...
come out exactly the same then that would be a test that could be applied to easily distinguish pseudo-random numbers from true-random numbers: true random numbers can have duplicates (and the standard birthday-paradox analysis would make short work of detecting the problem.)
Additionally, by measuring the change in the model’s performance when a variable’s values are permuted, we obtain a clear and quantitative measure of each variable’s importance. The repetition of the permutation process multiple times helps mitigate the effects of random variation, providing more...
For applications to expansion in Cayley graphs, “large” will mean “ for some constant independent of the size of “, but other regimes of are certainly of interest. The way we have set things up, the trivial group is infinitely quasirandom (i.e. it is -quasirandom for every ). ...
Avg. performance, left, and avg. forgetting, right, on permuted mnist sequence. Full size image \(\lambda \)is a trade-off between the allowed forgetting and the new task loss. We set\(\lambda \)to the largest value that allows an acceptable performance on the new task. For MAS, we...