How to remove the error edges on the material?

These are the final render for couple of material instances I made through a master material. I set up the pramaters for UV Tiling also. It came out like this and there are error edges showed up on the material. I thought it must be something to do with Texture coorndinate expression. So I went back to tweak the expression ~ set “Coordinate Index” to 0, UTiling and VTiling as 1. And it didn’t change anything. Not sure why and couldn’t find a solution online. Any suggestion or comment would be appreciated! Thank you so much!