To read current papers on DNN research and translate them into working models. To experiment with DNN-style regularization methods, including Dropout, Dropconnect, and L1 weight regularization.
For this lab, you will need to implement three different regularization methods from the literature, and explore the parameters of each.
You should turn in an iPython notebook that shows three plots, one for each of the regularization methods.
An example of my training/test performance for dropout is shown at the right.
NOTE: because this lab can be more computationally time consuming than the others (since we're scanning across parameters), you are welcome to turn in your plots and your code separately. (This means, for example, that you can develop and run all of your code using an IDE other than the Jupyter notebook, collect the data, and then run a separate little script to generate the plots. Or, a particularly enterprising student may use his or her new supercomputer account to sweep all of the parameter values in parallel (!) ). If you do this, you will need to zip up your images and code into a single file for submission to Learning Suite.
Your notebook will be graded on the following:
This lab is a chance for you to start reading the literature on deep neural networks, and understand how to replicate methods from the literature. You will implement 3 different regularization methods, and will benchmark each one.
To help ensure that everyone is starting off on the same footing, you should download the following scaffold code:
For all 3 methods, we will run on a single, deterministic batch of the first 1000 images from the MNIST dataset. This will help us to overfit, and will hopefully be small enough not to tax your computers too much.
Part 1: implement dropout
For the first part of the lab, you should implement dropout. The paper upon which you should base your implementation is found at:
The relevant equations are found in section 4 (pg 1933). You may also refer to the class slides for lecture 7.
There are several notes to help you with this part:
keep_probability, as discussed in class and in the paper.
Note that although we are training on only the first 1000 images, we are testing on the entire 10,000 image test set.
In order to generate the final plot, you will need to scan across multiple values of the
keep_probability. You may wish to refactor the provided code in order to make this easier. You should test at least the values
[ 0.1, 0.25, 0.5, 0.75, 1.0 ].
Once you understand dropout, implementing it is not hard; you should only have to add ~10 lines of code.
Also note that because dropout involves some randomness, your curve may not match mine exactly; this is expected.
Part 2: implement dropconnect
The specifications for this part are similar to part 1. Once you have implemented Dropout, it should be very easy to modify your code to perform dropconnect. The paper upon which you should base your implementation is
Important note: the dropconnect paper has a somewhat more sophisticated inference method (that is, the method used at test time). We will not use that method. Instead, we will use the same inference approximation used by the Dropout paper – we will simply scale things by the
You should scan across the same values of
keep_probability, and you should generate a similar plot.
Dropconnect seems to want more training steps than dropout, so you should run the optimizer for 1500 iterations.
Part 3: implement L1 regularization
For this part, you should implement L1 regularization on the weights. This will change your computation graph a bit, and specifically will change your cost function – instead of optimizing
cross_entropy, you must optimize
cross_entropy + lam*regularizer, where
lam is the \lambda parameter from the class slides.
You should place an L1 regularizer on each of the weight and bias variables (a total of 8). A different way of saying this is that the regularization term should be sum of the absolute value of all of the individual variables from all of the weights and biases; that entire sum is then multiplied by \lambda
You should experiment with a few different values of lambda, and generate a similar plot to those in Part 1 and Part 2. You should test at least the values
[0.1, 0.01, 0.001].
Note that, unlike the dropout/dropconnect regularizers, you may not be able to find a value of lambda that improves test time performance!
You can generate a random binary matrix by using
np.random.rand to generate a random matrix of values between 0 and 1, and then only keeping those that are below a certain threshold. This is easily vectorized!
Note that you should not call your regularization variable “lambda” because that is a reserved keyword in python.
Remember that the “masks” for both dropout and dropconnect change for every step in training.