用拓扑特征生成稀有时间序列，提升极端事件建模效果
PHINN: Persistent Homology Inspired Neural Network for Rare-Event Time Series Generation
- 以贝蒂数变化为条件，构建流匹配生成框架
- 在金融与流行病数据上，拓扑误差降41%-63%，事件检测准确率提84%
- 支持少样本生成与跨领域迁移，适合高风险场景建模
时间序列中的稀有事件至关重要却因数据稀缺难以建模。现有生成模型对极端值表现不佳。我们发现稀有事件会在点云嵌入中留下独特的拓扑指纹——贝蒂数的动态变化，其稳定性与判别性优于统计矩。提出PHINN，一种基于动态贝蒂曲线作为条件信号、结合持久性景观损失以保证同调一致性的流匹配框架。该方法可扩展至多变量数据，支持自然语言设定贝蒂目标、跨域元学习与少样本生成，并提供认证的对抗鲁棒性。在金融、流行病及多模态基准上，PHINN在拓扑保真度上优于统计与扩散基线（贝蒂-均方根误差降低41%-63%，过渡准确率提升84%），尾部覆盖能力媲美跳跃扩散模型，且形状保真度更优。所有结果均在95%置信区间内。
原文摘要 · Abstract (English)
Rare events in time series are critical to model but hard to learn due to data scarcity. Current generative models struggle with extreme values. We observe that rare events leave distinct topological fingerprints - transitions in Betti numbers from point-cloud embeddings - that are more stable and discriminative than statistical moments. We introduce PHINN, a flow-matching framework using dynamic Betti curves as conditioning signals and a persistence landscape loss for homology consistency. It scales to multivariate data, includes a natural-language interface to set Betti targets, supports cross-domain meta-learning and few-shot generation, and provides certified adversarial robustness. On financial, epidemiological, and multi-modal benchmarks, PHINN outperforms statistical and diffusion baselines in topological fidelity (beta-RMSE down 41-63%, transition accuracy up 84%) and matches jump-diffusion models in tail coverage while exceeding them in shape fidelity. All results have 95% confidence intervals.
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