用拓扑方法量化模型对输入的不确定性，提升异常检测可靠性。
Uncertainty of Network Topology with Applications to Out-of-Distribution Detection
- 基于贝叶斯神经网络设计新型拓扑不确定性度量pTU
- pTU在多种架构下表现稳定，且能有效识别分布外样本
- 适用于需要高可靠性的安全敏感场景
持久同调（PH）是计算拓扑中的关键概念，为空间提供多尺度拓扑描述，尤其在拓扑数据分析中具有重要意义，旨在从拓扑视角进行统计推断。本文提出一种新的贝叶斯神经网络拓扑摘要——预测拓扑不确定性（pTU），用于衡量模型与输入之间交互的不确定性。pTU从模型角度提供洞察：若两个样本以相似方式与模型交互，则认为它们来自同一分布。我们还证明pTU对模型架构不敏感。作为应用，该方法被用于解决分布外（OOD）检测问题，这对保障模型可靠性至关重要。未检测到分布外输入可能导致错误且不可靠的预测。为此，我们基于pTU提出了一个显著性检验，构建了针对该问题的统计框架。通过多项实验验证了该框架在统计功效、灵敏度和鲁棒性方面的有效性。
原文摘要 · Abstract (English)
Persistent homology (PH) is a crucial concept in computational topology, providing a multiscale topological description of a space. It is particularly significant in topological data analysis, which aims to make statistical inference from a topological perspective. In this work, we introduce a new topological summary for Bayesian neural networks, termed the predictive topological uncertainty (pTU). The proposed pTU measures the uncertainty in the interaction between the model and the inputs. It provides insights from the model perspective: if two samples interact with a model in a similar way, then they are considered identically distributed. We also show that the pTU is insensitive to the model architecture. As an application, pTU is used to solve the out-of-distribution (OOD) detection problem, which is critical to ensure model reliability. Failure to detect OOD input can lead to incorrect and unreliable predictions. To address this issue, we propose a significance test for OOD based on the pTU, providing a statistical framework for this issue. The effectiveness of the framework is validated through various experiments, in terms of its statistical power, sensitivity, and robustness.
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