• We covered the use of a this perceptron to calculate the effect of an AND gate on a pair of digital (logical) inputs. 
• We used this diagram in our explanation for to show that a line can separate the (1,1) input from all the other inputs, and therefore the equation of that line can supply the weights and bias to implement the AND function. 
• For the AND function, the weights were: w(1)11 = w(1)12 = 1 and b(1) = -1.5. 
• We also found that by moving the dividing line down, we could separate the input (0,0) at the origin from the other 3 inputs, to accomplish an OR function, with the weights being w(1)11 = w(1)12 = 1 and b(1) = -0.5

There are 4 excellent(!) Youtube videos on how neural networks work from 3Blue1Brown.  Watch at least the first one by the time we return, and more if possible.  Keep the following questions in mind:

• How did he decide on the number of nodes in his network architecture: namely how many hidden layers and the number of nodes in each hidden layer?
  
• How do you calculate the number of weights given the details (above) of the architecture?
  
  
• Here are some terms I'll use below:
  • an Image-Cal is the process of showing the network a single image
  • a Cost-Calc is the process of showing the network every image from the entire set of training images: this process produces a single instance of the cost function's value(s)
  • Training-Calc is process of repeating CC many, many times to train the network and adjust its weights to an optimal value
• Do the following calculation:
  • (Calc 1): if his network is presented with a single image, how many operations (each multiplication is an operation, as is an addition) does it take to calculate the single result (the list of 10 probabilities) from that image (the Image-Calc)?  Ignore the calculation of the sigmoid function, and we're only looking for approximate values (+- 10%).
  • (Calc 2): Having done that, now calculate that for a run 30,000 different images (the Cost-Calc). When finished, you've now calculated one data point measuring how well the network classifies (initially, it classifies very poorly). 
  • (Calc 3): Assume that it takes 100,000 data points (trials) to train the network.  If each operation takes a 10 nanoseconds (a single core processor), how long does does training take assuming you had only a single-core processor (the Training-Calc)?  Ignore the work of backpropagation, if you know about that.  Use the most reasonable humanly understandable time unit (secs or hours or days or fortnights or millenea...)
• Put the answers into the Comments-to-Teacher

How costly is it to do such calculations?  Read this article from MIT's Technology Review.

1. Extract your CSV code from the Jupyter notebook
2. Use a text editor (not a word-processor) to remove any extraneous code, like testing code, etc. leaving only the DoIt() function.  If your function expects a single list parameter, with the 2nd element being the input-filename and the 3rd being the output-filename, then modify (if you haven't already) the top part of the DoIt() definition code to look like the code below (using your preferred parameter name)...
   
   import sys
   def DoIt(alist = None):
     if not alist:
        alist = sys.argv
   
3. The last line of  your program should be (not indented):
   DoIt()
4. Suppose your program filename is sumit.py and your test input file is fred.csv .  Test your program from your system's command-line by executing:
   python3 sumit.py fred.csv answer.csv
   ... and check answer.csv for correctness.  Fix if necessary.
5. Once working, upload to the new CSV Tester homework slot.  Then go to View Homework and press the Test Program button, and wait breathlessly for the results.  If "Passed" then the rest of your life will be easy.  If not, fix and resubmit and test.  If frustrated and at wit's end, email me.

In a Jupyter notebook, create a function called DoIt(alist=None), that either takes a list as a parameter, or if no list is available, uses sys.argv as the list for incoming arguments (os.argv will be used when we extract this code from the notebook and run it on the command-line).  The incoming arguments are: 

1. the name of the program (any name will do, this is ignored)
2. the name of an input CSV file
3. the name of an output CSV file

So, when you supply a list to DoIt(), it must contain 3 elements.

Create an input file for testing.  The file should have one line, consisting of one or more positive integers (only digits) and some optional non-integers, separated by commas (any number of them).  The function will read this file, compute the number of numbers and their sum and output those two results onto a single line CSV file.

So, if the input file contained:
1,2,3
the output file should contain:
3,6

Test this notebook and upload it to the homework server.

1. Go to the main class link page (http://bert.stuy.edu/pbrooks)
2. Click on the Homework/Grade server link
3. Choose the Profile menu item
4. Choose your period and name
5. Log in with your OSIS number as your password
6. Fill out your email address and preferred first name only, DO NOT CHANGE YOUR PASSWORD YET.
7. Save: (Change Profile button)...
8. (optional, but recommended): now you can change your password for this Homework server, if you want.
9. REMEMBER this password!