CoLaDe: Competitive Latent Compression and Lag-Aware Decoding for Time Series Forecasting

Multivariate time series forecasting relies on compact representations that preserve both temporal and inter-variable dependencies. Latent-bottleneck encoder–decoder models achieve this by compressing patch tokens from all variables into a small set of latent tokens and decoding future patches with learnable target queries. However, standard cross-attention does not regulate how latents allocate their attention across the input, which can lead to redundant compression. To address this limitation, this paper proposes Competitive Latent Compression and Lag-Aware Decoding (CoLaDe), which augments latent cross-attention with a signed competition term that reweights attention to tokens according to their relative preference across latents. The competition strength is learned per attention head, which allows latents either to specialize in distinct input regions or to share them. To retrieve historical information, a relative-lag prior explicitly models the temporal distance between each target query and observed patch. A lightweight low-rank correction then adapts this prior for each variable, accommodating heterogeneous temporal dependencies. Extensive evaluations on several real-world benchmark datasets show that CoLaDe achieves superior forecasting performance compared with state-of-the-art baselines.