arXiv:2510.10465v1 Announce Type: cross Abstract: Modern Internet of Things (IoT) systems generate massive, heterogeneous multivariate time series data. Accurate Multivariate Time Series Forecasting (MTSF) of such data is critical for numerous applications. However, existing methods almost universally employ a shared embedding layer that processes all channels identically, creating a representational bottleneck that obscures valuable channel-specific information. To address this challenge, we introduce a Shared-Auxiliary Embedding (SAE) framework that decomposes the embedding into a shared base component capturing common patterns and channel-specific auxiliary components modeling unique deviations. Within this decomposition, we \rev{empirically observe} that the auxiliary components tend to exhibit low-rank and clustering characteristics, a structural pattern that is significantly less apparent when using purely independent embeddings. Consequently, we design LightSAE, a parameter-efficient embedding module that operationalizes these observed characteristics through low-rank factorization and a shared, gated component pool. Extensive experiments across 9 IoT-related datasets and 4 backbone architectures demonstrate LightSAE's effectiveness, achieving MSE improvements of up to 22.8\% with only 4.0\% parameter increase.