Ok, it's time to begin to get our projects in line. Projects can be just about anything; you need to talk to me individually (or as a small group) to see if I agree to your proposal. That is, while the range is unrestricted, your project will need to achieve a level of competence that demonstrates your acquisition of skills relating to neural networks.
I've heard from a few of you regarding general ideas for direction, but the rest of you have not yet indicated even that. Of course, I haven't been asking and indeed I told you to wait a while. However, now would be a good moment to start doing some thinking. Finance, psychology and quantum computing have already been mentioned, as have psychophysics and, of course, math!
A project proposal should contain the following elements:
For example, the problem might be to determine whether or not there is an inherent tendency in a given language for the frequencies of middle formants in the speech sounds accompanying basic consonant-vowel utterances (like "ba", "ga", "pa", etc.) to provide a linear model of the midpoint as a function of the onset. Slope of the line would be a speaker-dependent invariant enabling disambiguation of multiple speakers (the ``cocktail party problem''); i.e., the original problem is interesting if only because it sheds light on the well-known and important cocktail party problem. Of course, it is also important since it goes to the heart of speech understanding.
But this would not be a good _neural network_ problem as currently posed since, while it requires tools, they don't seem to have much to do with neural networks, and we haven't yet addressed the evaluation issue. In fact, this problem has been studied (see, e.g., the journal Brain and Behavioral Science - I've got the reference someplace if you are interested.) It turns out that such a linear relationship does exist. But perhaps there are nonlinear relationships involving other pairs of phonetic signals, and a neural network certainly might be useful in finding them. In the linear case here, as I recall the experiments yielded scatter-plots which could then be measured for the correlation values with particular straight-lines. So the standard statistical methodology would be applicable.
However, a project need not involve a real psychophysical experiment. In general, such experiments are amazingly demanding of resources and, to make matters worse, there are very strict guidelines involving any use of human subjects. (That's one reason that many psychophysicists use themselves as guinea pigs - that and the reason that these experiments can even be fun!) But one could design a theory of how to apply neural networks to predict or control such experiments.
For a biologically minded student, one might consider a project on the application of neural network techniques to ``genomics'' as is treated in the new (and excellent) book by Wu and McLarty that I will show you in class.
For mathematically oriented folks, here are some interesting areas. I am not specifying particular problems. Find a neural network approach to (i) detecting topological form (e.g., discriminate spheres from torii) based on a sequence of data or (ii) detect whether a function is odd or even (or is a _shifted_ odd or even!). Still another broad area: Use the special properties of the unit quaternions or octonions to design a new type of neural network. (I have a couple of weird ideas for novel nets that I will share with a suitably masochistic student ;-)
Paul C. Kainen, Department of Mathematics, Georgetown University; 202-687-2703; kainenp@gusun.georgetown.edu; home(ly) page neural page or classroom page .
Oct. 9, 2000; Washington, DC