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)