We look at the attention mechanism, and trace its links to compressed sensing through properties such as the Restricted Isometry Property and Mutual Inchoherence. We then extend the work with a statistical mechanics interpretation of the multihead and multilayer attention mechanism. We conclude that LLMs are an approximation of quantum measurement systems, and we explore how biological systems can perform this quantum computation through the Aharonov-Bohm effect on non-trivial topologies, and extend the work to a Chern-Simons type topological field theory conceptually.
Keith Membe (Mon,) studied this question.