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.
>There's no reason to visit a doctor for the common cold.
That's such an american thing to say. A flu can be swine flu and fever can be Malaria or Dangue and one day delay can mean losing your life, so people in many parts of the world take fever and flu seriously.
Yes, it is very normal in an unstructured life, many very smart graduate students at the top universities struggle with it. It is the curse of freedom. People don't realize a regular 9-5 job gives them routine, social commitments and a visible positive feedback on a good job done in a timely manner, and a negative feedback otherwise (both positive and negative social feedback are stronger than self-awarded rewards and punishments).
Full paper https://arxiv.org/html/2603.13552v1