I am a software development engineer at AMD, and we are currently in the process of implementing support for the ROCm/HIP in the Eigen codebase. This support will be analogous to what is currently present for CUDA.
At this point we are ready to submit an initial PR so that you can have a chance to review the changes we have made so far. I do not know what is the process that we need to follow here, and hence filing this bug.
Please let me know if we can proceed with the PR or if there is something more that needs to be done before that.
Making a PR sounds like a good idea, if you have some working/reviewable changes. If you are more at a proof-of-concept phase, I'd suggest just publishing a URL to a fork.
Both preferably also on the public mailing list, because barely anyone is following the bug-tracker.
How much changes is it?
If it mostly requires re-defining EIGEN_DEVICE, I see no reason to block this.