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 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 ultralow-dimensional frequency latent space through learnable rank-constrained filters. By reducing the parameter scale of a downsampled n-length input/output onelayer 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 existing models with significantly fewer parameters (0.1K), which makes it well-suited for deployment on devices with limited computational capacity. Recent research has started to process local and global components differently. One approach, found in models like DeepGate (Park et al., 2022) , decomposes the time series first. However, such a method *