# FrameSum: Leveraging Framing Theory and Deep Learning for Enhanced News Text Summarization
## 3 News Text Summarization Model Based on Framing Theory
### News Framing Recognition Module (NFRM) Based on Deep Learning
#### 3.2.3 Design of NFRM
News Frame Classification and Prediction  
News frame classification and prediction is a key innovation in our approach. While it builds upon existing multi-class classification techniques, our method incorporates novel elements specifically designed for frame identification. We consider news frame recognition as a multi-class classification problem, where each news text belongs to only one frame type. The set of news frame labels is defined as \(L=\{l_{1},l_{2},\ldots,l_{7}\}\), corresponding to the fact frame, responsibility frame, conflict frame, human interest frame, economic consequences frame, morality frame, and leadership frame respectively. For each frame category \(l_{i}\in L\) (\(i=1\), \(2\), \(\ldots\), \(7\)), its semantic feature representation \(\Phi_{l_{i}}\) can be obtained from Section 3.2.3. A key innovation in our approach is the use of a frame-aware attention mechanism to perform weighted aggregation on the contextual semantic representation \(H\) of the text sequence using the frame features \(\Phi_{l_{i}}\). This allows us to obtain the text representation vector \(s_{i}\) under that frame. \[ \begin{split} e_{ij}=v_{i}^{\top}tanh(W_{h}h_{j}+W_{f}\Phi_{l_{i}})\\ \alpha_{ij}=\frac{exp(e_{ij})}{\sum_{i=1}^{N}exp(e_{ik})}\\ s_{i}=\sum_{j=1}^{N}\alpha_{ij}h_{j}\end{split}  \tag{1}\]  
where \(e_{ij}\) is the attention score of the \(j\)-th hidden state under the \(i\)-th frame, \(\alpha_{ij}\) is the corresponding attention weight, \(v_{i}\in\mathbb{R}^{d_{a}}\), \(W_{h}\in\mathbb{R}^{d_{a}\times d_{h}}\) and \(W_{f}\in\mathbb{R}^{d_{a}\times d_{i}}\) are the attention parameters. \(s_{i}\in\mathbb{R}^{d_{h}}\) is the aggregated text representation under the \(i\)-th frame. We then concatenate the text representations of all frames \(S=[s_{1};s_{2};\ldots;s_{7}]\). Through a multi-layer perceptron (MLP), we obtain the final classification probability distribution:  
\[ \begin{split} P=softmax(MLP(S))\\ \hat{l}=argmax_{i}P_{i}\end{split}  \tag{2}\]  
where \(S\in\mathbb{R}^{7d_{h}}\) is the concatenated text representation vector, _MLP_ is the multi-layer perceptron, and \(P\in\mathbb{R}^{7}\) is the predicted probability distribution. We select the frame with the highest predicted probability as the final classification result, where \(\hat{l}\in L\) is the predicted frame category label. 1. Loss Function and Optimization Strategy  
In multi-class classification tasks, we typically use the cross-entropy loss function to measure the difference between the predicted probability distribution and the true label distribution. \[L=-\frac{1}{N}\sum_{x=1}^{N}\sum_{y=1}^{7}l_{xy}log\big{(}P_{xy}\big{)} \tag{3}\]  
where \(N\) is the number of training samples, \(l_{xy}\in\{0,1\}\) is the true label of the \(x\)-th sample on the \(y\)-th frame, and \(P_{xy}\) is the predicted probability of the \(x\)-th sample on the \(y\)-th frame. To minimize the loss function, we use the Adam [53] optimization algorithm as implemented in the PyTorch library [54]. The update rule for the Adam optimizer is as follows:  
\[ \begin{split} m_{t}=\beta_{1}m_{t-1}+(1-\beta_{1})g_{t},& \quad v_{t}=\beta_{2}v_{t-1}+(1-\beta_{2})g_{t}^{2}\\ \hat{m}_{t}=\frac{m_{t}}{1-\beta_{1}^{2}},&\quad \hat{v}_{t}=\frac{v_{t}}{1-\beta_{2}^{2}}\\ \theta_{t}=\theta_{t-1}-\alpha\frac{\hat{m}_{t}}{\sqrt{v_{t}+ \epsilon}}\end{split}  \tag{4}\]  
where \(m_{t}\) and \(v_{t}\) are the first and second moment estimates of the gradient, respectively, \(\beta_{1}\) and \(\beta_{2}\) are the decay rates, \(\hat{m}_{t}\) and \(\hat{v}_{t}\) are the corrected estimates, \(\theta_{t}\) is the value of the model parameter at \(t\)-th step, \(\epsilon\) is the learning rate, and \(\epsilon\) is the smoothing term. In the training phase, we train the model on a news dataset containing annotated frame labels and use a validation set for hyperparameter tuning to select the optimal hyperparameter configuration.