Neural Network Fundamentals Series 2 - Building Intelligence: Multilayer Perceptrons and the Mystery of Deep Learning

In our last article, Neural Network Fundamentals Series 1 - Neural Network Enlightenment: Demystifying Artificial Intelligence, we explored the basic concepts and history of neural networks. We learned about the origins of neural networks and how they evolved from simple biological inspiration to the complex computational models they are today. We introduce the basic terms of neurons, weights, and activation functions, and explain how these terms work together to form the simplest form of neural network, the single-layer perceptron. In addition, we explore how neural networks learn through the basic concepts of loss function and backpropagation, which lays the foundation for understanding more complex neural network models.

Now, we're going to take the next step and dive deeper into Multilayer Perceptron (MLP). MLP is a more complex and powerful neural network structure that introduces multiple layers, including one or more hidden layers. These additional layers enable the network to learn more complex patterns and relationships, which is the cornerstone of deep learning. In this article, we'll take a closer look at how MLP is structured, how it works, and why it's important in modern deep learning. With this article, we hope to enable readers to better understand how multilayer perceptrons have become a core concept in the field of artificial intelligence and machine learning, and to prepare for further exploration of more advanced neural network concepts.

Introduction to Multilayer Perceptron (MLP).

Definition and Historical Context

The Multilayer Perceptron (MLP) is a more advanced neural network structure. By definition, MLP is a feedforward neural network consisting of multiple layers, typically including an input layer, one or more hidden layers, and an output layer. Each layer contains multiple neurons that pass information to each other through weighted connections. A key feature of MLP is the presence of its hidden layers that can capture complex and abstract patterns in the input data.

From a historical point of view, the concept of multilayer perceptrons originated from the research of single-layer perceptrons in the 50s of the last century. The original perceptron model was limited by its limited capabilities (e.g., inability to solve nonlinear separable problems such as XOR problems). With further research into neural network theory, scientists began to explore adding multiple layers to overcome these limitations. By the 1980s, with the advent of backpropagation algorithms, MLP became an important part of deep learning and modern neural network research.

Comparison of MLP with single-layer perceptrons

The biggest structural difference between MLP and the original single-layer perceptron is the introduction of a hidden layer. In a single-layer perceptron, the input is passed directly to the output layer, which means it can only learn simple patterns. MLP, on the other hand, enables the network to capture more complex data features by introducing one or more hidden layers. With each additional hidden layer, the network's ability to learn and represent more complex functions increases significantly.

The addition of hidden layers allows MLP to solve problems that cannot be solved by single-layer perceptrons, such as nonlinearity problems in classification and regression. This is because hidden layers are capable of extracting and combining features from input data, resulting in more complex representations of data. For example, for an image recognition task, the first hidden layer might recognize edges, the second hidden layer might recognize shapes, and a deeper layer might recognize more complex object features.

All in all, multilayer perceptrons mark an important shift from simple linear models to advanced models capable of handling complex, nonlinear data patterns. This shift not only enhances the ability of neural networks to solve real-world problems, but also lays the foundation for the future development of deep learning.

The role of hidden layers

引入隐藏层（Hidden Layers）的概念

The hidden layer is a core component of the Multilayer Perceptron (MLP). In the most basic terms, the hidden layer sits between the input and output layers and is invisible to the outside world (hence the name "hidden" layer). These layers contain neurons that receive data from the input layer, process it through weights and activation functions in the network, and then pass the results on to the next layer. The number of hidden layers and the number of neurons in each layer can be adjusted according to the specific application and data complexity.

Explain the importance of hidden layers in complex functional simulations

Hidden layers play a crucial role in MLP because they enable the network to capture and learn complex patterns and features in the input data. Each hidden layer can be seen as a transformation that maps the input data to a new space that may be easier to classify or other types of data processing.

For different hidden layers, they may focus on learning different aspects of the data. For example, in image processing, the first hidden layer may recognize simple edges and lines, while as the network layers deeper, subsequent layers may recognize more complex structures, such as shapes and local combinations of objects. This ability to extract features layer by layer is key to the powerful performance of deep learning.

The relationship between the hidden layer and the depth of the network

Network depth, i.e., the number of hidden layers, is an important factor in determining the complexity and capabilities of MLP. In general, deeper networks are able to learn more complex patterns and relationships. However, increasing the depth of the network also presents challenges such as overfitting (the phenomenon in which a model performs well on training data but not well on new data) and vanishing/exploding (gradients become very small or very large during training, making the model difficult to train).

