I keep thinking about the Particle Filters AI method, so might as well right some of it down. Note that in AI Particle Filters has a particular meaning, different from the physics for particles in a real-world simulation or in a video game. In AI filtering is a method for localization of an object, which could be a large physical object like a robot. It involves probabilistic methods (Monte Carlo techniques) for predicting where the object might be, combined with sensory feedback. Typically it requires a pre-existing map of the territory (which for a robot is real, but which could be highly abstract in other cases) and a method for matching the feedback to the map. It has been most notably used as an essential software component of the Google self-driving car. A somewhat more extensive overview can be found at Particle Filters.
The reason I keep thinking about it is because I started noticing how I consciously (and probably subconsciously) localize myself in the physical world. Most notably, when I am navigating in the dark in my house. I do this to avoid backtracking: turning on a light, going back to the prior switch & turning it off, etc. In any case I know my house well, but in just a few feet in the dark it is easy to get a bit off course and bump into furniture or a wall where I expected a doorway. The stairs can be tricky too.
So I walk a few feet in what I guess is the right direction based on experience. Then I reach out to touch what I expect is a wall or piece of furniture. Or I note a change from rug to bare floor, or spot an LED. Usually I get the feedback I expect, but sometimes I find I am off course and need to make a correction.
In Particle Filter Localization terms, I project a probabilistic range of particles representing where I, the human robot, might be next. Then I check. Often I know exactly where I am after a check, but sometimes all I know is that I am not near a wall or furniture piece. Then I make another mental projection, take a step or two depending on my expectations and level of caution, and try again to touch something. I go through similar mental gymnastics when driving a car or taking a daylight walk, but the feedback is visual rather than touch.
I went through a similar analysis process after reading Jeff Hawkins theory of predictive memory in On Intelligence. The theory is that the brain largely operates by making constant predictions, based on memory of historical patterns, and checking them against sensory input. When input varies from predictions, neurons send special signals about detecting novelty to higher brain centers that deal with novelty. For instance, as you read this your brain knows a number of words might be included in this zebra. See, you expected "sentence" or maybe "essay" or the like, you were not expecting "zebra", and so the normal flow of processing was interrupted.
I have not seen a neural network model for particle filters. It could be that the resemblance between how human brains seem to work is only superficially like particle filters. More generally we are talking about feedback systems, which can take a number of forms. Even very primitive animals that lack differentiated neurons have feedback systems, so there could be many types of neural feedback schemes operating in the human brain.
I often notice my dog doing something that makes me think that most mammals, including pre-sapiens homo species, can do that. Yet when these processes, say chasing a rabbit, are abstracted, they can become quite complex. I can imagine chasing a rabbit. I can plan to chase a rabbit into a trap. I can pursue something more abstract, say a solution to a construction problem or even a math problem in a way that resembles chasing a rabbit. Let's see, the answer to the solution of this differential equation has disappeared, it is not obvious. I'll beat the bushes, using three techniques known to help solve this type of equation, most-likely technique first. Hopefully one technique will put the problem in a form that I recognize from the standard map for solving such equations.
How would particle filters be implemented with neural networks? Let me know your thoughts.