Table 2. Forward and backward sequence equations of the graph LSTM.

Forward sequence	Backward sequence
$$i{g}_t=\sigma (w_{ig}{x}_t+U_{ig}{h}_{p\left(t\right)}+V_{ig}{h}_{\mu \left(t\right)}+b_{ig})$$ (6)	$$i{g}_t=\sigma (w_{ig}{x}_t+U_{ig}{h}_{s\left(t\right)}+V_{ig}{h}_{k\left(t\right)}+b_{ig})$$ (11)
$$f{g}_t=\sigma (w_{fg}{x}_t+U_{fg}{h}_{p\left(t\right)}+V_{fg}{h}_{\mu \left(t\right)}+b_{fg})$$ (7)	$$f{g}_t=\sigma (w_{fg}{x}_t+U_{fg}{h}_{s\left(t\right)}+V_{fg}{h}_{k\left(t\right)}+b_{fg})$$ (12)
$$h{g}_t=\sigma (w_{hg}{x}_t+U_{hg}{h}_{p\left(t\right)}+V_{hg}{h}_{\mu \left(t\right)}+b_{hg})$$ (8)	$$h{g}_t=\sigma (w_{hg}{x}_t+U_{hg}{h}_{s\left(t\right)}+V_{hg}{h}_{k\left(t\right)}+b_{hg})$$ (13)
$$c_t=w_c{x}_t+U_c{h}_{p\left(t\right)}+V_c{h}_{\mu \left(t\right)}+b_c$$ (9)	$$c_t=w_c{x}_t+U_c{h}_{s\left(t\right)}+V_c{h}_{k\left(t\right)}+b_c$$ (14)
$$o{p}_t=\sigma (w_{op}{x}_t+U_{op}{h}_{p\left(t\right)}+V_{op}{h}_{\mu \left(t\right)}+b_{op})$$ (10)	$$o{p}_t=\sigma (w_{op}{x}_t+U_{op}{h}_{s\left(t\right)}+V_{op}{h}_{k\left(t\right)}+b_{op})$$ (15)