[Martin Taylor 2005.12.07.09.52]
[From Bjorn Simonsen (2005.12.07,09:00 EUST)]
In response to [Marc Abrams (2005.12.06,1256)]
When I look at your graph there is an Output Signal going to the
environments and also to the input function. I tried to put these
information into Rick's Spreadsheet, and I lost the negative feedback.
Then the model was not able to perceive what it wished to perceive.
Since Marc's diagram was the same as mine, in most respects, I think your comment should be aimed at me, too. I can answer it on my behalf, anyway.
Marc says his is merely a metaphor. I say mine is an incomplete circuit diagram. It's incomplete in that the "World Model" is not specified, and the manner in which the output of the "World Model" contributes to the PIF is not specified.
You say you "put" the connection through the world model into Rick's spreadsheet, and lost the negative feedback. You don't say just what you mean by "put". I assume you just added it in, but I can't see how that would make you lose the negative feedback, so I'm probably wrong.
The most simple-minded conception I have of how I would make the connection is a weighted average, where the perceptual signal is formed by a weighted average of the normal (sensory data only) PIF output and the output of the World Model (which emits the imagined result of what would be perceived given the actual output of the control system's output function). If we call the normal PIF output Ps (Perception sensory) and the output of the world model Pi (Perception imaginary), then the perceptual signal would be k*Ps + (1-k)*Pi.
The "World Model" is supposed to behave the way the actual world would do if influenced by the same output. I imagine that in your modelling, both connections from the output were simple connections, with no lags or complicated functions. That's fine, but if that's what you did, I can't see how you lost the negative feedback. All that should have happened is that the loop gain correcting for disturbances should have been reduced by the factor k.
In a more realistic use of the model, there must be provision for determining the value of k, and for determining the structure of the World Model. In the real world, even at the lowest level, the output has an effect on the outer world, and thus on the perceptual signal, that is extended in time. The World Model ideally should duplicate that, without itself being able to influence the outer world. How can this be done?
One approach to this is to use Bill P's ideas about the "Artificial Cerebellum", which uses the ongoing time pattern of the error signal to derive what amounts to an inverse world model in the output function, so that the time pattern of the output balances out the temporal fluctuations inherent in the environmental feedback path. The difference is that the World Model imagination connection doesn't balance out the effects on the real world, but replicates those effects in its structure. What it would proesumably use to do that is to compare its outputs with the actual Ps, and use those to alter its structure over time.
This approach to evolving the structure of the World Model also provides a means of arriving at "k" in the simplistic "weighted average" approach to merging the Ps with the Pi. The closer Ps and Pi have been over recent time, the greater the weight placed on Pi in the merging process.
As I imagine it, there are other things that influence "k", especially in a system that contains many interacting control loops. Among them are whether the current output is actually switched to influence the real world, and whether the data required to create Ps are currently available (which requires a separate perceiving system to make that determination). This latter enables a system with a good World Model to maintain stability (though not resistance to disturbance) when the perceptual input is disconnected. It is needed, because if there is no such "data available" signal in a control system, the loss of perceptual input would be treated the same as a massive disturbance, and the output would be likely to go crazy.
Which brings up a third factor affecting "k". Assuming a well developed World Model, if perceptual input is indeed coming in, and the Ps signal differs substantially from Pi, either a significant disturbance has occurred, or the World Model no longer correctly represents the environmental feedback path. Something has changed in the environment. In either case, k should be very small.
So there are three factors that affect how the output of the World Model should be expected to merge with the sensory input to generate the perceptual signal: (1) The mid-term accuracy of the World Model when compared with the purely sense-based perception (which, of course, might include imaginary components from lower levels in the presumed hierarchy), (2) the state of the switches (whether the control system's output is actually going to the outer world or the perceptual signal is coming in from the outer world), and (3) whether there is current significant difference between Ps and Pi.
Anyway, that's more or less how I conceive of completing the circuit diagram that is sketched in my figure. If you want to model it, using the spreadsheet or anything else, I'd be delighted. If that's what you have already modelled, I'd like to get a copy of th spreadsheet, to se where my ideas went wrong.