Add reLU layer implementation

[handwriting-recognition.git] / README.md

diff --git a/README.md b/README.md
index 3af0686d6972af783a60d8ca377d150c54e01cad..b309254a3a2a67284c24db6f1af08e704bc8ffaf 100644 (file)
--- a/README.md
+++ b/README.md
@@ -72,10 +72,10 @@ 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
  - 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: [0.50863223 0.50183558 0.50357349 0.50056673 0.50285531 0.5043152
- 0.51588292 0.49403    0.5030618  0.51006963]
-classification of first image: 6 with confidence 0.5158829224337754; real label 7
-correctly recognized images after initialization: 9.58%
+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
 cost after training round 0: 1.0462266880961681
 [...]
 cost after training round 99: 0.4499245817840479


@@ -85,3 +85,39 @@ real 1m51.520s
 user   4m23.863s
 sys    2m31.686s
 ```
 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
+```
+
+- 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
+```