Simplify code

[handwriting-recognition.git] / README.md

diff --git a/README.md b/README.md
index 96974c990119387ee722e8f5d809536d0885233c..d48ebf3bc0fd713a836bbb238992941d5504f7aa 100644 (file)
--- a/README.md
+++ b/README.md
@@ -6,6 +6,7 @@ Basics:
  - [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:
@@ -49,3 +50,65 @@ output vector of first image: [    0.         52766.88424917     0.
 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 voilà, 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
+```