sample from cube by sampling a lot of these lanes and picking a random one and the number of bits you need to encode the index the the random one that you picked out of them it's just the KL divergence just log K so the visionary log K bits um so this achieves the bits back cut length without many bits back the trade-off is computational complexity because the concurrency could have to collect a lot of samples and finally there's this other paper which has a very different flavor from the ones that we were talking about this is a paper about