# Integrating Merkle Trees with Transformer Networks for Secure Financial Computation
## 2 Related Works
### Financial Computation Model Based on Transformer  
In the subsection on Transformer-based financial computation models, the Transformer's exemplary performance in various domains, particularly in finance, is emphasized since its introduction [22]. This model, proposed by [PERSON] et al. in 2017 [23], revolutionized sequence data processing with its \"Self-Attention\" mechanism. Compared to traditional recurrent neural networks (RNNs) [24] and long short-term memory networks (LSTMs) [25], the Transformer addresses long-distance dependencies more effectively, a critical aspect in financial time-series data analysis. The core of the Transformer is its self-attention mechanism, allowing the model to consider other elements while processing each element in a sequence, thereby capturing complex patterns in data more effectively. The computation of self-attention can be represented as follows:  
\[\text{Attention}(Q,K,V)=\text{softmax}\bigg{(}\frac{QK^{T}}{\sqrt{d_{k}}} \bigg{)}V \tag{3}\]  
Here, \(Q\), \(K\), and \(V\) represent the query, key, and value, respectively, with \(d_{k}\) denoting the dimension of the key. This mechanism enables the model to allocate different attention weights to each element in a sequence, as shown in Figure 2.  
Figure 2: Illustration of the multi-head attention mechanism.  
The Transformer model also includes two main parts: an encoder and a decoder. The encoder consists of multiple identical layers, each with a self-attention mechanism and a simple feed-forward neural network. The decoder comprises multiple identical layers, but each decoder layer includes an additional attention mechanism focusing on the encoder's output. In financial computation models, the Transformer is employed for various tasks, such as stock price prediction, risk assessment, and market trend analysis [26]. In these applications, the Transformer effectively captures complex patterns and long-term dependencies in financial time-series data. For instance, in stock price prediction models, the Transformer can be represented by the following formula [27]:  
\[P_{t}=f(\text{Transformer}(S_{t-n},\dots,S_{t-1})) \tag{4}\]  
where \(P_{t}\) denotes the stock price prediction at time \(t\), and \(S_{t-n},\dots,S_{t-1}\) represent the stock price series at previous \(n\) time points, with \(f\) being the function linking the Transformer output to the prediction result.  
Another significant application of the Transformer in finance is fraud detection [28]. In this scenario, the model must identify anomalous patterns from a vast array of transaction data. With its self-attention mechanism, the Transformer can efficiently identify these complex fraud patterns. A Transformer model for fraud detection can be represented as follows:  
\[F_{t}=\text{Transformer}(\text{Transaction}_{t},\dots,\text{Transaction}_{t}) \tag{5}\]  
where \(F_{t}\) represents the fraud detection outcome at time \(t\), and \(\text{Transaction}_{1},\dots,\text{Transaction}_{t}\) denote the transaction sequence up to time \(t\). In conclusion, the Transformer model plays a crucial role in financial computation models due to its efficient handling of long-distance dependencies and capturing of complex patterns. A deeper understanding of the Transformer's structure and principles enables the design of more accurate and efficient financial computation models, achieving breakthroughs in areas like stock price prediction, risk assessment, and fraud detection. In the Merkle-Transformer model, these advantages of the Transformer will be utilized, combined with the security of Merkle trees, to provide a secure and efficient solution for financial data processing.