Okay I think I figured something out. If we compose the natural log function in the sigmoid function we get the symmetric property I talked about in Symmetric Rebase Upgrade Proposal, we can “scale” x to balance out expansion and contraction. I modified the code in @aalavandhan1894 notebook to illustrate this:
Google Colab
I think with this we may get the best of both worlds… no longer skewing rebases to faster expansions followed by slower contractions, but also giving us the tools to elegantly cap each side and tune the shape
Edit: Cross-posting from the Symmetric Rebase post, @Togenkyo made a nice visualization of all the rebase functions we’ve been evaluating. Symmetric Rebase Upgrade Proposal - #8 by Togenkyo