This is of course entirely expected. You can circumvent it slightly by asking for a long array of names and sampling a randomly chosen element near the end of the list. Say ask for 50 names and use the 41-50th element stochastically.
Not perfect, more expensive, but it helps a little. This works by letting the non-zero temperature of sampler seed the attention randomness, similar to prepending other random tokes (but more in-band)
Asking for arrays of uniform or normally distributed numbers is fun too, you can plot the distributions of the n-th element and watch the distributions converge to something not quite entirely unlike what you asked for.
Often there's some bias between element indices too, eg. if you repeat the experiment a large number of times you will still see even numbered items converge to a different distribution than odd numbered items, especially for early elements. Hence the stochastic averaging trick over the last few elements.
Comments
This is of course entirely expected. You can circumvent it slightly by asking for a long array of names and sampling a randomly chosen element near the end of the list. Say ask for 50 names and use the 41-50th element stochastically.
Not perfect, more expensive, but it helps a little. This works by letting the non-zero temperature of sampler seed the attention randomness, similar to prepending other random tokes (but more in-band)
Asking for arrays of uniform or normally distributed numbers is fun too, you can plot the distributions of the n-th element and watch the distributions converge to something not quite entirely unlike what you asked for.
Often there's some bias between element indices too, eg. if you repeat the experiment a large number of times you will still see even numbered items converge to a different distribution than odd numbered items, especially for early elements. Hence the stochastic averaging trick over the last few elements.