From: Martin Pitt <martin@piware.de>
Date: Sat, 29 Aug 2020 19:59:56 +0000 (+0200)
Subject: Tweak network structure
X-Git-Url: https://piware.de/gitweb/?a=commitdiff_plain;h=72f90468f63b736bca28d0fc5ebf3f7d1989de4f;p=handwriting-recognition.git

Tweak network structure

Increase first layer size, otherwise the network does not "see" enough
detail in the input.  Drop second layer, it makes the recognition rate
actually much worse.
---

diff --git a/README.md b/README.md
index 3af0686..d48ebf3 100644
--- 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
-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
@@ -85,3 +85,30 @@ 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
+```
diff --git a/train.py b/train.py
index 012e2c7..5ff7666 100755
--- a/train.py
+++ b/train.py
@@ -13,15 +13,13 @@ nnet_batch = 10000
 # neural network structure: two hidden layers, one output layer
 #                   (input)--> [Linear->Sigmoid] -> [Linear->Sigmoid] -->(output)
 # handle 10,000 vectors at a time
-Z1 = nnet.LinearLayer(input_shape=(rows * cols, nnet_batch), n_out=20)
+Z1 = nnet.LinearLayer(input_shape=(rows * cols, nnet_batch), n_out=80)
 A1 = nnet.SigmoidLayer(Z1.Z.shape)
-Z2 = nnet.LinearLayer(input_shape=A1.A.shape, n_out=16)
-A2 = nnet.SigmoidLayer(Z2.Z.shape)
-ZO = nnet.LinearLayer(input_shape=A2.A.shape, n_out=10)
+ZO = nnet.LinearLayer(input_shape=A1.A.shape, n_out=10)
 AO = nnet.SigmoidLayer(ZO.Z.shape)
-net = (Z1, A1, Z2, A2, ZO, AO)
+net = (Z1, A1, ZO, AO)
 
-res = nnet.forward(net, train_images[:, 0:10000])
+res = nnet.forward(net, test_images[:, 0:10000])
 print(f'output vector of first image: {res[:, 0]}')
 digit, conf = nnet.classify(res[:, 0])
 print(f'classification of first image: {digit} with confidence {conf}; real label {test_labels[0]}')
@@ -30,6 +28,11 @@ print(f'correctly recognized images after initialization: {nnet.accuracy(net, te
 train_y = nnet.label_vectors(train_labels, 10)
 for i in range(100):
     for batch in range(0, num_train, nnet_batch):
-        cost = nnet.train(net, train_images[:, batch:(batch + nnet_batch)], train_y[:, batch:(batch + nnet_batch)])
+        cost = nnet.train(net, train_images[:, batch:(batch + nnet_batch)], train_y[:, batch:(batch + nnet_batch)], learning_rate=1)
     print(f'cost after training round {i}: {cost}')
 print(f'correctly recognized images after training: {nnet.accuracy(net, test_images, test_labels)}%')
+
+res = nnet.forward(net, test_images[:, 0:10000])
+print(f'output vector of first image: {res[:, 0]}')
+digit, conf = nnet.classify(res[:, 0])
+print(f'classification of first image: {digit} with confidence {conf}; real label {test_labels[0]}')