How far does a hash-only sender go? A pre-registered map of sender memory versus bits for short text messages

Abstract

Can a sender that only computes hashes, with a language model only at the receiver, transmit short human text more cheaply than a classical sender trained on the same domain? We answer with one pre-registered run on 1,000 English user utterances from Taskmaster-1. The primary endpoint is the cost per message to deliver 100% of the messages (hash bits, plus a 2-byte negative acknowledgement and the raw text when the first attempt fails), paired against an in-domain PPM order-1 sender. The hash-only sender delivered 857 of 1,000 messages on the first attempt and cost 192.8 bits per message, 18.4 bits more than PPM order 1 (95% bootstrap interval 10.9 to 26.3); by the pre-registered rule it spends more and is not equivalent within one byte. As secondary results we map measured sender memory against bits. The hash-only sender (8,190 B on a host build, keyed BLAKE2b tag included, as in every method) was the cheapest point in bits from 8,190 B up to, but excluding, PPM order 1 at 24,844 B, 45 to 46 bits below smaz2 and Unishox2; from PPM order 1 upwards, in-domain senders spend fewer bits, except order 2 pruned to 16 KiB. In airtime it loses to PPM order 1 on all five links priced, to Un