LogSig-SSM: Efficient Time-Series Modelling with Multi-Scale Log-Signature Compression for SSMs

Time-series data are often sampled irregularly at high frequencies and exhibit long-range dependencies, which makes long-horizon modelling expensive in both time and memory. Continuous-time models such as neural controlled differential equations (NCDEs) and neural rough differential equations (NRDEs) can handle irregular sampling, but they scale poorly to long sequences. Selective state-space models (SSMs) such as Mamba scale linearly with sequence length, but provide limited cross-channel mixing within a single block. We propose LogSig-SSM (Log-Signature Compression for State-Space Models), which first compresses long multivariate time series into a shorter sequence of tokens using multi-scale windowed log-signatures, and then processes these tokens with a selective SSM backbone. These tokens capture higher-order cross-channel interactions that a single diagonal SSM block cannot represent, and are invariant to time reparameterisation within each window. They are computed once, offline, at a cost of roughly 1\% of a training run, and the shortened sequence divides the cost of the recurrent scan by the compression factor. Across long-sequence classification (UEA), high-frequency physiological regression (PPG-DaLiA), multivariate weather forecasting and irregularly sampled clinical prediction (PhysioNet Sepsis), LogSig-SSM matches or exceeds strong SSM and continuous-time baselines, leading on average on three of the four, while training up to $30\times$ faster and using up to $37\times$ less GPU memory than Mamba on the longest sequences.