All reviewers read the author response and engaged actively in the discussion. During the discussion, R2 and R3 defended their positive stance while R4 stayed negative. R2 praised the stopping mechanism as an important contribution of the paper, while R3 particularly liked the empirical validation and ablation experiments. R1 found the paper incremental, but novel. I acknowledge the concerns of R4 regarding better comparison to a wider spectrum of graph neural network approaches. Like R1, I also believe it would be more compelling to test on problems less related to the shortest path problem. That said, I agree with R1, R2 and R3 that this paper makes an interesting contribution and strongly encourage the authors to work towards incorporating the feedback of all reviewers but in particular R4 and R1. The AC also discussed this paper with the senior AC, and both agree that the paper has merits that warrant publication. I am therefore recommending acceptance of the paper.