This is the Github repository for my masters thesis about backpropagation with matrices.
This repository contains all the code I wrote and some examples of how to use it.
The different implementations for the automatic differentiation part are in folder ./src/app/AD.
The implementations for backpropagation with examples for feed forward neural networks can be found in ./src/app/Backpropagation.
There are some unit test files in the ./src/app/Tests folder, they can be used to check the correctness of the algorithms.
To run the code, you need cabal, here we use version 2.4.
You need GHC with base version >=4.11 and < 5, we used base version 4.13.3.0.
GHC can easily be installed or changed versions using ghcup.
You need to have the MNIST dataset files downloaded and know the path to the folder they are in, you need the four files at the top of this page.
Lastly, you need to have the hmatrix library installed, you can find their installation guide here.
To run the examples in the ./src/app/Backpropagation folder, you can follow these steps.
In the command line you start in the folder where you downloaded this github page.
$ cd src
$ cabal run Matrix-Backpropagation "[path to MNIST dataset]"
Here you need to replace [path to MNIST dataset] with the actual path where you have downloaded the MNIST dataset on you computer.
To change what examples run when running that command, you can change the ./src/app/Main.hs file to the examples you want.
This runs the test files and executes 4 examples.
The first 2 examples use the following network without hidden layers to train on the MNIST dataset:
The last 2 examplles use this network with 4 hidden layers to train on the MNIST dataset:
The result of these commands will look like this.
------------------
Start Tests
------------------
Cases: 7 Tried: 7 Errors: 0 Failures: 0
Cases: 11 Tried: 11 Errors: 0 Failures: 0
Cases: 16 Tried: 16 Errors: 0 Failures: 0
Cases: 8 Tried: 8 Errors: 0 Failures: 0
Cases: 4 Tried: 4 Errors: 0 Failures: 0
------------------
Finished Tests
------------------
Loaded data.
[Epoch 1]
(Batch 1)
Trained on 50 points.
Training error: 78.00%
Validation error: 87.00%
(Batch 2)
Trained on 50 points.
Training error: 52.00%
Validation error: 56.00%
(Batch 3)
Trained on 50 points.
Training error: 34.00%
Validation error: 62.00%
(Batch 4)
Trained on 50 points.
Training error: 26.00%
Validation error: 42.00%
(Batch 5)
Trained on 50 points.
Training error: 22.00%
Validation error: 50.00%
... (The same for every Epoch)
[Epoch 5]
(Batch 1)
Trained on 50 points.
Training error: 16.00%
Validation error: 22.00%
(Batch 2)
Trained on 50 points.
Training error: 18.00%
Validation error: 23.00%
(Batch 3)
Trained on 50 points.
Training error: 6.00%
Validation error: 21.00%
(Batch 4)
Trained on 50 points.
Training error: 12.00%
Validation error: 24.00%
(Batch 5)
Trained on 50 points.
Training error: 18.00%
Validation error: 18.00%
------------------
Backprop: 6746.063842521s
------------------
Loaded data.
[Epoch 1]
(Batch 1)
Trained on 5000 points.
Training error: 12.98%
Validation error: 14.46%
(Batch 2)
Trained on 5000 points.
Training error: 9.18%
Validation error: 10.27%
(Batch 3)
Trained on 5000 points.
Training error: 9.68%
Validation error: 10.44%
(Batch 4)
Trained on 5000 points.
Training error: 10.48%
Validation error: 10.73%
(Batch 5)
Trained on 5000 points.
Training error: 8.42%
Validation error: 9.83%
... (The same for every Epoch)
[Epoch 5]
(Batch 1)
Trained on 5000 points.
Training error: 7.50%
Validation error: 8.44%
(Batch 2)
Trained on 5000 points.
Training error: 7.62%
Validation error: 9.00%
(Batch 3)
Trained on 5000 points.
Training error: 6.94%
Validation error: 8.44%
(Batch 4)
Trained on 5000 points.
Training error: 8.82%
Validation error: 10.62%
(Batch 5)
Trained on 5000 points.
Training error: 7.56%
Validation error: 8.45%
------------------
Indexed Backpropagation: 14.391924205s
------------------
Loaded data.
[Epoch 1]
(Batch 1)
Trained on 5000 points.
Training error: 89.04%
Validation error: 88.68%
(Batch 2)
Trained on 5000 points.
Training error: 62.04%
Validation error: 62.65%
(Batch 3)
Trained on 5000 points.
Training error: 30.50%
Validation error: 30.01%
(Batch 4)
Trained on 5000 points.
Training error: 19.50%
Validation error: 19.92%
(Batch 5)
Trained on 5000 points.
Training error: 14.66%
Validation error: 16.15%
... (The same for every Epoch)
[Epoch 5]
(Batch 1)
Trained on 5000 points.
Training error: 4.34%
Validation error: 6.24%
(Batch 2)
Trained on 5000 points.
Training error: 4.82%
Validation error: 6.80%
(Batch 3)
Trained on 5000 points.
Training error: 4.50%
Validation error: 6.47%
(Batch 4)
Trained on 5000 points.
Training error: 4.06%
Validation error: 6.09%
(Batch 5)
Trained on 5000 points.
Training error: 4.08%
Validation error: 6.09%
------------------
Indexed Backpropagation Mutable Arrays: 1656.247498055s
------------------
Loaded data.
[Epoch 1]
(Batch 1)
Trained on 5000 points.
Training error: 88.88%
Validation error: 89.72%
(Batch 2)
Trained on 5000 points.
Training error: 65.24%
Validation error: 65.07%
(Batch 3)
Trained on 5000 points.
Training error: 51.04%
Validation error: 51.94%
(Batch 4)
Trained on 5000 points.
Training error: 30.90%
Validation error: 30.10%
(Batch 5)
Trained on 5000 points.
Training error: 23.20%
Validation error: 23.79%
... (The same for every Epoch)
[Epoch 5]
(Batch 1)
Trained on 5000 points.
Training error: 4.04%
Validation error: 5.91%
(Batch 2)
Trained on 5000 points.
Training error: 4.66%
Validation error: 6.23%
(Batch 3)
Trained on 5000 points.
Training error: 4.90%
Validation error: 6.42%
(Batch 4)
Trained on 5000 points.
Training error: 3.94%
Validation error: 5.93%
(Batch 5)
Trained on 5000 points.
Training error: 3.78%
Validation error: 5.59%
------------------
Indexed Backpropagation Static: 376.700868944s
------------------
For every example it follows the same structure, for every Epoch and Batch it shows the number of datapoints it has trained on and the training- and testerror at that point in the trainingprocess. At the end of each example it shows the execution time needed to run that example. The percentages and execution time differ a little bit every time, but should be more or less the same.