# AI-Driven Optimization of Blockchain Scalability, Security, and Privacy Protection
## 2 Introduction to Related Technologies
### XGBoost Model
#### 2.2.2 Deep Learning
This operation not only enhances computational efficiency but also increases the model's tolerance to minor spatial transformations [100]. 3. Fully Connected Layer: The fully connected layer integrates the features extracted from previous layers and is primarily used for classification or regression tasks. In this layer, each neuron is connected to all neurons in the preceding layer, resembling hidden layers in traditional neural networks. Through weighted summation and activation functions, the fully connected layer produces the final classification output or task-specific predictions [101]. 3. LSTM Model  
LSTM is a specialized type of Recurrent Neural Network (RNN) designed to process and predict time-series or sequential data with long-term dependencies [102]. It effectively mitigates the vanishing and exploding gradient problems present in traditional RNNs. The fundamental unit of an LSTM consists of three gating mechanisms--the forget gate, input gate, and output gate--along with a cell state [103]. These three gates regulate the flow of information using the sigmoid activation function and element-wise multiplication, ensuring that the strength of the information flow is controlled without introducing additional information. The LSTM unit structure diagram is illustrated in Figure 6c. In the figure, \(C_{t-1}\) represents the cell state (memory state) at time \(X_{t}\) is the current input, and \(h_{t-1}\) denotes the output of the neural unit at time \(t-1\). The forget gate's output at time \(t\) is \(f_{t}\), the input gate's output is \(i_{t}\), and the output gate's output is \(o_{t}\). The function \(\sigma\) represents the sigmoid activation, while \(C_{t}\) is the cell state at time \(t\), and \(h_{t}\) is the neural unit's output at time \(t\). To prevent excessive memory retention from interfering with the processing of new inputs, the forget gate determines how much information from the previous cell state should be preserved. It computes a weight based on \(x_{t}\) and \(h_{t-1}\), processed through a sigmoid activation function to produce a vector with values between 0 and 1--where0 signifies forgetting and 1 indicates full retention. The forget gate is mathematically expressed as follows:  
\[f_{t}=\sigma\Big{(}W_{f}\cdot[h_{t-1},X_{t}]+b_{f}\Big{)} \tag{7}\]  
In Equation (7), \(W_{f}\) represents the forget gate weight, \(b_{f}\)denotes the bias, and \(\sigma\) is the sigmoid function. The input gate determines how much of the current input information should be retained in the state of the neural unit at the current time step, thereby controlling the information that needs to be updated [104]. The input \(X_{t}\) and \(h_{t-1}\) output values pass through the input gate and are then combined with the input and output values processed by a tanh function to generate new control parameters. The mathematical expression for the input gate is as follows:  
\[i_{t}=\sigma(W_{i}\cdot[h_{t-1},X_{t}]+b_{i}) \tag{8}\]  
\[\tilde{C}_{t}=\tanh(W_{c}\cdot[h_{t-1},X_{t}]+b_{c}) \tag{9}\]  
\[C_{t}=f_{t}*C_{t-1}+i_{t}*\tilde{C}_{t} \tag{10}\]  
In Equation (10), the cell state is updated as \(C_{t}\), and \(W_{i}\) represents the input gate weight. The output gate determines which information from the current cell state is transmitted to \(h_{t}\). Both \(X_{t}\) and \(h_{t-1}\) first pass through the output gate to define the scope of the output information. Then, in combination with the tanh function, a selected \(C_{t}\) portion of the memory information is processed, and the final neural network output value \(h_{t}\) is determined. The mathematical expression for the output gate is as follows:  
\[o_{t}=\sigma(W_{o}\cdot[h_{t-1},X_{t}]+b_{o}) \tag{11}\]  
\[h_{t}=o_{t}*\tanh(C_{t}) \tag{12}\]  
In Equations (8) and (9), \(W_{o}\) represents the output gate weight.