Stuck on Notation
by JS
I’m stuck on what should be the easiest section of my proposal to write because it is the only section I’ve already published. The problem is that, in the time since I worked on that paper, my whole conception of “what’s going on” has changed. At least I had the presence of mind at the time to coin the phrase “sensorimotor embedding” in a way that is quite similar though much less precise than what I’m doing in my proposal.
The problem is that I have a number of equations that describe how saccades (quick eye movements) can affect sensor activation if the sensor has a foveated structure (more resolution in the center and less resolution on the periphery — just like your eyes and mine). These equations all reference the state of the system, which is really just the sensor pose. The problem is that the whole point of the paper is to infer the pose, because the agent does not know the pose.
So I have all these equations that utilize unknown sensor pose to describe how an agent can learn the sensor pose, which ends up being sort of circular unless you understand clearly where the dividing line is between what an agent knows and what an agent is trying to learn. This problem keeps cropping up in my proposal. I need to figure out a way to make if clear that the point is to figure out a way to infer the unknown from the known, and what parts of the model the agent is “filling in” when it goes about learning. It’s gotten so bad that I am basically highlighting unknown parts of the model in red.
Is there a better way? I know in graphical models there’s a specific notation for observed variables versus hidden variables. But I’m not using graphical models (for reasons that are somewhat too complicated to explain in one post), so is there a notation that I can use in (not necessarily probabilistic) formulas directly that doesn’t involve drawing a bunch of graphs like in graphical models?
