发表机构
Washington State University; European Molecular Biology Laboratory（华盛顿州立大学; 欧洲分子生物学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
TopTimeNet通过固定拓扑特征提取与轻量分类器解耦，以极少的参数在非线性动力学基准上达到与更大模型相当的准确率，并揭示特征级与信号级鲁棒性的差异。
AI 中文摘要
区分时间序列中的周期性与混沌动力学是物理学和工程学中的一个基本挑战。然而，端到端学习的架构必须从数据中发现表示和决策边界，代价高昂。我们引入了TopTimeNet，它解耦了这些任务：一个固定的、非学习的阶段从Takens延迟嵌入和持续同调中提取42维几何和拓扑描述符，而一个轻量级可学习阶段执行分类。在包含49个非线性动力系统的基准测试中，一个具有1,638个参数的配置匹配了具有33倍可训练参数配置的平均准确率。此外，该方法提供的平均准确率可与卷积神经网络相媲美，并超过收敛的Transformer模型的平均性能，同时所需的可训练参数少三到四个数量级。鲁棒性也强烈依赖于噪声引入的位置：TopTimeNet在对其预计算特征的扰动下优雅地退化，但当噪声引入原始信号并重新计算整个特征提取流程时，其性能急剧下降，这表明对预计算特征扰动的鲁棒性并不意味着完整原始信号到预测流程的鲁棒性。这些结果表明，将固定的几何和拓扑特征构建与轻量级判别阶段解耦，可以在大幅减少可训练参数的情况下实现相当的分类准确率。
英文摘要
Distinguishing periodic from chaotic dynamics in a time series is a fundamental challenge in both physics and engineering. Yet, end-to-end learned architectures must discover both a representation and a decision boundary from data, at substantial cost. We introduce TopTimeNet, which decouples these tasks: a fixed, non-learned stage extracts a $42$-dimensional geometric and topological descriptor from Takens delay embeddings and persistent homology, and a lightweight learnable stage performs classification. On a benchmark of $49$ nonlinear dynamical systems, a $1{,}638$-parameter configuration matches the mean accuracy of one with $33\times$ more trainable parameters. Additionally, this approach delivers mean accuracy comparable to convolutional neural networks and surpasses the average performance of converged Transformer models, while requiring three to four orders of magnitude fewer trainable parameters. Robustness also depends sharply on where noise is introduced: TopTimeNet degrades gracefully under perturbations to its precomputed features, but degrades sharply when noise is introduced into the raw signal and the full feature-extraction pipeline is recomputed, showing that robustness to perturbations of the precomputed features does not imply robustness of the complete raw-signal-to-prediction pipeline. These results show that decoupling fixed geometric and topological feature construction from a lightweight discriminative stage can achieve comparable classification accuracy with substantially fewer trainable parameters.
Comments23 pages, 6+4 figures
