Refering to this paper "SimplE Embedding for Link Prediction in Knowledge Graphs" by Seyed Mehran Kazemi and David Poole in 2018 :

In page 4, about the proof of SimpLE being fully expressive,

I understand that $h_{e_i} =1 \text{ if }(n \text{ mod }|\mathcal{E}|)=i \text{ and }0 \text{ otherwise }$, $v_{r_j}=1 \text{ if }(n \text{ div } |\mathcal{E}|)=j \text{ and }0 \text{ otherwise }. $ and that the $(j*|\mathcal{E}|+i$)-th element of $t_{e_k}$ is $1$ if $(e_i,r_j,e_k)$ holds and $-1$ otherwise. From that we get $\langle h_{e_i},v_r, t_{e_k}\rangle=1$ But what about $v_{r^{-1}}$?


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