## 3 MTQADC Model
### Feature Extraction Module  
Given a question, the language model ALBERT is used to obtain the state of the last hidden layer. The question context is then transformed into a semantic matrix using ALBERT. \[\mathbf{Q}_{\text{A}}=\mathbf{W}_{\text{A}}\text{ALBERT}(\mathbf{q}_{\text{text {text}}}) \tag{4}\]  
Through a learnable projection matrix \(\mathbf{W}_{\text{A}}\text{ALBERT}\), the initial embedding vector \(\mathbf{q}_{\text{text}}\) is transformed into the target embedding matrix \(\mathbf{Q}_{\text{A}}\), using the index A to represent the use of the ALBERT model. Here, \(\mathbf{Q}_{\text{A}}=[\mathbf{q}_{\text{CLS}},\mathbf{q}_{1},\cdots,\mathbf{ q}_{\text{N}}]\) is the \(\mathbf{D}\times\mathbf{N}\) embedding matrix, where \(\mathbf{D}\) denotes the embedding dimension, representing the dimension of each token embedding. \(\mathbf{N}\) refers to the number of tokens, indicating the number of words in the input sequence. \(\mathbf{W}_{\text{A}}\) is a learnable projection matrix with \(\mathbf{D}\times\mathbf{D}_{\text{A}}\), where \(\mathbf{D}_{\text{A}}\) is the output dimension, corresponding to the dimension of the ALBERT hidden layers. \(\mathbf{q}_{\text{CLS}}\) represents the embedding of the \([\text{CLS}]\) token, which contains the context information of the entire input sequence. \(\mathbf{q}_{1}\) to \(\mathbf{q}_{\text{N}}\) are the embedding representations of the other tokens in the input text, with \(\mathbf{q}_{1}\) corresponding to the first token in the input text, \(\mathbf{q}_{\text{N}}\) to the second token, and so on. Multi-granularity time data are typically presented at a daily time granularity, such as \"19 March 2008\". Embeddings of temporal knowledge graphs at the daily granularity contain only the time information for each day. However, certain tasks may require handling a larger time granularity, such as year or month, and this information cannot be directly obtained from pre-trained daily granularity embeddings. To address this issue, a multi-granularity time aggregation module is used, as shown in Figure 4. This module aims to extract coarser-grained temporal semantic information, such as monthly granularity, from the daily granularity embeddings. For example, in the case of annual time aggregation, suppose we need to aggregate all related monthly granularity time information from a specific year to obtain the time semantics related to that year. Figure 3: Data processing. In this process, the first step is to extract all the monthly granularity timestamps \(\text{m}_{1},\text{m}_{2},\cdots\text{m}_{Z}\) related to the specific year, along with the temporal embeddings \(\text{t}_{1},\text{t}_{2},\cdots\text{t}_{Z}\) corresponding to those timestamps. Here, Z represents the number of months related to the year, which is 12 for a year. Therefore, Z equals 12. To obtain the yearly granularity temporal representation, these monthly embeddings are constructed into a temporal semantic matrix \(\mathbf{T}_{\text{m}}\). \[\mathbf{T}_{\text{m}}=[\text{t}_{1},\text{t}_{2},\cdots\text{t}_{Z}] \tag{5}\]  
In this process, \(\mathbf{T}_{\text{m}}\in\mathbf{R}^{\mathbf{M}\times\mathbf{S}}\) represents the number of days related to the target month, while \(\mathbf{S}\) is the dimension of each timestamp embedding. To enhance the sequentiality of the temporal information, sinusoidal positional encoding is introduced [18]. Specifically, for the \(h\)-th position in \(\mathbf{T}_{\text{m}}\), the positional information is encoded as follows:  
\[\text{PE}(h,a)= \begin{cases}\sin\left(h/10000^{\frac{2l}{\theta}}\right),if \ a=2l\\ \cos\left(h/10000^{\frac{2l}{\theta}}\right),if\ a=2l+1\end{cases}  \tag{6}\]  
\(l\) is the index of the position in the matrix, and \(a\) is the exponent in the dimension of the positional encoding, which represents the \(a\)-th dimension of the positional encoding. \(\mathbf{D}\) is the dimension of the positional encoding.