Title: SDSC:A Structure-Aware Metric for Semantic Signal Representation Learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: self-supervised learning, representation learning, time series, structure-aware metric, Signal Dice Similarity Coefficient (SDSC)

Abstract: We propose the Signal Dice Similarity Coefficient (SDSC), a novel structure-aware metric for time series self-supervised representation learning. Most existing methods rely on distance-based objectives such as mean squared error, which are sensitive to amplitude, often under-penalize waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. The SDSC quantifies structural agreement between temporal signals based on signed amplitude intersections, extending the Dice Similarity Coefficient from segmentation to continuous signals. Although originally defined as a metric, SDSC can also be used as a loss by subtracting from 1 and applying a differentiable Heaviside approximation. A hybrid loss that combines SDSC with MSE further improves stability and preserves amplitude when necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance relative to MSE, particularly in in-domain and low-resource scenarios. These results suggest that enforcing structural fidelity enhances semantic representation quality and motivates the reconsideration of structure-aware objectives as alternatives to conventional distance-based losses.

TL;DR: We identify limitations of MSE for time-series SSL and introduce SDSC, a structure-sensitive metric that captures signal semantics.