train.py

   1 #!/usr/bin/python3
   2
   3 import numpy as np
   4
   5 import mnist
   6
   7 # use a constant seed to keep things reproducible
   8 rg = np.random.default_rng(1)
   9
  10 # transfer functions
  11
  12 # https://en.wikipedia.org/wiki/Sigmoid_function
  13 # classic, differentiable, apparently worse for training
  14 def sigmoid(x):
  15     return 1 / (1 + np.exp(-x))
  16
  17
  18 def sigmoid_prime(x):
  19     return sigmoid(x) * (1 - sigmoid(x))
  20
  21
  22 # https://en.wikipedia.org/wiki/Rectifier_(neural_networks)
  23 # mostly preferred these days, not differentiable at 0, but slope can be defined arbitrarily as 0 or 1 at 0
  24 def reLU(x):
  25     return np.maximum(x, 0)
  26
  27
  28 def reLU_prime(x):
  29     return np.heaviside(x, 1)
  30
  31
  32 train_images, train_labels, rows, cols = mnist.load('train-images-idx3-ubyte', 'train-labels-idx1-ubyte')
  33 test_images, test_labels, rows2, cols2 = mnist.load('t10k-images-idx3-ubyte', 't10k-labels-idx1-ubyte')
  34 assert rows == rows2
  35 assert cols == cols2
  36
  37 # neural network structure: two hidden layers, one output layer
  38 SIZES = (rows * cols, 20, 16, 10)
  39 NUM_LAYERS = len(SIZES)
  40
  41 # initialize weight matrices and bias vectors with random numbers
  42 weights = []
  43 biases = []
  44 for i in range(1, NUM_LAYERS):
  45     weights.append(rg.normal(size=(SIZES[i], SIZES[i-1])))
  46     biases.append(rg.normal(scale=10, size=SIZES[i]))
  47
  48
  49 def feed_forward(x, transfer=sigmoid):
  50     '''Compute all z and output vectors for given input vector'''
  51
  52     a_s = [x]
  53     z_s = []
  54     for w, b in zip(weights, biases):
  55         x = w @ x + b
  56         z_s.append(x)
  57         a_s.append(transfer(x))
  58     return (z_s, a_s)
  59
  60
  61 def classify(y):
  62     # the recognized digit is the index of the highest-valued output neuron
  63     return np.argmax(y), np.max(y)
  64
  65
  66 def test():
  67     """Count percentage of test inputs which are being recognized correctly"""
  68
  69     good = 0
  70     num_images = test_images.shape[1]
  71     for i in range(num_images):
  72         # the recognized digit is the index of the highest-valued output neuron
  73         y = classify(feed_forward(test_images[:, i])[1][-1])[0]
  74         good += int(y == test_labels[i])
  75     return 100 * (good / num_images)
  76
  77
  78 res = feed_forward(test_images[:, 0])
  79 print(f'output vector of first image: {res[1][-1]}')
  80 digit, conf = classify(res[1][-1])
  81 print(f'classification of first image: {digit} with confidence {conf}; real label {test_labels[0]}')
  82 print(f'correctly recognized images after initialization: {test()}%')