# Integrating Merkle Trees with Transformer Networks for Secure Financial Computation
## 3 Materials and Method
### Merkle-Transformer
#### 3.3.2 Verifiable Computation Module Based on Merkle Tree  
The verifiable computation module based on Merkle trees is a core component of the model, playing a vital role in safeguarding data security and integrity throughout the computation process. The design of this module merges the data verification mechanism of Merkle trees with the efficient computation capability of deep learning, aiming to provide a secure and efficient framework for financial data processing. The design details of this module follow the basic principles of Merkle trees, where data blocks are hashed to form a tree-like structure, with each non-leaf node being the hash of the hash values of its child nodes. In our model,  
Figure 3: Overview of the Merkle-Transformer.  
this concept is extended to the outputs of the intermediate layers of deep learning models. Specifically, for each intermediate layer of the model, the hash value of its output is calculated, and these hash values are organized in the manner of a Merkle tree.  
Considering that each layer in deep learning can be viewed as a data transformation, the outputs of each layer are treated as data blocks. For instance, if the model's first layer is a two-dimensional convolutional layer with input \(x\) and output \(h_{1}\), then the hash value \(H(h_{1})\) of \(h_{1}\) can be calculated. Similarly, the hash value \(H(h_{2})\) for the output \(h_{2}\) of the second layer is computed, and so on. These hash values are then paired and hashed again to form the parent nodes of the Merkle tree, continuing until the root hash is formed. Mathematically, this process can be expressed as follows:  
\[h_{\text{parent}}=H(h_{\text{left}}||h_{\text{right}}) \tag{8}\]  
where \(h_{\text{parent}}\) is the hash value of the parent node, \(h_{\text{left}}\) and \(h_{\text{right}}\) are the hash values of the child nodes, \(H\) is the hash function, and \(||\) denotes concatenation. In practical applications, our deep learning model may include various types of layers, such as convolutional layers (Conv2D), pooling layers, and dense layers. These layers are stacked in sequence to form a network capable of extracting and processing complex features. For example, a typical stacking structure might involve the input passing through two convolutional layers, followed by a pooling layer, several more convolutional layers, and finally, a dense layer to produce the output. The output of each layer is used not only for the input of the next layer but also for constructing the Merkle tree. The output dimensions of each convolutional or dense layer depend on the layer's configuration and the dimensions of the input. For example, the output dimension of a convolutional layer might be a function of the number of filters, stride, and padding. The advantage of this design is that it combines the efficient computational capability of deep learning models with the data integrity verification mechanism provided by Merkle trees. This combination not only enhances the model's performance in processing financial data but also increases the security of the data processing. Any unauthorized alteration to the data or model output will be reflected in the root hash of the Merkle tree and can, therefore, be quickly detected. Additionally, due to the structure of the Merkle tree, which makes the verification process highly efficient, only a small portion of nodes need to be verified to ensure the integrity of the entire dataset, significantly reducing computational and storage overhead. In financial computation tasks, this design is particularly important as it not only ensures the reliability and auditability of data processing but also allows for rapid response to potential security threats. Whether in scenarios of financial transaction detection or stock price prediction, ensuring the security and integrity of data is of utmost importance.