# Guarantees on Dynamical System Distinguishability for LLM Token Generation

arXiv: https://arxiv.org/abs/2607.28667 · HTML: https://mlsanity.com/paper/2607.28667/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 25 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [SAC3: Reliable Hallucination Detection in Black-Box Language Models via Semantic-aware Cross-check Consistency](https://mlsanity.com/paper/2311.01740/) (2023)
- [Low-Cost Black-Box Detection of LLM Hallucinations via Dynamical System Prediction](https://mlsanity.com/paper/2605.05134/) (2026)
- [Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees](https://mlsanity.com/paper/2311.18769/) (2023)

## Built on by (most cited first, 1 of 1)

- [Enforcing LLM Safety through DMD-based Classification of Prompt-Response Embedding Dynamics](https://mlsanity.com/paper/2608.19579/) (2026)

## Abstract (arXiv)

Recent work has shown that classifying large language models (LLMs)' responses can be distinguished by modeling token embeddings as trajectories of a black-box dynamical system (DS) and comparing prediction residuals of two DSs. Despite the empirical success of this dynamical approach, a theoretical understanding of why it works, how well it scales as a function of the token sequence, and when it transfers across embedding models remains lacking. We address these questions by formalizing the classification task as a binary hypothesis test between two stochastic linear DSs. We show that the total variation distance between the stationary marginal distributions of the two DSs can be arbitrarily small even when the dynamics differ substantially, which provides a fundamental accuracy floor for any classifier that ignores token dynamics. We then show that the misclassification probability of DS-based classification decays exponentially in the sequence length L, with the decay governed by a dynamical discriminability quantity δ2 that captures the spectral distance between the two DSs. We also characterize cross-embedding generalization by introducing an approximate intertwining condition between embedding models and establishing a lower bound on the transferable discriminability in terms of the intertwining map's smallest singular value. Together, these results explain the empirical performance of DS-based classification and motivate further investigation into using DS theory to analyze AI systems, in contrast to the more common approach of using AI to model dynamical systems.