Demystifying Neural Networks: A Beginner’s Guide (Part 1) | 揭秘神经网络：小白也能懂的入门指南（一）

Hello everyone! Today, let's delve into the mysterious and powerful world of neural networks. Don't worry, I'll use the simplest and easiest-to-understand way to unveil its secrets step by step.

大家好！今天我们来深入探讨神经网络这个神秘而又强大的领域。别担心，我会用最简单易懂的方式，带你一步步揭开它的面纱。

1. What is a Neural Network?

什么是神经网络？

Imagine that our brain is a complex network composed of billions of neurons. These neurons are interconnected and transmit electrical signals to process information, enabling us to think, learn, and make decisions. Neural networks are computational models inspired by this structure.

想象一下，我们的大脑是由数十亿个神经元组成的复杂网络。这些神经元相互连接，通过传递电信号来处理信息，使我们能够思考、学习和做出决策。神经网络就是受此启发而诞生的计算模型。

In simple terms, a neural network is a computer model that mimics the structure of the brain. It consists of a large number of interconnected nodes (called neurons) that can receive, process, and transmit information. The goal of a neural network is to discover patterns in large amounts of data through learning and to use these patterns for prediction or classification.

简单来说，神经网络是一种模仿大脑结构的计算机模型。它由大量相互连接的节点（称为神经元）组成，这些节点可以接收、处理和传递信息。神经网络的目标是通过学习大量数据来发现其中的模式，并利用这些模式进行预测或分类。

2. How do Neural Networks Work?

神经网络如何工作？

The working principle of a neural network is like a relay race, where information is passed between neurons. Each neuron performs a weighted sum of the received information, processes it through an activation function, and then passes the processed information to the next neuron.

神经网络的工作原理就像接力赛，信息在神经元之间传递。每个神经元都会对接收到的信息进行加权求和，然后通过激活函数进行处理，最后将处理后的信息传递给下一个神经元。

• Weighted Sum: Each input signal has a weight, which represents its degree of influence on the next neuron. The greater the weight, the greater the influence.
• 加权求和： 每个输入信号都有一个权重，表示它对下一个神经元的影响程度。权重越大，影响越大。
• Activation Function: The activation function is like a filter that determines whether a neuron should be activated and the degree of activation. Common activation functions include the sigmoid function and the ReLU function.
• 激活函数： 激活函数就像一个过滤器，它决定了神经元是否应该被激活，以及激活的程度。常见的激活函数有 sigmoid 函数、ReLU 函数等。

3. Structure of a Neural Network

神经网络的结构

A neural network is typically composed of multiple layers:

神经网络通常由多个层组成：

• Input Layer: Receives raw data and passes it to the next layer.
• 输入层： 接收原始数据，并将数据传递给下一层。
• Hidden Layers: Process and transform the data, extracting features. There can be multiple hidden layers, and the number of neurons in each layer can vary.
• 隐藏层： 对数据进行处理和转换，提取特征。隐藏层可以有多个，每一层的神经元数量可以不同。
• Output Layer: Outputs the final result, such as a classification result or a predicted value.
• 输出层： 输出最终结果，例如分类结果或预测值。

Hidden layers are the most critical part of a neural network. They enable the neural network to model complex data by learning feature representations of the data. While we don't fully understand how hidden layers work, they are believed to play a key role in identifying patterns and features in data, such as recognizing subcomponents or edges of numbers.

隐藏层是神经网络中最关键的部分。它们通过学习数据的特征表示，使得神经网络能够对复杂的数据进行建模。虽然我们还不能完全理解隐藏层的工作原理，但它们被认为在识别数据中的模式和特征方面起着关键作用，例如识别数字的子组件或边缘。

4. The Importance of Weights

权重的重要性

Weights are the most important parameters in a neural network. They determine the degree of influence of each input signal on the output result. By adjusting the weights, we can change the behavior of the neural network and make it better at completing tasks.