Therefore, when designing an MLP, it is an important decision to select the appropriate number of hidden layers and neurons in each layer, which needs to take into account the complexity of the data, the magnitude of the training data, and the limitations of computing resources. Properly configuring these parameters can significantly impact the performance and efficiency of your model.

Overall, the introduction of hidden layers provides MLPs with the ability to handle complex, non-linear problems, but at the same time requires careful design and tuning to maximize their effectiveness. With the appropriate configuration of hidden layers, MLP can be effectively applied to a variety of complex machine learning and deep learning tasks.

The importance of activation functions

解释激活函数（Activation Functions）的概念

Activation functions play a crucial role in neural networks. They are nonlinear functions applied to the output of a neuron, determining whether that neuron should be activated or not, i.e. whether it contributes to the final output of the network. The introduction of these functions allows neural networks to capture and learn the complex, nonlinear relationships necessary to process real-world data.

Types and characteristics of common activation functions

• ReLU (Rectified Linear Unit): The ReLU function provides a simple but effective nonlinear transformation. Its formula is f(x) = max(0, x), which means that when the input is positive, the output is the input itself, and when the input is negative, the output is zero. The main advantage of ReLU is that it reduces the problem of vanishing gradients and is computationally efficient. However, it also has the problem of so-called "dead neurons", which in some cases may never be activated.
• Sigmoid: The Sigmoid function is a classic activation function that is shaped like an S-curve. It squeezes any value between 0 and 1, so it is often used in the output layer, especially in binary classification problems. However, in deep networks, the Sigmoid function can cause vanishing gradient issues because its derivative is very close to zero when the input value is very large or very small.
• Tanh (hyperbolic tangent): The Tanh function is similar to Sigmoid, but it compresses the output value to between -1 and 1. This makes the output more normalized during training, helping to increase the speed of learning. However, it can likewise face the problem of gradient vanishing.

The role of activation functions in neural networks

The main role of activation functions in neural networks is to introduce nonlinearity. Without a nonlinear activation function, a neural network is always equivalent to a single-layer network, no matter how many layers it has, because the superposition of linear layers is still linear. Nonlinear activation functions allow networks to learn more complex patterns and decision boundaries, whether in image recognition, language processing, or complex games.

In addition, different activation functions can affect the learning speed and stability of the network. Choosing the right activation function can help the network converge faster and reduce problems during training, such as vanishing gradients or explosions.

In conclusion, activation functions are a key element in neural network design, and their selection and application have a significant impact on the performance and efficiency of the network. Understanding the characteristics and application scenarios of different activation functions is essential for building effective neural network models.

Build a basic MLP model

This section describes how to design the structure of MLP

Building a multilayer perceptron (MLP) model involves carefully designing the network structure to ensure that it can effectively learn and simulate the desired data patterns. The basic structure of MLP consists of three main parts: the input layer, the hidden layer, and the output layer. The input layer is responsible for receiving the data, the hidden layer is responsible for processing the data, and the output layer produces the final predictions. The number of neurons in each layer needs to be determined when designing, where the number and size of hidden layers are usually determined based on the specific problem and the complexity of the dataset.

Basic steps

1. Data Entry: Start by determining the size of the input layer, which should match the dimensions of the feature data. For example, when processing a 28x28 pixel image, the input layer should have 784 neurons.
2. Weight setting: Each neuron's input is weighted by a set of weights that are constantly updated during training. The initial weight is usually set to a small random number.
3. Activation Function Selection: Select the appropriate activation function for the hidden layer and the output layer. For example, a hidden layer can use the ReLU activation function, while for a binary classification problem, the output layer can use the Sigmoid activation function.
4. Output layer design: The design of the output layer depends on the specific task. For classification tasks, the number of neurons in the output layer is usually equal to the number of classes, while for regression tasks, the output layer usually has only one neuron.

