Table 2 Summary of key equations and their purpose.

Equation (10)

\(\textbf{H}_t=tanh((1-\textbf{U}_r)\odot \textbf{H}_{t-1}+\textbf{U}_r\odot \textbf{I}_r)\odot \textbf{0}_r\)

Filter key information, suppress redundancy

Equation (11)

\(\textbf{R}_t=tanh((1-\textbf{U}_c)\odot \textbf{R}_{t-1}+\textbf{U}_c\odot \textbf{I}_c)\odot \textbf{O}_c\)

Equation (16)

\(\textbf{H}_t^{final}=LayerNorm\left( \beta \cdot \textbf{H}_t^{att}+(1-\beta )\cdot \textbf{H}_t\right)\)

Capturing long-distance dependencies

Equation (17)

\(\parallel \delta \parallel _p=Normalize(\textbf{W}_4\cdot ReLU(\textbf{W}_3\cdot \textbf{p}_\textrm{rand}+\tilde{\textbf{b}_1})+\tilde{\textbf{b}_2})\)

Generate adversarial noise

Equation (18)

\(v=sigmoid(\textbf{W}_d\cdot {ReLU}(\textbf{W}_c\cdot \parallel \delta \parallel _p+\tilde{\textbf{b}_c})+\tilde{\textbf{b}_d) }\)

Screening for meaningful adversarial noise

Equation (21)

\(\textbf{H}_t^{noise}=\textbf{H}_t+\epsilon \varvec{\cdot }{(v\cdot \parallel \delta \parallel _p+(1-v)\cdot \textbf{p}_{\textrm{rand}})}\)

Adding adversarial noise

Equation (22)

\(\textbf{R}_t^{noise}=\textbf{R}_t+\epsilon \varvec{\cdot }{(v\cdot \parallel \delta \parallel _p+(1-v)\cdot \textbf{p}_{\textrm{rand}})}\)

Equation (27)

\(\mathscr {L}_{intra-H}=-\sum _{i=1}^{|\mathscr {N}_t|}\log \frac{S_{intra-pos,i}^H}{\sum _{k=1}^{|\mathscr {N}_t|}S_{intra-neg,k}^H}\)

Capturing short-term dynamic features

Equation (30)

\(\mathscr {L}_{inter-H}=-\sum _{i=1}^{|\mathscr {N}_t|}\log \frac{S_{inter-pos,i}^H}{\sum _{k=1}^{|\mathscr {N}_t|}S_{inter-neg,k}^H}\)

Capturing global temporal relationships

Equation (32)

\(\textbf{P}_{score}^\mathscr {N}=\sigma (\textbf{H}^{mdgu}\cdot {ConvTransE}(\textbf{n}_{s,t},\textbf{r}_t+\textbf{H}_t^{final}\cdot {ConvTransE}(\textbf{n}_{s,t},\textbf{r}_t))\)

Calculating entity prediction scores