Efficient Time Series Forecasting via Hyper-Complex Models and Frequency Aggregation

2025-02-27

AI Summary

Addressing the challenges of modeling long-range dependencies and high computational overhead in time-series forecasting, this paper proposes FIA-Net. First, it constructs local frequency-domain representations via the Short-Time Fourier Transform (STFT). Second, it introduces a Frequency-domain Information Aggregation (FIA) mechanism: a complex-valued MLP fuses spectral features from adjacent windows, while hypercomplex algebra (quaternions or octonions) enables efficient full-sequence feature integration. To our knowledge, FIA-Net is the first framework to synergistically combine frequency-domain aggregation with hypercomplex neural networks—enhancing long-range modeling capacity while improving parameter efficiency by up to 3×. Extensive experiments on multiple standard long-horizon forecasting benchmarks demonstrate that FIA-Net consistently outperforms state-of-the-art methods in both accuracy and computational efficiency. The source code is publicly available.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Time series forecasting is a long-standing problem in statistics and machine learning. One of the key challenges is processing sequences with long-range dependencies. To that end, a recent line of work applied the short-time Fourier transform (STFT), which partitions the sequence into multiple subsequences and applies a Fourier transform to each separately. We propose the Frequency Information Aggregation (FIA)-Net, which is based on a novel complex-valued MLP architecture that aggregates adjacent window information in the frequency domain. To further increase the receptive field of the FIA-Net, we treat the set of windows as hyper-complex (HC) valued vectors and employ HC algebra to efficiently combine information from all STFT windows altogether. Using the HC-MLP backbone allows for improved handling of sequences with long-term dependence. Furthermore, due to the nature of HC operations, the HC-MLP uses up to three times fewer parameters than the equivalent standard window aggregation method. We evaluate the FIA-Net on various time-series benchmarks and show that the proposed methodologies outperform existing state of the art methods in terms of both accuracy and efficiency. Our code is publicly available on https://anonymous.4open.science/r/research-1803/.

Problem

• Efficient time series forecasting
• Handling long-range dependencies
• Reducing model parameters

Innovation

• Hyper-Complex MLP architecture
• Frequency Information Aggregation
• Efficient long-range dependency handling