以下网络的代码运行正常,但速度太慢。 This site意味着网络在100个时代之后应该达到99%的准确率,学习率为0.2,而我的网络即使在1900年以后也不会超过97%。
Epoch 0, Inputs [0 0], Outputs [-0.83054376], Targets [0]
Epoch 100, Inputs [0 1], Outputs [ 0.72563824], Targets [1]
Epoch 200, Inputs [1 0], Outputs [ 0.87570863], Targets [1]
Epoch 300, Inputs [0 1], Outputs [ 0.90996706], Targets [1]
Epoch 400, Inputs [1 1], Outputs [ 0.00204791], Targets [0]
Epoch 500, Inputs [0 1], Outputs [ 0.93396672], Targets [1]
Epoch 600, Inputs [0 0], Outputs [ 0.00006375], Targets [0]
Epoch 700, Inputs [0 1], Outputs [ 0.94778227], Targets [1]
Epoch 800, Inputs [1 1], Outputs [-0.00149935], Targets [0]
Epoch 900, Inputs [0 0], Outputs [-0.00122716], Targets [0]
Epoch 1000, Inputs [0 0], Outputs [ 0.00457281], Targets [0]
Epoch 1100, Inputs [0 1], Outputs [ 0.95921556], Targets [1]
Epoch 1200, Inputs [0 1], Outputs [ 0.96001748], Targets [1]
Epoch 1300, Inputs [1 0], Outputs [ 0.96071742], Targets [1]
Epoch 1400, Inputs [1 1], Outputs [ 0.00110912], Targets [0]
Epoch 1500, Inputs [0 0], Outputs [-0.00012382], Targets [0]
Epoch 1600, Inputs [1 0], Outputs [ 0.9640324], Targets [1]
Epoch 1700, Inputs [1 0], Outputs [ 0.96431516], Targets [1]
Epoch 1800, Inputs [0 1], Outputs [ 0.97004973], Targets [1]
Epoch 1900, Inputs [1 0], Outputs [ 0.96616225], Targets [1]
我使用的数据集是:
0 0 0
1 0 1
0 1 1
1 1 1
使用辅助文件中的函数读取训练集,但这与网络无关。
import numpy as np
import helper
FILE_NAME = 'data.txt'
EPOCHS = 2000
TESTING_FREQ = 5
LEARNING_RATE = 0.2
INPUT_SIZE = 2
HIDDEN_LAYERS = [5]
OUTPUT_SIZE = 1
class Classifier:
def __init__(self, layer_sizes):
np.set_printoptions(suppress=True)
self.activ = helper.tanh
self.dactiv = helper.dtanh
network = list()
for i in range(1, len(layer_sizes)):
layer = dict()
layer['weights'] = np.random.randn(layer_sizes[i], layer_sizes[i-1])
layer['biases'] = np.random.randn(layer_sizes[i])
network.append(layer)
self.network = network
def forward_propagate(self, x):
for i in range(0, len(self.network)):
self.network[i]['outputs'] = self.network[i]['weights'].dot(x) + self.network[i]['biases']
if i != len(self.network)-1:
self.network[i]['outputs'] = x = self.activ(self.network[i]['outputs'])
else:
self.network[i]['outputs'] = self.activ(self.network[i]['outputs'])
return self.network[-1]['outputs']
def backpropagate_error(self, x, targets):
self.forward_propagate(x)
self.network[-1]['deltas'] = (self.network[-1]['outputs'] - targets) * self.dactiv(self.network[-1]['outputs'])
for i in reversed(range(len(self.network)-1)):
self.network[i]['deltas'] = self.network[i+1]['deltas'].dot(self.network[i+1]['weights'] * self.dactiv(self.network[i]['outputs']))
def adjust_weights(self, inputs, learning_rate):
self.network[0]['weights'] -= learning_rate * np.atleast_2d(self.network[0]['deltas']).T.dot(np.atleast_2d(inputs))
self.network[0]['biases'] -= learning_rate * self.network[0]['deltas']
for i in range(1, len(self.network)):
self.network[i]['weights'] -= learning_rate * np.atleast_2d(self.network[i]['deltas']).T.dot(np.atleast_2d(self.network[i-1]['outputs']))
self.network[i]['biases'] -= learning_rate * self.network[i]['deltas']
def train(self, inputs, targets, epochs, testfreq, lrate):
for epoch in range(epochs):
