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mnist.py
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mnist.py
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import time
import random
import numpy as np
import idx2numpy
import matplotlib.pyplot
from tqdm import tqdm
##################################
# load dataset
train_img: np.ndarray = idx2numpy.convert_from_file('data/train-images.idx3-ubyte') # (60k, 28, 28)
train_lab: np.ndarray = idx2numpy.convert_from_file('data/train-labels.idx1-ubyte') # (60k,)
test_img: np.ndarray = idx2numpy.convert_from_file('data/t10k-images.idx3-ubyte') # (10k, 28, 28)
test_lab: np.ndarray = idx2numpy.convert_from_file('data/t10k-labels.idx1-ubyte') # (10k,)
# num = 12
# print(train_lab[num])
# matplotlib.pyplot.imshow(train_img[num], cmap="Greys", interpolation="None")
# matplotlib.pyplot.show()
##################################
def sigmoid(x: np.ndarray):
return 1 / (1 + np.exp(-x))
def sigmoid_d(sigx: np.ndarray):
return sigx * (1 - sigx)
def leaky_relu(x: np.ndarray):
return np.maximum(x, 0.01 * x)
def leaky_relu_d(lrx: np.ndarray):
return np.where(lrx > 0, 1, 0.01)
def softmax(x: np.ndarray):
# x : 1 x 10
s = np.exp(x)
return s / s.sum()
def softmax_d(smx: np.ndarray):
# x : 1 x 10
# smx : 1 x 10
def f(i, j):
return (smx[0][i] * (1 - smx[0][i])) if i == j else (- smx[0][i] * smx[0][j])
return np.array([[f(i, j) for j in range(10)] for i in range(10)]) # 10 x 10
def cross_entropy(pred, lab):
# pred : 1 x 10
# lab : 0 - 9
return - np.log(pred[0][lab])
def cross_entropy_d(pred, lab):
# pred : 1 x 10
# lab : 0 - 9
d = np.zeros((1, 10))
d[0][lab] = -1. / pred[0][lab]
return d # 1 x 10
class mnist_net:
def __init__(self, size_h1, size_h2, act, act_d):
self.size = {
'in': 28*28, # input = 784
'h1': size_h1, # hidden 1
'h2': size_h2, # hidden 2
'out': 10, # output
}
self.w = [
np.random.randn(self.size['in'], self.size['h1']) * np.sqrt(1./self.size['h1']), # 784 x h1
np.random.randn(self.size['h1'], self.size['h2']) * np.sqrt(1./self.size['h2']), # h1 x h2
np.random.randn(self.size['h2'], self.size['out']) * np.sqrt(1./self.size['out']), # h2 x 10
]
self.act = act
self.act_d = act_d
def forward(self, img):
# img : 1 x 784
p1 = img @ self.w[0] # 1 x h1
a1 = self.act(p1) # 1 x h1
p2 = a1 @ self.w[1] # 1 x h2
a2 = self.act(p2) # 1 x h2
p3 = a2 @ self.w[2] # 1 x 10
a3 = softmax(p3) # 1 x 10
return a3
def backward(self, img, lab, lr):
# img : 1 x 784
# lab : 0 - 9
# forward
p1 = img @ self.w[0] # 1 x h1
a1 = self.act(p1) # 1 x h1
p2 = a1 @ self.w[1] # 1 x h2
a2 = self.act(p2) # 1 x h2
p3 = a2 @ self.w[2] # 1 x 10
a3 = softmax(p3) # 1 x 10
# loss = cross_entropy(a3, lab)
# backward
delta_w = {}
err = cross_entropy_d(a3, lab) @ softmax_d(a3) # 1 x 10, L / p3
delta_w[2] = np.outer(a2, err) # h2 x 10, L / w2
err = err @ self.w[2].T # 1 x h2, L / a2
err = err * self.act_d(a2) # 1 x h2, L / p2
delta_w[1] = np.outer(a1, err) # h1 x h2, L / w1
err = err @ self.w[1].T # 1 x h1, L / a1
err = err * self.act_d(a1) # 1 x h1, L / p1
delta_w[0] = np.outer(img, err) # 784 x h1, L / w0
# update
for i in range(3):
self.w[i] -= delta_w[i] * lr
def test(self):
loss = 0
right = 0
for i in range(10_000):
img = test_img[i].reshape(1, 784) / 255.
lab = test_lab[i]
p: np.ndarray = self.forward(img)
loss += cross_entropy(p, lab)
if np.argmax(p) == lab:
right += 1
print('----- test result -----')
print('avg loss = ', loss / 10000.)
print('accuracy = ', right / 100., '%')
def train(self, lr, num):
print('----- train -----')
for _ in tqdm(range(num)):
i = random.randrange(60_000)
img = train_img[i].reshape(1, 784) / 255.
lab = train_lab[i]
self.backward(img, lab, lr)
##################################
net = mnist_net(256, 64, leaky_relu, leaky_relu_d)
net.test()
print('')
for i in range(70):
print('epoch = ', i + 1)
net.train(0.001 if i < 30 else 0.0001, 1000)
net.test()
print('')