# Resources
Basics:
- [Learn numpy](https://numpy.org/learn/)
- [MNIST database of handwritten digits](http://yann.lecun.com/exdb/mnist/)
- [Neuron](https://en.wikipedia.org/wiki/Artificial_neuron)
- [Perceptron](https://en.wikipedia.org/wiki/Perceptron)
- [Backpropagation](https://en.wikipedia.org/wiki/Backpropagation)
- [Understanding & Creating Neural Networks with Computational Graphs from Scratch](https://www.kdnuggets.com/2019/08/numpy-neural-networks-computational-graphs.html)
- [3Blue1Brown video series](https://www.youtube.com/playlist?list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi)
Too high-level for first-time learning, but apparently very abstract and powerful for real-life:
- [keras](https://keras.io/)
- [tutorial how to recognize handwriting with keras/tensorflow](https://data-flair.training/blogs/python-deep-learning-project-handwritten-digit-recognition/)
# Dependencies
sudo dnf install -y python3-numpy python3-matplotlib
# Steps
- Do the [NumPy quickstart tutorial](https://numpy.org/devdocs/user/quickstart.html); example:
```py
import numpy as np
import matplotlib.pyplot as plt
grad = np.linspace(0,1,10000).reshape(100,100)
plt.imshow(grad, cmap='gray')
plt.show()
plt.imshow(np.sin(np.linspace(0,10000,10000)).reshape(100,100) ** 2, cmap='gray')
# non-blocking does not work with QT_QPA_PLATFORM=wayland
plt.show(block=False)
plt.close()
```
- Get the handwritten digits training data with `./download-mnist.sh`
- Read the MNIST database into numpy arrays with `./read_display_mnist.py`. Plot the first ten images and show their labels, to make sure the data makes sense:
![visualize training data](screenshots/mnist-visualize-training-data.png)
- Define the structure of the neural network: two hidden layers with parametrizable sizes. Initialize weights and biases randomly. This gives totally random classifications of course, but at least makes sure that the data structures and computations work:
```
$ ./train.py
output vector of first image: [ 0. 52766.88424917 0. 0.
14840.28619491 14164.62850135 0. 7011.882333
0. 46979.62976127]
classification of first image: 1 with confidence 52766.88424917019; real label 5
correctly recognized images after initialization: 10.076666666666668%
```
- Add backpropagation algorithm and run a first training round. This is slow, as expected:
```
$ time ./train.py
output vector of first image: [ 0. 52766.88424917 0. 0.
14840.28619491 14164.62850135 0. 7011.882333
0. 46979.62976127]
classification of first image: 1 with confidence 52766.88424917019; real label 5
correctly recognized images after initialization: 10.076666666666668%
round #0 of learning...
./train.py:18: RuntimeWarning: overflow encountered in exp
return 1 / (1 + np.exp(-x))
correctly recognized images: 14.211666666666666%
real 0m37.927s
user 1m19.103s
sys 1m10.169s
```
- This is way too slow. I found an [interesting approach](https://www.kdnuggets.com/2019/08/numpy-neural-networks-computational-graphs.html) that harnesses the power of numpy by doing the computations for lots of images in parallel, instead of spending a lot of time in Python on iterating over tens of thousands of examples. Now the accuracy computation takes only negligible time instead of 6 seconds, and each round of training takes less than a second:
```
$ time ./train.py
output vector of first image: [0.51452796 0.49736819 0.51415083 0.50027547 0.48447025 0.49759904
0.52621162 0.48671402 0.517606 0.50214569]
classification of first image: 6 with confidence 0.526211616929459; real label 7
correctly recognized images after initialization: 7.75%
cost after training round 0: 1.0462266880961681
[...]
cost after training round 99: 0.4499245817840479
correctly recognized images after training: 11.35%
real 1m51.520s
user 4m23.863s
sys 2m31.686s
```
- Poor recognition quality after 100 iterations, as the network structure is apparently inappropriate. Having only 16 neurons in the first hidden layer makes the network not able to "see enough details" in the input. So let's use 128 neurons in the first hidden layer, and drop the second layer (it only seems to make things worse for me). Naturally a single training round takes much longer now, but voilĂ , after only 20 learning iterations it's already quite respectable:
```
$ time ./train.py
correctly recognized images after initialization: 9.8%
cost after training round 0: 0.44518003660592853
[...]
cost after training round 19: 0.10783488337150668
correctly recognized images after training: 89.09%
real 0m47.603s
user 2m12.141s
```
- And after 100 iterations, the accuracy improves even more, and the classification of the first test image looks reasonable:
```
cost after training round 99: 0.043068345296584126
correctly recognized images after training: 94.17%
output vector of first image: [1.11064478e-02 5.59058012e-03 5.40483856e-02 7.93664914e-02
2.22662031e-03 3.50355065e-03 2.57506703e-04 9.60761429e-01
2.68869803e-03 5.26559410e-03]
real 4m10.904s
user 11m21.203s
```
- Replace [Sigmoid](https://en.wikipedia.org/wiki/Sigmoid_function) activation function with [reLU](https://en.wikipedia.org/wiki/Rectifier_%28neural_networks%29). Some interesting effects, like a learning rate of 1 leads to "overshooting", and the cost function actually _increases_ during the learning steps several times, and the overall result was worse. Changing the learning rate to linearly fall during the training rounds helps. But in the end, the result is still worse:
```
cost after training round 99: 0.07241763398153217
correctly recognized images after training: 92.46%
output vector of first image: [0. 0. 0. 0. 0. 0.
0. 0.89541759 0. 0. ]
classification of first image: 7 with confidence 0.8954175907939048; real label 7
```