It appears that evolution has not quite figured out how best to construct hierarchies either! I have read numerous times that areal size of V1 in humans can vary by over a factor of 2! One researcher said 3X. People with different size V1's all have normal vision. People with an extra-large V1 have better acuity. Of course a monkey's vision is nearly as capable as ours, but dogs and cats less so, rats hardly see at all. I find it liberating to realize that cortex works under so many varied conditions with so many different types of inputs. We will have lots of opportunities to experiment with tweaks and variations.
Jeff From: nupic [mailto:[email protected]] On Behalf Of mariolakakis . Sent: Sunday, February 16, 2014 4:04 PM To: [email protected] Subject: Re: [nupic-discuss] What dictates the exact formation of the cortical hierarchy? Exactly. What feels strange is not that there is a tradeoff in the hierarchy, but that someone made the decision of what that tradeoff should be, and what practical is. What is practical is being selected by evolution and by evolution I mean the ability to adopt. There has to be a correlation between the size of a sensor and it's significance to the adoptability of the organism it is attached to. The size of a sensor determines the complexity of the patterns, which in result defines the structure of the hierarchy of the regions. For example, for us human beings the size of our visual cortex is huge because of the importance of our stereoscopic vision. I assume that the visual cortex has the highest and most complex hierarchy of regions. What happens if one day we want to build a different hierarchy of that which exists in the human brain? What if the dominant sensor (the most important one) has to learn air traffic patterns and not visual patterns? How do we model that? What will our guidance be? Mr. Hawkins I embrace your vision of billions of models but I believe that we have to model how to build hierarchies in the same way that you have modelled how to build regions. I'd like to get to the point of singularity faster :) instead of trying one hierarchy after another and watch as sensors become slightly better over the years, as it is happening right now with Siri, Google Now, etc. On Mon, Feb 17, 2014 at 12:00 AM, mariolakakis . <[email protected]> wrote: I know that the goal is efficiency in training and storage but how is the hierarchy in the neocortex done exactly? Is it a result of a mathematical equation? Or is it the throw it in the wall and see if it sticks process of evolution? My mathematical theory is very simple and it's based on binomial coefficients. Let's say that the human body consist of a K number of sensors. The number of regions X in the hierarchy should be equal to X = !K / (2! * (K - 2)!) + K (for each sensor). That's the number of all possible duplets of sensors with no repetitions. This equation creates a pool of the highest variety but least density that we can use for representations. And it also explains the tree like shape of the hierarchy and why it converges and diverges and you up and down. For example, if the human body consisted of just three sensors: S1 = Optic, S2 = Acoustic, S3 = Touch The number of regions would be X = 3 * 2 / (2 * 1) + 3 = 3 + 3 = 6 1. R1 = S1 (Optic) 2. R2 = S2 (Acoustic) 3. R3 = S3 (Touch) 4. R4 = R1, R2 (Optic + Acoustic) 5. R5 = R2, R3 (Acoustic + Touch) 6. R6 = R4, R5 (Optic + Acoustic + Touch) Let's consider the part of the neocortex that handles language. The number of characters in the alphabet is much smaller than the number of words and the number of words is tiny compared to the number of phrases. This simple observation makes me assume that the hierarchy in the brain is like this: 1. Letters (Highest level concepts) 2. Words 3. Phrases Using a single region we would have to assign columns to letters and sequences of cells to words. For example, the words "god" and "dog" would share the same spatial pattern but different temporal patterns. Since, the higher regions get only spatial patterns from below how does the distinction of those two gets communicated above? What happens if the word has multiple identical letters? Do the cells in a column connect to other cells in the same column? For example, the word "good" has two "o"s. To summarise, if one region wasn't enough and I wanted to reconstruct the human neocortex based on a K number of sensors, how would I know how many regions I would need, and in what way should I connect them to make it all work? Thats a problem you will face in the future. One day, one region won't be enough. I 've implemented a huge part of the CLA in Xcode and got it running on an iPhone, I've seen a dozen videos of Jeff Hawkins' presentations and I 've also bought the book On Intelligence but I haven't found any answers to these questions. I'm counting on you guys. :)
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