i = np.random.randint(0, len(inputs))
if epoch % testfreq == 0:
predictions = self.forward_propagate(inputs[i])
print('Epoch %s, Inputs %s, Outputs %s, Targets %s' % (epoch, inputs[i], predictions, targets[i]))
self.backpropagate_error(inputs[i], targets[i])
self.adjust_weights(inputs[i], lrate)
inputs, outputs = helper.readInput(FILE_NAME, INPUT_SIZE, OUTPUT_SIZE)
print('Input data: {0}'.format(inputs))
print('Output targets: {0}\n'.format(outputs))
np.random.seed(1)
nn = Classifier([INPUT_SIZE] + HIDDEN_LAYERS + [OUTPUT_SIZE])
nn.train(inputs, outputs, EPOCHS, TESTING_FREQ, LEARNING_RATE)
答案 0 :(得分:1)
主要的错误是你只有20%的时间进行前进,即epoch % testfreq == 0
时:
for epoch in range(epochs):
i = np.random.randint(0, len(inputs))
if epoch % testfreq == 0:
predictions = self.forward_propagate(inputs[i])
print('Epoch %s, Inputs %s, Outputs %s, Targets %s' % (epoch, inputs[i], predictions, targets[i]))
self.backpropagate_error(inputs[i], targets[i])
self.adjust_weights(inputs[i], lrate)
当我从predictions = self.forward_propagate(inputs[i])
中取出if
时,我会更快地获得更好的结果:
Epoch 100, Inputs [0 1], Outputs [ 0.80317447], Targets 1
Epoch 105, Inputs [1 1], Outputs [ 0.96340466], Targets 1
Epoch 110, Inputs [1 1], Outputs [ 0.96057278], Targets 1
Epoch 115, Inputs [1 0], Outputs [ 0.87960599], Targets 1
Epoch 120, Inputs [1 1], Outputs [ 0.97725825], Targets 1
Epoch 125, Inputs [1 0], Outputs [ 0.89433666], Targets 1
Epoch 130, Inputs [0 0], Outputs [ 0.03539024], Targets 0
Epoch 135, Inputs [0 1], Outputs [ 0.92888141], Targets 1
另外,请注意,术语 epoch 通常意味着单次运行所有您的训练数据,在您的情况下4.事实上,您正在做4时代少了。
<强>更新强>
我没有注意细节,因此错过了一些微妙而重要的笔记:
知道了这一点,我已经更新了数据并再次检查了脚本。运行10000次迭代的训练给出了约0.001的平均误差,因此模型是学习,只是不那么快。
简单的神经网络(没有嵌入式规范化机制)对特定的超参数非常敏感,例如初始化和学习速率。我手动尝试了各种值,这就是我所拥有的:
# slightly bigger learning rate
LEARNING_RATE = 0.3
...
# slightly bigger init variation of weights
layer['weights'] = np.random.randn(layer_sizes[i], layer_sizes[i-1]) * 2.0
这提供了以下表现:
...
Epoch 960, Inputs [1 1], Outputs [ 0.01392014], Targets 0
Epoch 970, Inputs [0 0], Outputs [ 0.04342895], Targets 0
Epoch 980, Inputs [1 0], Outputs [ 0.96471654], Targets 1
Epoch 990, Inputs [1 1], Outputs [ 0.00084511], Targets 0
Epoch 1000, Inputs [0 0], Outputs [ 0.01585915], Targets 0
Epoch 1010, Inputs [1 1], Outputs [-0.004097], Targets 0
Epoch 1020, Inputs [1 1], Outputs [ 0.01898956], Targets 0
Epoch 1030, Inputs [0 0], Outputs [ 0.01254217], Targets 0
Epoch 1040, Inputs [1 1], Outputs [ 0.01429213], Targets 0
Epoch 1050, Inputs [0 1], Outputs [ 0.98293925], Targets 1
...
Epoch 1920, Inputs [1 1], Outputs [-0.00043072], Targets 0
Epoch 1930, Inputs [0 1], Outputs [ 0.98544288], Targets 1
Epoch 1940, Inputs [1 0], Outputs [ 0.97682002], Targets 1
Epoch 1950, Inputs [1 0], Outputs [ 0.97684186], Targets 1
Epoch 1960, Inputs [0 0], Outputs [-0.00141565], Targets 0
Epoch 1970, Inputs [0 0], Outputs [-0.00097559], Targets 0
Epoch 1980, Inputs [0 1], Outputs [ 0.98548381], Targets 1
Epoch 1990, Inputs [1 0], Outputs [ 0.97721286], Targets 1
平均精度在1000次迭代后接近98.5%,在2000次迭代后接近99.1%。它比承诺的要慢一些,但还不错。我确信它可以进一步调整,但这不是这个玩具练习的目标。毕竟,tanh is not最好的激活函数和分类问题最好用交叉熵损失(而不是L2损失)来解决。因此,我不会过分担心这个特定网络的性能,并继续进行逻辑回归。就学习速度而言,这肯定会更好。