MixLinear: Extreme Low Resource Multivariate Time Series Forecasting with $0.1K$ Parameters

Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. Significant challenges exist in LTSF due to its complex temporal dependencies and high computational demands. Although Transformer-based models offer high forecasting accuracy, they are often too compute-intensive to be deployed on devices with hardware constraints. In this paper, we propose MixLinear, which synergistically combines orthogonal segment-based trend extraction in the time domain with adaptive low-rank spectral filtering in the frequency domain. Our approach exploits the complementary structural sparsity of time series: local temporal patterns are efficiently captured through mathematically linear transformations that separate intra-segment and inter-segment correlations, while global trends are compressed into an ultra-low-dimensional frequency latent space through learnable rank-constrained filters. By reducing the parameter scale of a downsampled $n$-length input/output one-layer linear model from $O(n^2)$ to $O(n)$, MixLinear achieves efficient computation without sacrificing accuracy. Extensive evaluations show that MixLinear achieves forecasting performance comparable to, or surpasses, state-of-the-art models with significantly fewer parameters ($0.1K$), which makes it well suited for deployment on devices with limited computational capacity.