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 1-10 at /group/teaching/cnv/topographica/doc/Tutorials/som_retinotopy.html on a DICE machine, developing a basic SOM map for retinotopy. It is important that you use the copy of Topographica already installed in /group/teaching/cnv/topographica, because that is the only version that I have tested with these instructions (and different versions would need slightly different instructions).

  1. As described in step 11, try varying these parameters:

    weight_seed
    Random set of weight patterns
    radius_0
    Initial neighborhood radius
    alpha_0
    Initial learning rate
    retina_density
    Retina density

    re-running the simulation each time, in order to be able to answer these questions about each of these four parameters:

    1. What is the effect of varying the parameter?
    2. How sensitive is SOM to that parameter? If there are changes, are they dramatic, or relatively minor? Explain.
    3. Explain why the behavior you observe occurs, referring to specific equations (by number) in chapter 3 of the CMVC text, or to the Euclidean distance activation function from the class notes.

    Note that you usually won't need to run all the way to 40000 iterations to see what's happening, as it should be clear by about 10000 iterations whether it is going to organize properly or not. Also note that changing any density effectively also changes the weight_seed, because the pattern of weights will differ for different sizes.

  2. Make a copy of the som_retinotopy.ty file. Add these lines somewhere before input_pattern:

    import random
    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)
    
    and replace the lines specifying x and y in the input_pattern with:
        x = xfn
        y = yfn
    

    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. Your mark will be based on how you are reasoning about it, not on whether what you expect to occur does happen.

  3. Try self-organizing using the different input distribution. 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 grid plot from your final organized network, in .png or .pdf format.

The overall goal of this part is to demonstrate that you understand how the SOM algorithm works, and particularly how the behavior is determined by the parameters and the distribution of input patterns, so be sure to make this clear in your responses.

Part 2: Self-organized Gaussian OR map

First, follow the tutorial instructions at /group/teaching/cnv/topographica/doc/Tutorials/lissom_oo_or.html on a DICE machine, testing a LISSOM map self-organized on oriented Gaussians. A snapshot of the already-organized map is in /group/teaching/cnv/topographica/examples/lissom_oo_or_10000.typ.

  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
    smoothing:
    edge smoothing

    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 the value of that parameter encoded in a useful way in the map activity? Explain.
    2. How sensitive is LISSOM to that parameter? If there are changes, are they dramatic, or relatively minor? Explain.
    3. Do you think the LISSOM response is biologically realistic, based on the biological background presented in this course? Why or why not?
    4. Explain why the behavior you observe occurs, referring to specific equations (by number) in chapter 4 of the CMVC text, and to the self-organized Projection plots.

    Note that when varying the scale or offset, it is very easy to get confused by the plots. The bitmaps in Topographica generally plot a range from 0.0 to 1.0 as colors black to white, with all values below 0.0 appearing black, and all values above 1.0 appearing white. With a large enough scale or offset, the onscreen plot will appear to be solid white, obscuring the actual pattern seen by the network. In such cases, you can turn on the Normalize button to see the pattern, but then changes in the scale are often entirely invisible. Even so, it should be clear enough as long as you keep these limitations in mind.

  2. Explain why the LGNOnAfferent weights to V1 neurons 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 the mean luminance? What effect will it have for darker lines? What does this indicate about the suitability of the chosen training pattern as a model for natural images?
  3. For any of the cases where you argued that the behavior was not biologically realistic, compare the LISSOM results to those from a model we are currently developing called GCA-LISSOM (in examples/gca_lissom.ty). A snapshot of the already-organized map is in /group/teaching/cnv/topographica/examples/gca_lissom_10000.typ. Does GCA-LISSOM provide more realistic results? Can you see any obvious problems?

Submission

Your work must be submitted by the specified time on the due date using the submit command on Informatics DICE machines (type man submit for more details). Your work should be in the form of one PDF file per problem, named as listed below.

Late submissions will not be accepted without good reason, and if accepted will be penalized according to the standard university policy of 5% penalty per working day or part of a day. To repeat, good reason is required for late coursework; late work is not simply accepted automatically. Good reason does not include working on other coursework, because managing such commitments is part of the standard university workload.

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.

Please read and follow my list of writing tips.

Last update: assignment1.html,v 1.11 2011/01/04 21:45:31 jbednar Exp


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