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ScatterFusion: A Hierarchical Scattering Transform Framework for Enhanced Time Series Forecasting

Wei Li

TL;DR

ScatterFusion tackles multi-scale dependencies and non-stationarity in time series forecasting by integrating wavelet scattering with hierarchical attention. It introduces four components—HSTM, SAFE, MRTA, and TSR—that jointly produce invariant, scale-aware representations and enable efficient multi-resolution dependency modeling. Empirical results on seven benchmarks show ScatterFusion achieves lower MSE and MAE than strong baselines across short- and long-horizon forecasts. The work advances practical time-series forecasting by combining rigorous mathematical properties of scattering with adaptable attention mechanisms, with potential for transfer learning and improved handling of structural patterns in complex time series.

Abstract

Time series forecasting presents significant challenges due to the complex temporal dependencies at multiple time scales. This paper introduces ScatterFusion, a novel framework that synergistically integrates scattering transforms with hierarchical attention mechanisms for robust time series forecasting. Our approach comprises four key components: (1) a Hierarchical Scattering Transform Module (HSTM) that extracts multi-scale invariant features capturing both local and global patterns; (2) a Scale-Adaptive Feature Enhancement (SAFE) module that dynamically adjusts feature importance across different scales; (3) a Multi-Resolution Temporal Attention (MRTA) mechanism that learns dependencies at varying time horizons; and (4) a Trend-Seasonal-Residual (TSR) decomposition-guided structure-aware loss function. Extensive experiments on seven benchmark datasets demonstrate that ScatterFusion outperforms other common methods, achieving significant reductions in error metrics across various prediction horizons.

ScatterFusion: A Hierarchical Scattering Transform Framework for Enhanced Time Series Forecasting

TL;DR

ScatterFusion tackles multi-scale dependencies and non-stationarity in time series forecasting by integrating wavelet scattering with hierarchical attention. It introduces four components—HSTM, SAFE, MRTA, and TSR—that jointly produce invariant, scale-aware representations and enable efficient multi-resolution dependency modeling. Empirical results on seven benchmarks show ScatterFusion achieves lower MSE and MAE than strong baselines across short- and long-horizon forecasts. The work advances practical time-series forecasting by combining rigorous mathematical properties of scattering with adaptable attention mechanisms, with potential for transfer learning and improved handling of structural patterns in complex time series.

Abstract

Time series forecasting presents significant challenges due to the complex temporal dependencies at multiple time scales. This paper introduces ScatterFusion, a novel framework that synergistically integrates scattering transforms with hierarchical attention mechanisms for robust time series forecasting. Our approach comprises four key components: (1) a Hierarchical Scattering Transform Module (HSTM) that extracts multi-scale invariant features capturing both local and global patterns; (2) a Scale-Adaptive Feature Enhancement (SAFE) module that dynamically adjusts feature importance across different scales; (3) a Multi-Resolution Temporal Attention (MRTA) mechanism that learns dependencies at varying time horizons; and (4) a Trend-Seasonal-Residual (TSR) decomposition-guided structure-aware loss function. Extensive experiments on seven benchmark datasets demonstrate that ScatterFusion outperforms other common methods, achieving significant reductions in error metrics across various prediction horizons.
Paper Structure (14 sections, 2 theorems, 3 equations, 2 figures, 3 tables)

This paper contains 14 sections, 2 theorems, 3 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Problem Formulation and Framework Overview
  5. Theoretical Properties of Hierarchical Scattering Transform
  6. Hierarchical Scattering Transform Module (HSTM)
  7. Scale-Adaptive Feature Enhancement (SAFE)
  8. Multi-Resolution Temporal Attention (MRTA)
  9. Trend-Seasonal-Residual (TSR)
  10. Experiments
  11. Datasets and Experimental Setup
  12. Comparison with Other Methods
  13. Ablation Study and Computational Efficiency Analysis
  14. Conclusion

Key Result

Theorem 1

For the scattering transform $S$ of order $m$ with learnable wavelet filters $\{\psi_{j,\theta}\}$, there exists a constant $C$ such that:

Figures (2)

  • Figure 1: Overall architecture of the ScatterFusion framework. The model consists of an embedding layer, a Hierarchical Scattering Transform Module (HSTM), a Scale-Adaptive Feature Enhancement (SAFE) module, and a Multi-Resolution Temporal Attention (MRTA) mechanism. Each component is designed to address specific challenges in time series forecasting, such as capturing multi-scale patterns and modeling dependencies at varying time horizons.
  • Figure 2: Architecture of ScatterFusion modules: (a) Hierarchical Scattering Transform Module (HSTM) that extracts multi-scale invariant features from time series data; (b) Scale-Adaptive Feature Enhancement (SAFE) module that dynamically adjusts feature importance across different scales; (c) Multi-Resolution Temporal Attention (MRTA) mechanism that efficiently models dependencies at varying time horizons.

Theorems & Definitions (2)

  • Theorem 1: Deformation Stability
  • Theorem 2: Translation Invariance