Rubato: Signature Attention for Irregular Multivariate Time Series Forecasting

Irregular multivariate time series (IMTS) are sampled at non-uniform timestamps and asynchronous across channels, their dependencies are shaped by time gaps, local ordering, and channel-specific sampling patterns. Building a faithful attention mechanism for IMTS exposes two limitations of existing work. First, current irregular-time attention methods typically regularize raw inputs into interpolated, aligned, or continuous-time-embedded forms before applying attention, which blurs exactly these irregular cues that determine how two observations relate. Second, beyond representation, standard dot-product attention scores pairs through learned token projections with no intrinsic tie to the shape of the underlying series, and an attention that does reflect this shape becomes costly to compute in high-channel IMTS. We propose Rubato, which reads two views directly from the raw irregular input: per-channel local dynamics, and a path signature that summarizes the joint multi-channel series. Attention in Rubato then scores pairs by a signature-kernel measure of series similarity rather than by a generic dot product, and a structured random projection (SORF) keeps this comparison affordable when the channel count is large. We prove that the structured projection introduces only a controlled bias that vanishes as the number of channels grows, and experiments on multiple IMTS benchmarks show that Rubato consistently outperforms strong baselines.