# Decision Potential Surface: A Theoretical and Practical Approximation of Large Language Model Decision Boundary

arXiv: https://arxiv.org/abs/2510.03271 · HTML: https://mlsanity.com/paper/2510.03271/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 15 of 15)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [BadNets: Identifying Vulnerabilities in the Machine Learning Model Supply Chain](https://mlsanity.com/paper/1708.06733/) (2017)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Camels in a Changing Climate: Enhancing LM Adaptation with Tulu 2](https://mlsanity.com/paper/2311.10702/) (2023)
- [Characterizing the Decision Boundary of Deep Neural Networks](https://mlsanity.com/paper/1912.11460/) (2019)
- [Understanding the Decision Boundary of Deep Neural Networks: An Empirical Study](https://mlsanity.com/paper/2002.01810/) (2020)
- [LLMs Don't Know Their Own Decision Boundaries: The Unreliability of Self-Generated Counterfactual Explanations](https://mlsanity.com/paper/2509.09396/) (2025)
- [On the Decision Boundary of Deep Neural Networks](https://mlsanity.com/paper/1808.05385/) (2018)
- [BARREL: Boundary-Aware Reasoning for Factual and Reliable LRMs](https://mlsanity.com/paper/2505.13529/) (2025)
- [Does Low Rank Adaptation Lead to Lower Robustness against Training-Time Attacks?](https://mlsanity.com/paper/2505.12871/) (2025)
- [Investigating Decision Boundaries of Trained Neural Networks](https://mlsanity.com/paper/1908.02802/) (2019)

## Abstract (arXiv)

Decision boundary, the subspace of inputs where a machine learning model assigns equal classification probabilities to two classes, is pivotal in revealing core model properties and interpreting behaviors. While analyzing the decision boundary of large language models (LLMs) has attracted increasing attention recently, constructing it for mainstream LLMs remains computationally infeasible due to the enormous sequence-level output spaces and the autoregressive nature of LLMs. To address this issue, in this paper we propose Decision Potential Surface (DPS), a new notion for analyzing the properties of LLM decisions. DPS is derived from the confidence in distinguishing different classes for each input, which naturally captures the potential of the decision boundary. We prove that the zero-height isohypse in DPS is equivalent to the decision boundary of an LLM, with enclosed regions representing decision regions. By leveraging DPS, for the first time in the literature, we propose a practical decision boundary approximation algorithm, namely K-DPS, which only requires only K finite sequence samples to approximate an LLM's decision boundary with negligible error. We theoretically derive the upper bounds for the absolute error, expected error, and the error concentration between K-DPS and the ideal DPS, demonstrating that such errors can be traded off against sampling times.