Machine Problem #6 Solution

Description

Note: The assignment will be autograded.  It is important that  you do not use additional libraries, or change the provided functions input  and output.

 

Part 1:  Setup

 

• Remove connect to a EWS machine.

 

ssh (netid)@remlnx.ews.illinois.edu

 

 

• Load python module, this will also load pip and virtualenv

 

module load python/3.4.3

 

 

• Reuse the virtual environment from mp0.

 

source ~/cs446sp_2018/bin/activate

 

 

• Copy mp6 into your svn directory, and change directory to mp6.

 

cd ~/(netid)

svn cp https://subversion.ews.illinois.edu/svn/sp18-cs446/_shared/mp6 . cd mp6

 

 

• Install the requirements through  pip.

 

pip install -r requirements.txt

 

 

 

Part 2:  Exercise

 

In this exercise, you will implement the deep net from the written  section and train  it using stochastic  gradient  descent.   The  deep net  should be implemented  from scratch  in python (i.e.  forward pass and back-propagation).  Do not use Tensorflow, Pytorch,  Chainer  etc.  to implement the network.  Consider the number of input  layers to be 2, the number of hidden layers to be 3, the number  of output layers to be 1 and the batch  size to be 3.  The loss to

 

m

m

be optimized is  1  P

Em , where m is the bach size and Em is the L2 loss from the written

 

part,  associated with the mth  sample.

Hint:  Think how the derivatives  computed  in the written  part  will change when considering this new loss.

 

 

 

1

 

 

 

 

 

 

Description of the functions to be implemented:

 

• Method sigmoidPrime of the class Neural Network : computes the derivative  of a sig- moid function.  The input  to this method  is the sigmoid’s output.

 

• Method forward of the class Neural Network : implements the forward propagation  of the deep net described in the written  section.

 

• Method d loss o of the class Neural Network : computes the derivative of the loss with respect to the network’s output c.

 

• Method error at layer2  of the  class Neural Network :  computes  the  derivative  of the loss with respect to the second fully connected layer’s output h (Written section, Part b).

 

• Method error at layer1  of the  class Neural Network :  computes  the  derivative  of the loss with respect to the first fully connected layer’s output z (Written section, Part  e).

 

• Method derivative of w of the class Neural Network :  computes  the  derivative  of the loss with respect to W (Written section, Part  c).

 

• Method derivative of f of the  class Neural Network :  computes  the  derivative  of the loss with respect to f (Written section, Part  d).

 

• Method derivative of u of the class Neural Network :  computes  the  derivative  of the loss with respect to U (Written section, Part  f ).

 

• Method derivative of e of the class Neural Network :  computes  the  derivative  of the loss with respect to e (Written section, Part  g).

 

• Method backward of the  class Neural Network :  computes  the  gradients  of the  pa- rameters  W , U , e and f , and performs the  gradient  descent  update  rule.  The  back- propagation  should be implemented  using the matrix  form of the parameters (i.e.  do not use any for loops).

 

Relevant  File:  back prop.py

 

Part 3:  Writing Tests

In test.py, we have provided basic test-cases.  Feel free to write more.  To test  the code, run:

 

nose2

 

 

 

Part 4:  Submit Submitting the code is equivalent to committing  the code.  This can be done with the follow command:

 

svn commit -m “Some meaningful comment here.”

 

 

Lastly, double check on your browser that  you can see your code at

 

https://subversion.ews.illinois.edu/svn/sp18-cs446/(netid)/mp6/