Recommendation Systems

[Falco]

@CollinsEM

As I think about grid cells, I see them serving the role of modeling a continuum of configurations (or state space). That is to say that they are useful for representing properties which can take on specific values from a continuous range of values.

@rhyolight

You might think of each dimension in space as a state. If GCMs can represent N-dimensional space, it would be possible to represent a rich feature in each dimension.

Yes, I see now. You’re both right. Thanks.

[CollinsEM]

@Falco

I don’t think grid cells have that much in common with a state space. (Unless I have a wrong idea of a state space).

Perhaps state space was the wrong terminology. State space sometimes comes with connotations of discrete configurations (e.g. finite state machine). I was trying to distinguish between discrete and continuous variables. I think we have two different ways of representing these concepts in our minds. While each ultimately results in a sparse distributed representation in the brain, I believe the mechanism for navigating between similar items/concepts is different when your are exploring along a continuous range of values as opposed to a discrete set of values. Grid cell modules are good candidates for modeling the former, while some form of auto-associative memory (or displacement modules) might be necessary for the latter. I’ve not thought as much about the discrete case, so I don’t have a good mental model for it yet.

@Falco

Also @Shahar didn’t say he was making a recommendation system for movies. That was just an example. If one wants to build a general purpose recommendation system, it kind of makes sense to generate connections without knowing what the sensed data represents.

I was attempting to be generic in my descriptions, but I tried to provide a specific example to drive home my points. Hopefully, my intent was clear.

The gist is that it is conceptually very difficult to interpolate between discrete categorical values in the same way that we interpolate along a continuum of values. I believe that there is another mechanism (other than grid cells) that allows us to make those jumps between categories.

I consider the category jump to be accomplished in a manner similar to a context switch or how we transition from one room to another. There’s a moment when you cross the threshold that your frame of reference shifts from one room to the next and the grid cells modules reanchor to the new environment. From that moment on, your perceptions and expectations are all in the context of that new reference frame.