aiqbench analysis
TopTimeNet addresses the computational cost of end-to-end learning in time-series analysis by decoupling feature extraction from classification. By leveraging fixed topological descriptors derived from Takens delay embeddings, the model achieves accuracy comparable to large Convolutional Neural Networks and Transformers with significantly fewer trainable parameters. This approach offers a more efficient alternative for distinguishing periodic from chaotic dynamics in nonlinear systems without relying on massive parameter counts.
TopTimeNet: Topologically-assisted time-series classification model
arXiv:2609.39792v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Computational Geometry (cs.CG); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD); Applied Physics (physics.app-ph)
arXiv:2609.39792 [cs.LG]
(or arXiv:2609.39792v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.39792 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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