A Novel Hyperdimensional Computing Framework for Online Time Series Forecasting on the Edge

TL;DR

This work reframes online time-series forecasting as task-free online hyperdimensional regression, mapping nonlinear inputs to a high-dimensional space via a trainable encoder and performing linear HD regression. It introduces co-training between the encoder and regressor and presents two frameworks, Autoregressive HD (AR-HDC) and Seq2Seq-HDC, with an autoregressive extension for long horizons. Across eight real-world datasets and synthetic shifts, TSF-HD delivers state-of-the-art accuracy with reduced latency, particularly on edge devices, demonstrating robust online adaptation without explicit drift detection. The approach promises practical, low-overhead forecasting on resource-constrained platforms and opens avenues for HD-based continual learning in streaming contexts.

Abstract

In recent years, both online and offline deep learning models have been developed for time series forecasting. However, offline deep forecasting models fail to adapt effectively to changes in time-series data, while online deep forecasting models are often expensive and have complex training procedures. In this paper, we reframe the online nonlinear time-series forecasting problem as one of linear hyperdimensional time-series forecasting. Nonlinear low-dimensional time-series data is mapped to high-dimensional (hyperdimensional) spaces for linear hyperdimensional prediction, allowing fast, efficient and lightweight online time-series forecasting. Our framework, TSF-HD, adapts to time-series distribution shifts using a novel co-training framework for its hyperdimensional mapping and its linear hyperdimensional predictor. TSF-HD is shown to outperform the state of the art, while having reduced inference latency, for both short-term and long-term time series forecasting. Our code is publicly available at http://github.com/tsfhd2024/tsf-hd.git

Figures (9)

• Figure 1: Distance preservation (linear relationship between distances) and orthogonality of the different components of the trainable encoder matrix $W_e$ across hyperdimensional mappings of input sequences $\mathbf{H}(x)=x.W_e$ (ETTm1 dataset), showing preservation of the properties detailed in mapping_cite_intro_rasanen.
• Figure 2: Autoregressive (AR-HDC) & Sequence-to-Sequence (Seq2Seq) frameworks for TSF-HD. Our novel co-training system jointly updates the encoder $\mathbf{H}(.)$ and regressor $\mathbf{R}(.)$ online.
• Figure 3: Evolution of the cumulative RSE during online learning with forecasting window $\tau=6$
• Figure 4: Visualization of the baseline and TSF-HD method performance as the tasks shift between four different autoregressive processes.
• Figure 5: Distance preservation across hyperdimensional mappings of input sequences $\mathbf{H}(x)$ for $\tau=6$