Learning and analyzing vector encoding of symbolic representations

We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query them. The learned representation (approximately) shares a simple linearity property with theoretical techniques for performing this task

Encoding discrete quantum algebras in a hierarchy of binary words

It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for which we also find that an effective arithmetic code is possible albeit of greater complexity. We also discuss possible applications associated with signal theory and waveform engineering on possible ways to embed discrete computational structures in an analog continuum substrate.Comment: 17 p., 6 figure