Question: In case of min/max, what are the values of "p" learned by GNP?
Evidence: As we discussed in Section 3, GNP generalizes sum, max, mean, and min. In order to confirm the facts experimentally, we showed in Figure how the learnable parameters p and q in GNP changed during training. For maxdegree, GNP as aggregation and readout functions approximated sum (i.e., p + ≈ 1 and q + ≈ 0) and max (i.e., p + 1 and q + ≈ 0), respectively, which performed best on the task. For µ post and shortest, GNP approximated mean (i.e., p + ≈ 1 and q + ≈ 1) and min (i.e., p − 0 and q − ≈ 0), respectively, which were the best performing baseline for the tasks. To sum up, empirically, GNP imitated the ideal pooling functions for each task if such pooling functions exist. We also observed that either GNP + or GNP − tends to dominate the other side in all considered graph-level tasks. Detailed results are provided in Appendix C.6.
As we discussed in Section 3, GNP generalizes sum, max, mean, and min. In order to confirm the facts experimentally, we showed in Figure how the learnable parameters p and q in GNP changed during training. For maxdegree, GNP as aggregation and readout functions approximated sum (i.e., p + ≈ 1 and q + ≈ 0) and max (i.e., p + 1 and q + ≈ 0), respectively, which performed best on the task. For µ post and shortest, GNP approximated mean (i.e., p + ≈ 1 and q + ≈ 1) and min (i.e., p − 0 and q − ≈ 0), respectively, which were the best performing baseline for the tasks. To sum up, empirically, GNP imitated the ideal pooling functions for each task if such pooling functions exist. We also observed that either GNP + or GNP − tends to dominate the other side in all considered graph-level tasks. Detailed results are provided in Appendix C.6.
As we discussed in Section 3, GNP generalizes sum, max, mean, and min. In order to confirm the facts experimentally, we showed in Figure 2 how the learnable parameters p and q in GNP changed during training. For maxdegree, GNP as aggregation and readout functions approximated sum (i.e., p + ≈ 1 and q + ≈ 0) and max (i.e., p + _x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f_x005f 1 and q + ≈ 0), respectively, which performed best on the task. For µpost and shortest, GNP approximated mean (i.e., p + ≈ 1 and q + ≈ 1) and min (i.e., p − _x001d_ 0 and q − ≈ 0), respectively, which were the best performing baseline for the tasks. To sum up, empirically, GNP imitated the ideal pooling functions for each task if such pooling functions exist. We also observed that either GNP+ or GNP− tends to dominate the other side in all considered graph-level tasks. Detailed results are provided in Appendix C.6.****Figure 2: Empirical behavior of GNP. We showed how the parameters p and q of GNP changed during training. For each task, GNP imitated the ideal pooling functions if such pooling functions exist. For example, for maxdegree, GNP as aggregation and readout functions approximated sum (i.e., p + ≈ 1 and q + ≈ 0) and max (i.e., p +  1 and q + ≈ 0), respectively, which performed best.
Answer: We demonstrated the empirical behavior of the values of "p" learned by GNP in Section 4.5. For details, please refer to Figure 2 and Section 4.5 (in the revised paper).