The Least Action Nature of AdvJudge-Zero: A Lagrangian Perspective on LLM Steering
In December 2025, Tony, Yuhao, and I have published AdvJudge-Zero: Binary Decision Flips in LLM-as-a-Judge via Adversarial Control Tokens https://arxiv.org/abs/2512.17375 . This post serves to clarify the underlying mathematical mechanics of our method, stripping away heuristic explanations to focus purely on Lagrangian optimization and the Principle of Least Action in discrete sequence generation.