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arxiv arXiv cs.LG · 8h ago

Time Series Classification through Diffeomorphic Time Warping (DiffTW)

The article introduces Diffeomorphic Time Warping (DiffTW), a theoretical framework for time series classification that learns mappings between real-valued functions to overcome the discrete point matching limitations of Dynamic Time Warping (DTW). DiffTW approximates diffeomorphic transformations using the method of characteristics to solve linear transport equations, providing a theoretically grounded dissimilarity measure.

arxiv arXiv cs.LG · 8h ago

Sublinearly Structured Deep Neural Networks Achieve Feature Learning Consistency for Compositional Functions

This study establishes feature-learning consistency guarantees for a broad subclass of deep neural networks characterized by sublinear growth in input/output dimensions and hidden neurons relative to sample size. The authors prove that these architectures achieve universal approximation for hierarchically compositional functions, even within the conventional over-parameterized regime where parameters exceed training samples.