Latent Dynamics · 2026-10-06
LogSig-SSM: Time-Series Modelling with Multi-Scale Log-Signature Compression for State-Space Models
Felix Oury, Nicolas Calvo Peiro, Reiko J. Tanaka
AI-assisted summary based on the paper. Consult the linked source for methods and limitations. Benchmark numbers appear after editor verification.
TL;DR
LogSig-SSM compresses long multivariate time series into shorter token sequences by computing multi-scale windowed log-signatures, then models long-range dependencies with a selective SSM backbone (Mamba-style). The authors give a continuous-time (NCDE/NRDE-style) interpretation where selectivity induces input-dependent rescaling of latent dynamics. They report faster training and lower GPU memory than Mamba on the longest sequences across four benchmarks.
Why it matters
The method targets long-horizon modeling with irregular, high-frequency sampling, where continuous-time models can be costly and SSMs may lose multivariate cross-channel mixing within a single selective-SM SSM block. By moving cross-channel path geometry into log-signature tokens and reducing the scan length, LogSig-SSM aims to combine accuracy with efficiency on long contexts.
Method
- Tokeniser: compress a multivariate time series into interval descriptors by computing truncated log-signature coordinate vectors on overlapping, strided windows at multiple scales; concatenate across scales to form a token stream.
- Backbone: process tokens with a selective SSM (Mamba block) whose discretisation step and projections are input-dependent, yielding input-dependent selectivity over the reduced sequence.
- Continuous-time view: interpret the selective SSM as a linear CDE/NRDE-style system driven by log-signature-derived controls, where selectivity corresponds to adaptive internal time rescaling.
Abstract (from arXiv)
Time-series data are often sampled irregularly at high frequencies and exhibit long-range dependencies, which makes long-horizon modelling difficult. 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 they provide limited recurrent mixing across hidden dimensions 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. LogSig-SSM is scalable and robust to irregular sampling, combining log-signature tokens that capture higher-order cross-channel interactions with a selective SSM that models long-range dependencies. The model also admits a continuous-time interpretation as an NCDE/NRDE-style system driven by a log-signature-based input, in which selectivity induces an input-dependent rescaling of the latent dynamics. Across four benchmarks, namely long-sequence classification on UEA, high-frequency physiological regression on PPG-DaLiA, multivariate weather forecasting, and irregularly sampled clinical prediction on PhysioNet Sepsis, LogSig-SSM outperforms or matches strong SSM and continuous-time baselines while training up to $30\times$ faster and using up to $37\times$ less GPU memory than Mamba on the longest sequences.
Related papers
- Correct then Forecast: Observer State-Space Models for Time Series Forecasting
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- CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting
Publication record
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First public release: 2026-10-04 · Indexed by Pub-AI: 2026-10-06 UTC
LogSig-SSM: Time-Series Modelling with Multi-Scale Log-Signature Compression for State-Space Models
Preprint posted: 2026-10-04 · Original record ↗
- arxiv
- 2610.05051
Explicit source versions (1)
- v1 · 2026-10-04
- Preprint available
Source date: 2026-10-04 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
Abstract · arxiv
Time-series data are often sampled irregularly at high frequencies and exhibit long-range dependencies, which makes long-horizon modelling difficult. 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 they provide limited recurrent mixing across hidden dimensions 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. LogSig-SSM is scalable and robust to irregular sampling, combining log-signature tokens that capture higher-order cross-channel interactions with a selective SSM that models long-range dependencies. The model also admits a continuous-time interpretation as an NCDE/NRDE-style system driven by a log-signature-based input, in which selectivity induces an input-dependent rescaling of the latent dynamics. Across four benchmarks, namely long-sequence classification on UEA, high-frequency physiological regression on PPG-DaLiA, multivariate weather forecasting, and irregularly sampled clinical prediction on PhysioNet Sepsis, LogSig-SSM outperforms or matches strong SSM and continuous-time baselines while training up to $30\times$ faster and using up to $37\times$ less GPU memory than Mamba on the longest sequences.