A theoretical bound on telling two language models apart, token by token

Two language models can produce nearly indistinguishable output on a short prompt while their internal dynamics are very different. A new arXiv preprint turns that observation into a theorem with a named rate.

The paper, Guarantees on Dynamical System Distinguishability for LLM Token Generation, recasts the problem of classifying a model's output as a binary hypothesis test between two stochastic linear dynamical systems. Each model's token stream is treated as a trajectory of a black-box DS, with the embedding of each token, the numerical shadow a model casts on that token, as the state. The authors then ask: how much output do you need before the trajectories separate?

Two results anchor the bound. First, the total variation distance between the stationary marginal distributions of the two systems can be arbitrarily small even when the dynamics differ, which sets a hard floor for any classifier that ignores token order. Second, the misclassification probability decays exponentially in the sequence length L, at a rate governed by a "dynamical discriminability" quantity δ², a spectral distance between the two systems.

A third result bounds cross-embedding generalization, but only under an "intertwining" condition the authors do not claim holds universally. The preprint has no conference acceptance and no demonstrated practical application, so the contribution is a theoretical floor for a specific two-model test, not a general AI-content detector.