Basically the same way your favorite codec knows how to decompress. It builds the predictor (in this case, a NN) from the known input. The predictor then assigns a symbol (or a series of symbols) to the next few bits - higher probabilities need fewer bits (I haven't checked for this specific technique, but there are techniques that don't even require an integer number of bits, e.g. range encoding).

See https://news.ycombinator.com/item?id=27244810

As I understand it, when starting up (beginning of stream) - the network does not compress, then guesses the next byte at every turn determininstically from input so far.

Decoding can "read" the fist byte, then proceed to learn and guess the second byte and so on.

see the (current) top comment

https://news.ycombinator.com/item?id=27244810

it's a very clever use of symmetry.

It's clever, but pretty much "standard" in compression. Earliest I'm aware of that used symmetry in the encoder and decoder to prevent explicitly transferring the parameters this way was LZ78 (Lempel, Ziv; 1978), but there could well be predecessors I'm not aware of.

LZ78 used it "just" to build a dictionary, but the general idea of using symmetry is there.

(A fascinating variant on this is Semantic Dictionary Encoding, by Dr Michael Franz in his doctoral dissertation (1994), that used this symmetry to compress partial ASTs to cache partially generated code for runtime code generation)