Next‑token probability distributions across disparate LLM families converge on an almost identical Fisher‑Rao metric. That convergence lets us apply a single low‑disturbance intervention to steer any transformer, state‑space or recurrent model safely.
Prior to this work, many existing control methods have employed Euclidean parameter updates; this paper introduces a Fisher‑Rao‑based alternative. The paper observes that activation geometry differs from output geometry and emphasizes that the latter provides a link to model behavior and controllability. Consequently, safe steering remained an ad‑hoc engineering problem rather than a principled one.
Applying the same correction improves steering, knowledge editing, feature attribution, dictionary learning and fine‑tuning, with up to two orders of magnitude less off‑target change [1]. The paper shows that this gain follows from a shared Fisher‑Rao geometry: output geometries of transformer, state‑space and recurrent networks align far more closely than their activation geometries, enabling a universal metric for minimum‑disturbance updates.
Estimating the Fisher‑Rao metric can involve extensive gradient calculations, potentially increasing computational cost for very large or multimodal models. The reported experiments cover several model families; further research is needed to evaluate scalability to trillion‑parameter vision–language systems.
If the geometric correction proves broadly effective, it could serve as a new baseline for future safe‑control benchmarks.
Will future LLM toolkits bake Fisher‑Rao‑driven controllers into every release?
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