我最近进入了人工智能和神经网络，我观看了这个3Blue1Brown视频系列解释反向传播的原理，然后我决定通过创建该系列中描述的神经网络来实现它（我使用 MNIST 数据集进行训练和测试）。在这里：
class Neural_Network :
def __init__(self):
# The Neural Network Layers
self.layer = [[],[],[],[]]
self.layer[0] = np.zeros(784)
self.layer[1] = np.zeros(16)
self.layer[2] = np.zeros(16)
self.layer[3] = np.zeros(10)
# The Weight Matricies
self.W = [[],[],[]]
np.random.seed(0) # Set seed for reproducibility
# Xavier/Glorot Initialization
self.W[0] = np.random.randn(16, 784) * np.sqrt(2/(784 + 16)) # Consider both input and output dimensions
self.W[1] = np.random.randn(16, 16) * np.sqrt(2/(16 + 16))
self.W[2] = np.random.randn(10, 16) * np.sqrt(2/(16 + 10))
# Biases Vectors
self.B = [[],[],[]]
self.B[0] = np.zeros(16)
self.B[1] = np.zeros(16)
self.B[2] = np.zeros(10)
def _sigmoid(self,x):
return 1 / (1 + np.exp(-x))
def _sigmoidP(self,x):
return np.exp(-x)/((1+np.exp(-x))**2)
# The output layer that was supposed to be true
def y(self,label):
a = np.zeros_like(self.layer[3])
a[label] = 1
return a
def test(self,test_data) :
c = 0
for i in range(len(test_data)):
self.feedforward(test_data[i][0])
if (np.argmax(self.layer[3]) == test_data[i][1]):
c += 1
acc = (c / len(test_data)) * 100
return acc
#Uses Stochastic Gradient Descent
def train(self,training_data,epochs,eta):
mb_size = 125
for epoch in range(epochs):
print(f"\nEpoch {epoch + 1} Starts \n")
# Dividing The Training data into mini batches
np.random.shuffle(training_data)
mini_batches = [ training_data[k:k+mb_size] for k in range(len(training_data)//mb_size)]
for mini_batch in mini_batches:
self.gradient_step(mini_batch,eta)
# caculate the gradient according to the mini batch, and update the weights and biases.
def gradient_step(self,mini_batch,eta):
# Gradient Vector (For Mini Batch) Initilizing
self.gw = [np.zeros_like(self.W[i]) for i in range(3)]
self.gb = [np.zeros_like(self.B[i]) for i in range(3)]
for image, label in mini_batch :
# Gradient Vector for a single Training Example Intilization
gw0 = [np.zeros_like(self.W[i]) for i in range(3)]
gb0 = [np.zeros_like(self.B[i]) for i in range(3)]
# Set the layer outputs
self.feedforward(image)
# Gradient of the activations, we will use it to backpropagate
ga = 2*(self.layer[3]-self.y(label))
# max index for weights and biases.
i = 2
# Note That since the activations and the parameters don't have the same index
# so a layer with index i, coresponds to bias with index i-1
while i>=0 :
# Caculating Z
z = self.W[i]@self.layer[i]+self.B[i]
gw0[i] = np.outer(self._sigmoidP(z)*ga,self.layer[i])
gb0[i] = self._sigmoidP(z)*ga
# using ga to backpropagate
ga = (self.W[i].T)@(self._sigmoidP(z)*ga)
i = i-1
# Accumilating all of the gradients
self.gw = [self.gw[i] + gw0[i] for i in range(3)]
self.gb = [self.gb[i] + gb0[i] for i in range(3)]
# getting the average by diving by the number of training example
self.gw = [self.gw[i] / len(mini_batch) for i in range(3)]
self.gb = [self.gb[i] / len(mini_batch) for i in range(3)]
self.W = [self.W[i] - eta * self.gw[i] for i in range(3)]
self.B = [self.B[i] - eta * self.gb[i] for i in range(3)]
def feedforward(self,input):
self.layer[0] = input
# Using the neural Network to determine the wirtten degit
for i in range(3):
z = self.W[i] @ self.layer[i]
z = z + self.B[i]
self.layer[i+1] = self._sigmoid(z)
NN = Neural_Network()
NN.train(load_training_data(),100,0.005)
我遇到的问题是，当我在训练后测试它时，准确率为10%，我仔细检查了算法实现，没有发现任何问题，训练数据也正确加载，之后我尝试玩epoch 数和学习率，我尝试了 100 epoch 和 0.005 学习率，但没有成功。
我用训练数据测试了网络，准确率为 89%。
这是为什么呢？我犯了什么错误？
您是否标准化了数据并尝试更改随机种子？