Learning Conjoint Attentions for Graph Neural Nets Supplementary Materials Tiantian He1,2 Y ew-Soon Ong 1,2 Lu Bai 1,2 1 Agency for Science, Technology and Research (A*ST AR) 2

To prove Theorem 1, we need to consider the two directions of the iff conditions. Obviously, the above equation does not hold as the terms in the summation operator are positive. Eq. (4), we have: null However, the RHS of Eq. (10) can be an RHS is an irrational number, while LHS is a rational number. Eq. (9) can be rewritten as: null To prove Theorem 2, we can follow the procedure which is used to prove Theorem 1. As Eq. (20) holds for any Obviously, the above equation does not hold as softmax function is positive.