  We investigate the construction of latent spaces through self-supervised
learning to support semantically meaningful operations. Analogous to
operational amplifiers, these "operational latent spaces" (OpLaS) not only
demonstrate semantic structure such as clustering but also support common
transformational operations with inherent semantic meaning. Some operational
latent spaces are found to have arisen "unintentionally" in the progress toward
some (other) self-supervised learning objective, in which unintended but still
useful properties are discovered among the relationships of points in the
space. Other spaces may be constructed "intentionally" by developers
stipulating certain kinds of clustering or transformations intended to produce
the desired structure. We focus on the intentional creation of operational
latent spaces via self-supervised learning, including the introduction of
rotation operators via a novel "FiLMR" layer, which can be used to enable
ring-like symmetries found in some musical constructions.
