M$^2$FMoE: Multi-Resolution Multi-View Frequency Mixture-of-Experts for Extreme-Adaptive Time Series Forecasting

2026-01-13

AI Summary

This work addresses the challenge of forecasting extreme events in time series, which exhibit high variance, sparsity, and irregular dynamics that severely degrade the performance of existing methods. To this end, we propose a multi-resolution, multi-view frequency-domain modeling framework that enables adaptive prediction by jointly learning both regular and extreme patterns. Our key innovations include the first introduction of a frequency-domain mixture-of-experts (MoE) mechanism that integrates band decomposition in both Fourier and wavelet domains, along with a multi-resolution adaptive fusion module and a dynamic temporal gating ensemble designed to effectively capture rare extreme fluctuations and their underlying dominant dynamics. Notably, the method operates without requiring explicit labels for extreme events and achieves significant performance gains over state-of-the-art approaches on real-world hydrological datasets.

Technology Category

Machine Learning: Mixture of Experts (MoE)Computer Vision: Multi-modal VisionIntelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsWeb Mining and Content Analysis: Large pretrained models with web dataUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Forecasting time series with extreme events is critical yet challenging due to their high variance, irregular dynamics, and sparse but high-impact nature. While existing methods excel in modeling dominant regular patterns, their performance degrades significantly during extreme events, constituting the primary source of forecasting errors in real-world applications. Although some approaches incorporate auxiliary signals to improve performance, they still fail to capture extreme events'complex temporal dynamics. To address these limitations, we propose M$^2$FMoE, an extreme-adaptive forecasting model that learns both regular and extreme patterns through multi-resolution and multi-view frequency modeling. It comprises three modules: (1) a multi-view frequency mixture-of-experts module assigns experts to distinct spectral bands in Fourier and Wavelet domains, with cross-view shared band splitter aligning frequency partitions and enabling inter-expert collaboration to capture both dominant and rare fluctuations; (2) a multi-resolution adaptive fusion module that hierarchically aggregates frequency features from coarse to fine resolutions, enhancing sensitivity to both short-term variations and sudden changes; (3) a temporal gating integration module that dynamically balances long-term trends and short-term frequency-aware features, improving adaptability to both regular and extreme temporal patterns. Experiments on real-world hydrological datasets with extreme patterns demonstrate that M$^2$FMoE outperforms state-of-the-art baselines without requiring extreme-event labels.

Problem

• extreme events
• time series forecasting
• high variance
• irregular dynamics
• sparse high-impact events

Innovation

• Frequency Mixture-of-Experts
• Multi-Resolution Modeling
• Multi-View Spectral Analysis
• Extreme-Adaptive Forecasting
• Temporal Gating Integration