Analysis of Python's underlying technology: how to implement neural networks

Analysis of Python's underlying technology: How to implement neural networks requires specific code examples

In the field of modern artificial intelligence, neural networks are one of the most commonly used and important technologies. . It simulates the working principle of the human brain and realizes complex tasks through the connection of multiple layers of neurons. As a powerful and easy-to-use programming language, Python provides extensive support and convenience for implementing neural networks. This article will delve into the underlying technology of neural networks and demonstrate its implementation through detailed code examples.

1. Structure of neural network

Neural network consists of three main parts: input layer, hidden layer and output layer. The input layer receives raw data or feature vectors, the hidden layer converts the input into a more abstract representation through a series of weights and activation functions, and finally the output layer produces the final prediction result.

2. Basic steps for implementing neural networks in Python

1. Import the necessary libraries

In Python, we can use NumPy for numerical calculations and Matplotlib for visualization operations . Therefore, these two libraries need to be imported first.

import numpy as np
import matplotlib.pyplot as plt

2. Define the class of neural network

In the code, we implement this by defining a class of neural network. This class contains initialization function, forward propagation function and back propagation function.

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        self.W1 = np.random.randn(self.input_size, self.hidden_size) 
        self.W2 = np.random.randn(self.hidden_size, self.output_size)

    def forward(self, X):
        self.z1 = np.dot(X, self.W1)
        self.a1 = self.sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.W2)
        self.output = self.sigmoid(self.z2)

    def backward(self, X, y):
        self.error = y - self.output
        self.delta_output = self.error * self.sigmoid_derivative(self.output)
        self.error_hidden = self.delta_output.dot(self.W2.T)
        self.delta_hidden = self.error_hidden * self.sigmoid_derivative(self.a1)

        self.W2 += self.a1.T.dot(self.delta_output)
        self.W1 += X.T.dot(self.delta_hidden)

3. Define the activation function and its derivatives

Commonly used activation functions include the sigmoid function and the ReLU function. The derivative of the activation function plays a key role in the backpropagation process. Below is sample code for these two functions.

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def sigmoid_derivative(x):
    return x * (1 - x)

def relu(x):
    return np.maximum(0, x)

4. Training neural network model

During the training process, we need to prepare training data and target labels. By continuously calling the forward propagation and back propagation functions, the weight parameters are gradually optimized so that the output of the neural network is as close as possible to the target label.

X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([[0], [1], [1], [0]])

nn = NeuralNetwork(2, 4, 1)

for i in range(10000):
    nn.forward(X)
    nn.backward(X, y)

print("Output after training:")
print(nn.output)

5. Results visualization

Finally, we can use the Matplotlib library to visualize the prediction results.

plt.scatter(X[:, 0], X[:, 1], c=nn.output.flatten(), cmap='viridis')
plt.title("Neural Network")
plt.xlabel("Input1")
plt.ylabel("Input2")
plt.show()

By running the above code, we can see the classification results of the input data by the neural network.

This article shows how to use Python's underlying technology to implement neural networks through detailed code examples. Using these technologies, we are able to build and train a variety of complex neural network models to solve various artificial intelligence tasks. I hope this article will help you understand the underlying implementation of neural networks and improve your Python programming skills. Let’s explore the power of neural networks together!

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