权重是神经网络中最重要的参数。它们决定了每个输入信号对输出结果的影响程度。通过调整权重，我们可以改变神经网络的行为，使其更好地完成任务。

5. How to Adjust Weights?

如何调整权重？

Neural networks learn how to adjust weights through training. The training process mainly includes the following steps:

神经网络通过训练来学习如何调整权重。训练过程主要包括以下步骤：

1. Forward Propagation: Pass the input data to the neural network to obtain the model's predicted output.
   • 前向传播： 将输入数据传递给神经网络，得到模型的预测输出。
2. Calculate Loss: Compare the model's predicted output with the actual value and calculate the value of the loss function. The loss function is used to measure the accuracy of the model's prediction.
   • 计算损失： 比较模型预测输出与实际值，计算损失函数的值。损失函数用于衡量模型预测的准确性。
3. Backpropagation: Starting from the output layer, calculate the gradient of each weight layer by layer. The gradient represents the sensitivity of the error to the weight. The larger the gradient, the more significant the effect of adjusting the weight on reducing the error.
   • 反向传播： 从输出层开始，逐层计算每个权重的梯度。梯度表示了误差对权重的敏感程度，梯度越大，表示调整该权重对减小误差的效果越明显。
4. Update Weights: Update the value of each weight based on the direction and magnitude of the gradient. Gradient descent is commonly used, which updates the weight in the opposite direction of the gradient to minimize the value of the loss function.
   • 更新权重： 根据梯度的方向和大小，更新每个权重的值。通常使用梯度下降法，即沿着梯度的反方向更新权重，以减小损失函数的值。

6. Weighted Sum and Activation Function

加权求和与激活函数

In a neural network, each neuron performs a weighted sum of the received input signals and then passes the result to the activation function.

在神经网络中，每个神经元都会对接收到的输入信号进行加权求和，然后将结果传递给激活函数。

• Weighted Sum (Weighted Sum): Weighted sum is a basic operation in neural networks for neurons to process input signals. It multiplies each input signal by its corresponding weight and then adds up all the products to obtain a sum. This sum reflects the combined effect of all input signals on the neuron's output.
  • 加权求和 (Weighted Sum): 加权求和是神经网络中神经元处理输入信号的基本操作。它将每个输入信号乘以对应的权重，然后将所有乘积相加，得到一个总和。这个总和反映了所有输入信号对神经元输出的综合影响。

z = w₁x₁ + w₂x₂ + ... + wₙxₙ + b

Where:

其中：

• z is the result of the weighted sum
  • z 是加权求和的结果
• w₁, w₂, ..., wₙ are the weights corresponding to each input signal
  • w₁, w₂, ..., wₙ 是每个输入信号对应的权重
• x₁, x₂, ..., xₙ are the input signals
  • x₁, x₂, ..., xₙ 是输入信号
• b is the bias term, which can be seen as an additional input with a value of 1 and a weight of b
  • b 是偏置项（bias），可以看作是一个额外的输入，其值为1，权重为b
• Activation Function (Activation Function): The role of the activation function is to transform the result of the weighted sum into the output of the neuron. The activation function introduces nonlinearity, enabling the neural network to learn and represent complex nonlinear relationships.
  • 激活函数 (Activation Function): 激活函数的作用是将加权求和的结果转换为神经元的输出。激活函数引入了非线性因素，使得神经网络能够学习和表示复杂的非线性关系。

Common activation functions:

常见的激活函数：

• Sigmoid Function (Logistic Function): Compresses the input value between 0 and 1.
  • Sigmoid 函数 (Logistic 函数): 将输入值压缩到 0 和 1 之间。σ(z) = 1 / (1 + exp(-z))
• ReLU Function (Rectified Linear Unit): Outputs the input when it is positive, otherwise outputs 0.
  • ReLU 函数 (Rectified Linear Unit): 当输入为正时输出