This is an ongoing series of posts related to my dissertation topic, which deals with a model of the neocortex.

Last entry, I gave a general overview of the neocortex, and introduced the idea that the minicolumn is the basic functional unit of the neocortex.

The cortical minicolumn is a cylindrical unit typically composed of about 60-100 neurons, though the size varies slightly between species and within your own brain. But it is reasonable to talk about the basic structure of the minicolumn as relatively similar both within and across species, enough to conclude that it is a canonical template of some kind.

There is much more variation in the number of minicolumns between species than in the general features of the minicolumns. Here are the rough estimates of the number of minicolumns in a few mammalian species:

mouse: 200,000
rat: 500,000
macaque: 30,000,000
human: 200,000,000

One theory is that evolution found a functional structure that allowed for the scalability of the neocortex. The idea I'm working under is that both quantitative and qualitative changes to cognition in mammals occurred as a result of changes to genes that regulated the number and organization of minicolumns.

But how are they organized, and what algorithm might they be carrying out? Jeff Hawkins and others propose that the key organizational motif of the neocortex is hierarchy, so the basic organization is something like a pyramid.

As for what the minicolumn is doing, Hawkins proposes that it has three primary functions:

1) To learn invariant representations of spatio-temporal patterns
2) To make inferences based on information coming from lower levels of the hierarchy, which are then passed up the hierarchy
3) To make predictions about what's going to happen next, and send those down the hierarchy

An invariant representation just means a pattern that you recognize even in slightly different form. For example, you recognize the song "Happy Birthday" no matter what key it's in. You recognize your friend's face even if it's turned slightly, or the lighting is different, or they're wearing glasses or a hat.

The idea is that the lower levels of the hierarchy learn basic building blocks that are then combined to form more complex ideas, which are then in turn used to form even more complex ideas. For example, in your visual system, the primary visual cortex, V1, is sensitive to very primitive stimuli, like lines, edges, and curves. The idea is that once these representations are learned, they can be combined into simple shapes like squares and circles. When you see a dog, all sorts of low-level information is hitting your retina in a stream. All that low-level information, including lines, edges, and color flows up the hierarchy to combine into more complex representations like the parts of the dog (snout, paws, eyes, etc.), until the concept of dog is activated at the top level.

A spatio-temporal pattern just means that the input has spatial and temporal structure. Some of these ideas come from Gestalt psychology. The basic idea is that we initially learn to form concepts for patterns that are close together in space and time. You learn to associate all the features of a dog with a dog because they co-occur in close proximity and the patterns hit your retina close together in time.

Hawkins says that the mechanism of Hebbian learning can explain much of his theory, but from what I've seen about their actual implementation, they aren't explicitly using those principles. Hebbian learning refers to a type of unsupervised learning which can be summarized as "neurons that fire together wire together". The idea is that if two neurons are active at the same time, there must be some correlation between them, and so the synaptic weight (or association) between them is strengthened. If neighboring neurons fire at the same time, and there's overlap in their firing (as when you see an object spatially and temporally localized), the connections between those neurons will be strengthened. Hebbian learning is a plausible mechanism for learning, and has support from neuroscience. The converse mechanism also has evidence, that neurons that fire out of synch tend to become dissociated.

So the idea is that minicolumns learn to fire in the presence of lower level features that occur close together in space and time. So depending on where it is in the hierarchy, a minicolumn may learn the pattern for a particular line orientation, or a feature like a hand, or even a specific representation like your grandmother. Each minicolumn is receiving evidence from the many minicolumns lower in the hierarchy, and that evidence determines the extent to which it fires, activating for the pattern it has learned.

Imagine a military operation organized hierarchically, with scouts bringing in information to people directly above them, whose information is combined in reports to people directly above them in the hierarchy. A given individual receives many pieces of information, and based on that information either reports the presence of something (e.g. a tank or troop formation, or airplane) or is silent. Information aggregates as it travels up the hierarchy, to the people at the top, who have a view of the big picture.

That's how the bottom up flow works. I think that's enough for now, so next time I'll talk about prediction, and how information might be flowing down the hierarchy.