神经网络总是在每个 epoch 中预测相同的类别

Question

I'm trying to implement a mnist classifier with DNN. However, the result I got is quite strange. enter image description here

In this epoch, this model can only predict number '0' correctly, and incorrect prediction for all the other numbers. This model could only predict a specific number for each epoch. (such predicted number is different in each epoch)

This is how I get the dataset.

from sklearn.datasets import fetch_openml
from keras.utils.np_utils import to_categorical
import numpy as np
from sklearn.model_selection import train_test_split
import time

x, y = fetch_openml('mnist_784', version=1, return_X_y=True)
x = (x/255.).astype('float32')
y = to_categorical(y)

x_train, x_val, y_train, y_val = train_test_split(x, y, test_size=0.15, random_state=42)

For this part, this is my model. A two-hidden-layers DNN with activation functions of Relu and softmax, Cross entropy loss for the error function. I'm not really sure if my backpropagation is correct or not. I think something is wrong here.

import numpy as np


class NN():
    def __init__(self, input_size, hidden_1_size, hidden_2_size, output_size):
        self.input_data = np.random.randn(1, input_size)
        self.w1 = np.random.randn(input_size, hidden_1_size)
        self.b1 = np.random.randn(1, hidden_1_size)
        
        self.w2 = np.random.randn(hidden_1_size, hidden_2_size)
        self.b2 = np.random.randn(1, hidden_2_size) 

        self.w3 = np.random.randn(hidden_2_size, output_size)
        self.b3 = np.random.randn(1, output_size)


    def Sigmoid(self, z):
        return np.clip(1 / (1.0 + np.exp(-z)), 1e-8, 1 - (1e-7))

    def Softmax(self, z):
        y_logit = np.exp(z - np.max(z, 1, keepdims=True))
        y = y_logit / np.sum(y_logit, 1, keepdims=True)
        return y

    def Relu(self, z):
        return np.maximum(z, 0)

    def acc_test(self, input_data):
        tmp_h1 = self.Relu(input_data.dot(self.w1) + self.b1)
        tmp_h2 = self.Relu(self.h1_out.dot(self.w2) + self.b2)
        tmp_out = self.Softmax(self.h2_out.dot(self.w3) + self.b3)
        return tmp_out

    # Feed Placeholder

    def forward(self, input_data):

        self.input_data = input_data
        self.h1_out = self.Relu(input_data.dot(self.w1) + self.b1)
        self.h2_out = self.Relu(self.h1_out.dot(self.w2) + self.b2)
        self.output_layer = self.Softmax(self.h2_out.dot(self.w3) + self.b3)

    # Backward Propagation

    def backward(self, target):

        # corss_entropy loss derivative
        Loss_to_z_grad = (self.output_layer - target) # correct

        self.b3_grad = Loss_to_z_grad
        self.w3_grad = self.h2_out.T.dot(Loss_to_z_grad) # correct



        Activation_2＿grad = Loss_to_z_grad.dot(self.w3.T) # correct
        Activation_2_grad[Activation_2_grad<0] = 0

        self.b2_grad = Activation_2＿grad
        self.w2_grad = self.h1_out.T.dot(Activation_2＿grad)

        
        Activation_1＿grad = Activation_2＿grad.dot(self.w2.T)
        Activation_1_grad[Activation_1_grad<0] = 0     

        self.b1_grad = Activation_1＿grad
        self.w1_grad = self.input_data.T.dot(Activation_1＿grad)


    # Update Weights
    def update(self, learning_rate=1e-06):
        self.w1 = self.w1 - learning_rate * self.w1_grad
        self.b1 = self.b1 - learning_rate * self.b1_grad

        self.w2 = self.w2 - learning_rate * self.w2_grad
        self.b2 = self.b2 - learning_rate * self.b2_grad

        self.w3 = self.w3 - learning_rate * self.w3_grad
        self.b3 = self.b3 - learning_rate * self.b3_grad

    # Loss Functions
    def cross_entropy(Y, Y_prediction):
        return -(np.matmul(Y, np.log(Y_prediction)) + np.matmul((1-Y), np.log(1-Y_prediction)))

    def print_accuracy(self):
        correct = 0
        loss = 0
        for i in range(y_val.shape[0]):
            self.acc_test(x_val[i])
            index = self.output_layer
            one_hot = 0
            for check in range(y_val[i].shape[0]):
                if y_val[i][check] == 1:
                    one_hot = check
                    break
            if np.argmax(index) == one_hot:
                correct += 1
                # print('correct: ',check)
            # else:
                # print('incorrect: ', check)
        print('accuracy = ', correct/y_val.shape[0])

import random
 mnist_nn = NN(input_size = 784, hidden_1_size = 200, hidden_2_size = 200,output_size = 10)


 
for i in range(1000):
    for j in range(2000):
        index = random.randint(0,x_train.shape[0]-1)
        mnist_nn.forward(x_train[[index]])
        mnist_nn.backward(y_train[index])
        mnist_nn.update()
    print(i)
    mnist_nn.print_accuracy()

The accuracy is terribly low since it can only predict one number. I've seen this article, Neural network always predicts the same class and I did change Relu to leaky Relu, but it doesn't really work.

I think my dataset should be ok cause I use the same dataset to train a DNN with pytorch, and it works. Also, the initial value of weights and bias are random values.

Answer 1

I've had a quick look over your code and if I understand it correctly, then there may be some issues:

• It seems like you want it to do multi-class classification with 10 classes, however I believe your cross entropy function looks like binary cross entropy, instead of general cross entropy . Also, you're using matrix multiplication, whereas I think you want to sum y * log(y_pred) over the 10 output probabilities and then take the mean across the batch, so you end up with a scalar valued loss.
• When doing the ReLU gradient, you should clip where the actual activation is negative, not where the gradient is negative, I think. So Activation_2_grad[Activation_2_grad<0] = 0 should be Activation_2_grad[self.h2_out < 0] = 0 .
• The rest of the backprop looks okay.

Answer 2

Try using tanh to make sure the algo is working properly. Relu can be finnicky, and only really dealt with if you have control over the dataset, as it requires a fairly even distribution of the classes. (Leaky_relu is hard to gauge as well)

In terms of whether or not your backprop is working properly, you might be better off using the keras sequential model, ie:

model = tf.keras.Sequential([
    input_layer,
    tf.keras.layers.Dense(128, activation="tanh"),
    tf.keras.layers.Dense([number of outputs], activation='softmax'),
])