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Re: [Phys-l] inversion goggles



On 05/13/2011 11:18 AM, Marc "Zeke" Kossover wrote:
You might think that the nerves that connect our eyes to our optical cortex in
the brain work that way, but I strongly suspect that they don't. The nerves do
not remain coherent nor organized and get crossed by the time they make it to
our brain.

So an image that starts out on the retina

0000000
0000000
1111111
0000000
0000000

might map to

0000101
0010000
1001001
0000000
0001000

on the cortex. Part of learning how to see is learning what spots on the cortex
are actually next to each other in the retina.

I'm pretty sure that's not true. It can't be true, because it would
be inconsistent with the purpose and the operational mechanism of the
brain.

The brain is known to work as a powerful analog computer. One of
the strategies that it relies on is to build /maps/. In the cortex
there are maps of things that are going on in the real world. There
are lots of little maps, not one big map. Different maps process the
input in different ways. Some are more-or-less direct geometrical
maps, while others are more abstract, more like generalized Hough
transforms.

This has been known since the 1940s (Sperry) and is mentioned in
Feynman volume I chapter 36. I'm not an expert, so for all I know
it could be even older than that. Since the 1970s there have been
detailed theories about how the neurons use the chemistry and physics
of diffusion and competition to set up the maps (Willshaw and von der
Malsburg).

Here's an overview:
Jack D. Cowan and A. Edward Friedman
"Eye-Brain Maps" (1995)
http://tuvalu.santafe.edu/research/publications/wpabstract/199510097

And another
Paul C. Bressloff, Jack D. Cowan, Martin Golubitsky, Peter J. Thomas, Matthew C. Wiener
"What geometric visual hallucinations tell us about the visual cortex" (2002)
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.83.1946&rep=rep1&type=pdf

Those papers cite the classic references. You can find more by
googling for buzzwords like "receptive field" and "hypercolumn".

In vertebrates there is considerable plasticity and there is such
a thing as "learning to see" as evidenced by the inverting-goggles
experiments. In invertebrates the connections are more static and
hard-wired.

I would predict that the plasticity and learning are /not/ sufficient
to overcome a random permutation of pixels, such as could be carried
out using goggles with scrambled optical fibers. I don't have any
proof of this, but I'm not sure that's my fault. I suspect that it
would be hard to get such a result published, because it would be a
negative result, and also an unsurprising result.

The logic here is simple: The brain is known to compute most things
locally. It /has/ to compute locally, because arbitrary long-distance
connections would be prohibitively wasteful. Another argument that
leads to the same conclusion is based on information theory, starting
from the observation that there are just too many random permutations.
A million factorial is a big number. There isn't enough time (or enough
training data) to allow the inverse permutation to be learned.

This has been a recurring motif in "neural networks" and machine
learning since the 1940s. The equation is:
random + learning = random = useless
Instead, you need to start with a lot of highly non-random preprocessing,
and then you can rely on learning to do the fine-tuning. This has
been discovered and repeatedly re-discovered ... and we understand
on theoretical grounds why it must be so: Vapnik-Chernovenkis
dimensionality et cetera.

Note that maps are not confined to visual cortex; the same strategy
is used in /auditory/ cortex (Kohonen). This leads to interesting
artifacts, because the dimensionality of the representation in the
map (2D) is different from the dimensionality of the things being
represented (five-dimensional "formant space" et cetera). This runs
afoul of the theorem that says you cannot change dimensionality in a
way that is one-to-one and continuous. So the map winds up being
piecewise continuous, with wild breaks here and there. I conjecture
that persons with different native languages tend to arrange the
discontinuities and overlaps differently. (Try explaining to an
Italian the difference between a ship and a sheep. It can be done,
but not easily or quickly. Major rewiring is required.)