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CNV: Assignment 1

In this assignment, you will explore simulations for the development of retinotopy and the function of an orientation map.

You are encouraged to work in pairs of your choosing. Just submit one copy of the assignment, listing your partner, and the mark will be allocated equally to each.

Part 1: SOM retinotopy

First, follow the tutorial instructions for steps 1-11 at /home/jbednar/public/topographica/doc/Tutorials/som_retinotopy.html on a DICE machine, developing a basic SOM map for retinotopy. You should use the copy of Topographica installed in /home/jbednar/public/topographica. Then:

1. As described in step 12, try varying the SOM initial neighborhood radius radius_0, initial learning rate alpha_0, and retina density Retina.density, re-running the simulation each time, in order to be able to answer these questions about each of these three parameters:
   1. Is SOM sensitive to that parameter? Explain.
   2. What is the effect of varying the parameter?
   3. Explain why you think the behavior you observe occurs, referring to specific equations in chapter 3 of the CMVC text.

2. Make a copy of the som_retinotopy.ty file and replace the lines specifying Gaussian.x and Gaussian.y with:

   def xfn():
      return random.gauss(0,0.2)
   
   def yfn():
      if (random.uniform(0,1)>0.5):
          return random.gauss(-0.25,0.1)
      else:
          return random.gauss(+0.25,0.1)
   
   topo.patterns.basic.Gaussian.x = DynamicNumber(xfn,softbounds=(-1.0,1.0))
   topo.patterns.basic.Gaussian.y = DynamicNumber(yfn,softbounds=(-1.0,1.0))
   

   Here random.uniform returns a uniform random number in the given range, while random.gauss returns a normally distributed (i.e., Gaussian) random number with the given (mean,stddev). What topographic grid pattern do you expect the SOM to develop in this case? Describe and briefly justify your expectations. Please do this part before the next question; what's important is that you try to reason out what the network will do, not that your prediction actually matches what you find in practice.

3. Try self-organizing using the different input distribution for a few thousand iterations. Is it developing as you expected? If not, what is different? Do the parameters need to be changed to give a good representation for this type of input? If so, determine which one(s), and re-run the simulation. In either case, include a screenshot of a sample Center of Gravity plot from your final organized network, in .png or .pdf format.

Part 2: Self-organized Gaussian OR map

First, follow the tutorial instructions at /home/jbednar/public/topographica/doc/Tutorials/lissom_oo_or.html on a DICE machine, testing a LISSOM map self-organized on oriented Gaussians.

1. For a Line stimulus, systematically vary the following input parameters and observe the V1 response (and LGN response, if appropriate):

   scale:

   Brightness of the line

   offset:

   Brightness of the background

   y:

   vertical location of the line

   orientation:

   Orientation of the line

   thickness:

   line thickness

   After varying each parameter, reset the values to the defaults using the button in the Test Pattern window, to ensure that the effect of each parameter is considered separately. For each parameter, report your observations on how the LISSOM map responds:

   1. Is LISSOM sensitive to that parameter? Explain.
   2. Is the value of that parameter encoded in a useful way in the map activity? Explain.
   3. Do you think the LISSOM response is realistic? Why or why not?
   4. Explain why the behavior you observe occurs, referring to specific equations in chapter 4 of the CMVC text and to the self-organized Projection plots.
   
   
2. Explain why the LGNOnAfferent weights to V1 in the Projection plot look very similar to each other, yet very different from the LGNOffAfferent weights to V1. What effect will this have on the ability to respond to lines that are brighter than or darker than the mean luminance? What does this indicate about the suitability of the chosen training pattern as a model for natural images?

Submission

Your work must be submitted by 10am Monday, 27 February, using the submit command on Informatics DICE machines (type man submit for more details). Your work should be in the form of one plain ASCII or PDF file per problem, named as listed below. PNG images can also be included for problems that require an image. Late submissions will not be accepted without good reason, and will be penalized according to the standard university policy of 5% penalty per working day or part of a day.

Example of submit command:

submit msc cnv 1 1.1.txt 1.2.txt 1.3.txt 1.3.png 2.1.txt 2.2.txt

Tips for getting a good mark

Be sure that you provide evidence that you did each part of this assignment. I can only judge what is actually submitted, so you should make sure that the files you submit make it clear that you have done everything, and thought about everything.

Be sure to cite any information that you use that is not from the course material or your own experience. Including such information is encouraged, but it must be properly cited. You can use the CMVC book Bibliography database for citation information for any paper cited in the CMVC text.

Submissions must use ASCII text or PDF; images can be added separately in .PNG format. I can be sure to be able to read those formats; others like .doc or .sxw have a certain probability of working, but the probability is far from 1.0. Naming the files as I suggest will make my job a lot easier, because I will be able to see exactly what you are submitting for each problem.

Read and follow my list of writing tips.

Last update: assignment1.html,v 1.10 2006/07/03 18:09:14 jbednar Exp