Clarification on Visualization Techniques for Graphs 4 and 7 under Linear Complexity Constraints

[FarisXiong]

I am currently examining the methodologies presented in your paper and am unclear about the techniques used to visualize Graphs 4 and 7 under linear complexity constraints. According to Equation 7, it seems infeasible to compute the attention scores between any two nodes using a linear approximation. Could you please clarify the specific approach utilized for these visualizations under the mentioned constraints? Additionally, if there are any potential modifications or alternative methods that could be recommended to handle these calculations more feasibly, I would appreciate your insights.

$$z_{(l+1)u} \approx \frac{\phi(q_{u}/\sqrt{\tau})^T\sum_{\nu=1}^N e^{g_{\nu}/\tau} \phi(k_{\nu}/\sqrt{\tau}) v_{\nu}^T}{\phi(q_{u}/\sqrt{\tau})^T\sum_{\omega=1}^N e^{g_{\omega}/\tau} \phi(k_{\omega}/\sqrt{\tau}) } $$