Author here. The short version: softmax's partition function has complex zeros — from e^{iπ}+1=0 — that are invisible on the real line but cap safe step sizes at ρₐ = π/Δₐ. One JVP to compute. The repo has Colab notebooks if you want to poke at it. Happy to answer questions.
Nice work! The paper feels verbose at times and could use some editing to slim it down (also, equation 6 is just equation 5 in a box) but I enjoyed it a lot nonetheless.
Full paper https://arxiv.org/html/2603.13552v1