Simple code examples

Below is a simple example of building a basic MLP model using the Keras library in Python. Let's say we're dealing with a simple binary classification problem.

from keras.models import Sequential
from keras.layers import Dense

# 创建模型
model = Sequential()

# 添加输入层和第一个隐藏层
model.add(Dense(128, input_dim=784, activation='relu'))

# 添加第二个隐藏层
model.add(Dense(64, activation='relu'))

# 添加输出层
model.add(Dense(1, activation='sigmoid'))

# 编译模型
model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])

# 输出模型摘要
model.summary()
           

In this example, we first create a Sequential model, then add two hidden layers, each with 128 and 64 neurons, and use the ReLU activation function. Finally, we add an output layer that uses the Sigmoid activation function to accommodate the binary classification task. The model is then compiled by specifying a loss function (in this case, binary cross-entropy), an optimizer (ADAM), and an evaluation metric (accuracy).

This simple example illustrates the process of building a basic MLP model, which may require more detailed configuration and tweaking depending on the specific problem.

Examples of MLP in practical applications

Case Study: Application of MLP to Solve Image Classification Problems

Multilayer perceptrons (MLPs) are widely used in many fields, and a typical example is image classification tasks. In this case, we will explore how to use MLP to classify images, such as distinguishing between different kinds of animals or objects.

In an image classification task, the input is the pixel values of an image, which are typically converted into one-dimensional arrays for easy processing. For example, a 28x28 pixel image would be converted into an array of 784 values. This array serves as the input to the input layer. This data is then processed through a series of hidden layers. Each hidden layer may learn different features of the image, such as edges, patches of color, or specific shapes.

Finally, the output layer makes classification decisions based on the learned features. In a classification task with multiple classes, the output layer usually has the same number of neurons as the classes, each corresponding to a class. Using an activation function, such as softmax, you can convert the output into a probability distribution that represents the probability that an image belongs to each category.

Case Study: Efficiency and Limitations of MLP in Image Classification

Efficiency:

• Fast implementation and training: Compared to more complex deep learning models, MLP is relatively simple and easy to implement and train.
• Good baseline model: For some less complex image datasets, MLP can be used as an effective baseline model.

Locality:

• Limited ability to process high-dimensional data: For high-resolution images or complex visual patterns, MLP may not be sufficient to effectively capture all key features.
• Inability to take advantage of the spatial structure of an image: Unlike convolutional neural networks (CNNs), MLP cannot effectively take advantage of the spatial relationships between pixels in an image. This means that it may not be able to recognize the same objects that change position in the image due to translation or rotation.
• The number of parameters can be very large: When working with large images, MLP may require a large number of parameters (i.e., weights), which leads to the risk of oversized and overfitting the model.

In summary, although MLP can provide some efficiency and convenience in some image classification tasks, it has limitations when processing complex or high-resolution images. In these cases, more advanced neural network structures, such as convolutional neural networks (CNNs), may be required to process image data more efficiently. However, MLP remains a valuable starting point for understanding how neural networks handle image classification tasks.

summary

In this article, we delve into the core concepts and applications of multilayer perceptrons (MLPs). As a basic neural network structure, MLP significantly improves the network's ability to deal with complex and nonlinear problems by introducing one or more hidden layers. We discuss the importance of activation functions in introducing nonlinearity and how MLP can be constructed and applied to solve real-world problems such as image classification.

MLP plays an important role in deep learning. Although it has limitations in handling certain types of tasks, such as high-resolution image recognition, it is still fundamental to understanding more complex network structures and provides effective solutions to many problems.

In the next article, Neural Network Fundamentals Series 3 - Feedforward Neural Networks, we'll take a deep dive into the architecture and features of feedforward neural networks. We'll discuss how data propagates forward in the network, as well as the basics of loss functions and optimizers. In addition, we will show how to build and train a simple feedforward network, further solidifying our understanding of the fundamentals of neural networks.

Important points not to be mentioned

Backpropagation algorithms are a key technology for training neural networks, especially MLP. This algorithm efficiently updates the loss function by calculating the gradient of these parameters with respect to these parameters. In MLP, backpropagation allows us to adjust the weights in the hidden layer to minimize output errors. This process involves complex chain derivatives, but it is at the heart of enabling deep learning.

In addition to traditional gradient descent methods, advanced optimization algorithms such as Adam and RMSprop also play an important role in training MLP. These optimization algorithms improve the speed and efficiency of training by adjusting the learning rate and other parameters. For example, the Adam optimizer, which combines the concepts of momentum and adaptive learning rate, generally converges faster and is more stable when dealing with complex optimization problems. These advanced optimization techniques are an integral part of modern deep learning training and are essential for improving the performance of MLP and other types of neural networks.