Before installation, you will need a computer that has Python and NumPy installed. If you are not familiar with installing these, we recommend installing Anaconda, which is a Python distribution that comes with a lot of extra packages, including NumPy. It is available here: https://www.continuum.io/downloads
The Python version can be 2.7, 3.4, or 3.5. If you do not have a preference among those versions, we tend to most commonly use 2.7.
Once you have this installed, go to the command line and do:
pip install nengo
pip install nengo_guiYou should now be able to run Nengo by running:
nengoIn Nengo GUI, if you click on the "open" icon in the top-left and select built-in examples and then tutorial you will find a list of tutorial models that cover a wide variety of Nengo functionality. For this first assignment, look through tutorials 00 through 10. This provides both a reminder of some of the things discussed in class and example code that provides the required programming syntax.
Build an Ensemble of 100 neurons (n_neurons=100) that represents one value (dimensions=1). Create a stimulus Node that has a value of [0] and a Connection that connects the Node to the Ensemble.
Run this model. Use a slider to adjust the input value, and display the decoded output value from the neurons. How accurate are these neurons at representing this value? What happens if you input values outside of the range -1 to 1? (you can right-click on the slider and select "Set range..." to adjust its range).
Increase the radius of the Ensemble to 10. Now what range of values is it good at representing? How does this affect the accuracy of the representation?
Increase the number of neurons to 500. How does this affect the accuracy of the representation?
Now build an Ensemble of 300 neurons that represents 3 values (dimensions=3). Provide it with input from a Node that also has three values ([0, 0, 0]). How well does this represent these three values? What happens if you try to feed in the value [1, 1, 1]? What sort of error does it make?
Adjust the radius to 1.7 and try representing [1, 1, 1] again. Has the representation accuracy improved? Why or why not?
Build two 1-dimensional Ensembles with 100 neurons each. Create an input Node with a value of [0] and connect that into the first Ensemble. Connect the first Ensemble to the second Ensemble.
Now when you vary the slider for the input Node, this should affect the represented value in both Ensembles.
On the Connection from the first Ensemble to the second, set the synapse to 0.1 (a 100ms synaptic time constant). How does this affect the communication of the value from the first to the second? What happens with a shorter time constant (0.001)? Or a longer one (1)? (Note: the default if you do not specify the synapse is 0.005).
Build the same network as the previous question, but when you make the Connection from the first Ensemble to the second, have it compute the square of the value. That is, have it compute this function:
def square(x):
return x[0]*x[0]
How accurate is this computation?
Try the function 10*x[0]*x[0]. How accurate is this? What could you change about the model to improve the accuracy?
Build a system where you have a two-dimensional input Node into a two-dimensional Ensemble. From that Ensemble form a Connection to a three-dimensional Ensemble where the function computed is (x[0]*x[0], x[0]*x[1], x[1]*x[1]) Now form a Connection from that three-dimensional Ensemble to a one-dimensional Ensemble that computes the function x[0]+2*x[1]+x[2].
What is this system doing? If your two inputs are a and b, what should the represented value in the last Ensemble be? How accurate is it? What input values does it have difficulty with?
How could you make this system more efficient, in terms of reducing the number of neurons while increasing the accuracy? As a hint, note that a*a + 2*a*b + b*b = (a+b)*(a+b) and that sometimes you don't need intermediate steps in a computation.
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