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Views from Artificial Intelligence

There have been a wide variety of theoretical models designed to explain the visual system. Once designed, these models are simulated on a computer, and the results are compared against the data reported by neuroscientists. Of particular interest to our current research has been the development of theoretical models of orientation selectivity and ocular dominance.

One of the earliest models to explain V1 is due to Ralph Linsker [Lin86c] [Lin86b] [Lin86a]. Linsker's model uses simple Hebbian neurons to make edge selectivity and ocular dominance. Hebbian neurons, postulated by Donald Hebb, are neurons which respond most strongly to inputs which occur most frequently. Although it does give an explanation of how neurons could do what they do, there are a few things which are not very satisfying about the theory. First, it doesn't really give a picture of why it is useful for the neurons to do what they do. They just have little local rules which result in these nice behaviors. Second, the neurons have some parameters that need to be set by the designer, and if the parameters are not in a fairly small range, then it doesn't work right. Piepenbrock [PRO97] found a model which makes ocular dominance and edge selectivity form, but it has an even narrower parameter range. The problem with this is that the neurons are specialized to do exactly what they are doing, and they can't really do anything else. This severely limits the nature of what neurons can learn. Mriganka Sur's work [SAS00] [vMPS00] would seem to indicate exactly the opposite of this assumption. Sur is a neuroscientist who managed to reroute the data coming down the visual tract in ferrets to the auditory cortex. Surprisingly, the ferret learned to see anyway! Prominent features from the visual cortex appeared in the ferret's auditory cortex, and the ferret was actually able to visually distinguish between different stimuli. This seems to indicate that the cells in the visual and auditory cortex are not specialized for their task at all; rather they do some analysis of the input that is entirely independent of their location in the brain. If this is true, then any good model of V1 must explain what that principle is and how it is implemented in the brain.

There are a number of theories which attempt to explain what the principles are at work. There are three theories of interest to our current research: sparse coding, temporal invariance, and independent component analysis.

Sparse coding says in essence that the brain is economic in its representation of the data it sees. It represents the data it perceives using as little information as possible. Field argues in [Fie94] that the data from the world typically occupies a small percentage of the much larger sample space it comes in, and that the percentage it occupies is usually very complex. In the introduction, the example of recognizing faces was used to show that any particular face can look vastly different (in terms of the colors of the pixels of an image of that face) depending on the lighting, position, orientation, and pose of the face. Faces form a very complex region of image space. They also form a very small region of image space. Consider picking the colors for the pixels in an image at random. The result will probably look like the fuzz from a TV that is not on a channel. The chance of an image picked at random actually looking like a face is exceedingly small. So faces certainly form a small, complex region of image space, and most data of interest also does. Sparse coding argues that the brain should spend its efforts representing what actually occurs; i.e. it should work hard to represent faces well since it sees them often, instead of spending time representing TV fuzz. The consequence is that it will be able to represent faces succinctly. The representations of common inputs are more compact than the representations of uncommon inputs. In [Ols01], Olshausen gives an algorithm for representing image data using sparse coding. The receptive fields of the simulated neurons that resulted from the model look similar to the receptive fields of real neurons.

The idea behind temporal invariance is that things in the world do not change near as often as the input does. Again, just a small change in the position of a face produces a large variation in the pixels of the image. But if the brain looks for properties of the image which change slowly, then hopefully it will find real objects, and the positions of those objects, and the properties of those objects, etc. Mitchison described in [Mit91] a means of doing this using gradient descent. Stone provides an information theoretic explanation of the principle in [Sto96]. Wiskott demonstrates a method in [WS02] based on linear algebra which finds the optimal functions with a non-adaptive algorithm. In [BW02], he uses this method to generate receptive fields, and they again look very much like the receptive fields of real neurons in V1.

Independent component analysis is generally credited to Bell and Sejnowski [BS95]. The idea behind ICA is that data comes from several sources, and that it would be convenient to process the data from each source independently. Therefore, the brain should split the information back into its original sources and process the data in that form. This explains the existence of ocular dominance columns. The data is coming from each eye separately, and at least the early processing should be done separately between the two eyes. So the data gets split into columns. Likewise, edge selectivity comes about because edges are the most independent components found in natural images [BS96].

None of the theories above have been researched very much in the context of spiking neurons. Instead, they assume that the spike rate of a neuron is the important thing, so neurons really convey continuous values. Thorpe argues in [TI89] and [FTDMT01] that there is not time for the brain to measure the spike rate of neurons. Given an input, people can respond within 150 ms. If the neurons communicate using spike rate, then each neuron has to fire several times in order for a neuron watching it to know how fast it is firing. But few cells even get to fire once in 150 ms, so the firing rate assumption doesn't fit the data well.

In conclusion, there is much known about the visual system, and several theories about it. However, there is still much that is not known about it, and the different theories highlight how little is really understood.


next up previous contents
Next: Bibliography Up: Neural Coding in the Previous: A View from Neuroscience   Contents
Jonathan Shaw 2003-09-30