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SDSC:A Structure-Aware Metric for Semantic Signal Representation Learning

Jeyoung Lee, Hochul Kang

TL;DR

The paper introduces the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric for time-series self-supervised representation learning that emphasizes local waveform structure through signed-amplitude overlap and area-based intersections. SDSC is bounded in $[0,1]$ and can be used as a loss via a differentiable Heaviside approximation, with a differentiable surrogate $\hat{H}(x)=\frac{1}{1+e^{-\alpha x}}$, and a hybrid objective $\mathcal{L}_{\text{hybrid}}=\lambda_{\text{sdsc}}\mathcal{L}_{\text{sdsc}}+\lambda_{\text{mse}}\mathcal{L}_{\mathrm{MSE}}$ to balance structure and amplitude. Evaluations on forecasting and classification tasks show SDSC-based pre-training yields comparable or improved downstream performance relative to MSE, particularly in in-domain and low-resource settings, and the hybrid loss provides robust performance across varied regimes. The study highlights the value of structure-aware reconstruction objectives and positions SDSC as a scalable alternative to traditional distance-based losses in time-series SSL.

Abstract

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

SDSC:A Structure-Aware Metric for Semantic Signal Representation Learning

TL;DR

The paper introduces the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric for time-series self-supervised representation learning that emphasizes local waveform structure through signed-amplitude overlap and area-based intersections. SDSC is bounded in and can be used as a loss via a differentiable Heaviside approximation, with a differentiable surrogate , and a hybrid objective to balance structure and amplitude. Evaluations on forecasting and classification tasks show SDSC-based pre-training yields comparable or improved downstream performance relative to MSE, particularly in in-domain and low-resource settings, and the hybrid loss provides robust performance across varied regimes. The study highlights the value of structure-aware reconstruction objectives and positions SDSC as a scalable alternative to traditional distance-based losses in time-series SSL.

Abstract

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

Paper Structure

This paper contains 36 sections, 1 theorem, 13 equations, 3 figures, 24 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Evaluation Metrics
  4. Time-series Modeling
  5. Signal Dice Similarity Coefficient
  6. Distance-based Metrics
  7. Definition of SDSC
  8. Hybrid Loss Integration
  9. Experiments
  10. Pre-training
  11. Forecasting
  12. Classification
  13. Conclusions
  14. Appendix
  15. Reproducibility Statement
  16. ...and 21 more sections

Key Result

Lemma 2.1

For any two discrete signals $E = \{E(s)\}_{s \in S}$ and $R = \{R(s)\}_{s \in S}$, the Signal Dice Similarity Coefficient, $\text{SDSC}(E, R)$, is bounded such that $0 \le \text{SDSC} \le 1$.

Figures (3)

  • Figure 1: Examples demonstrating the limitations of distance-based metrics in capturing structural similarity. SDSC offers a more faithful assessment in (a) phase-shifted signals, (b) scale-induced distortions, (c) structurally dissimilar but MSE-equivalent signals, and (d) noisy outputs with underestimated errors.
  • Figure 2: Example of intersection between two signals and discrete approximation.
  • Figure 3: Analysis of structural alignment in MSE-based pre-training. (a) The weak negative correlation between MSE and SDSC suggests limited alignment. (b, c) At a fixed MSE of $1.5\pm\epsilon$, the SDSC-based model achieves a distribution with higher structural scores.

Theorems & Definitions (2)

  • Lemma 2.1: Boundedness of SDSC
  • proof