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LogSig-SSM: Time-Series Modelling with Multi-Scale Log-Signature Compression for State-Space Models

NeurIPS 2026 · Time series › Long-term forecasting · approach: Lightweight long-term forecasters · 0 citations (OpenAlex)

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Proposes LogSig-SSM, which tokenises long irregular multivariate series with multi-scale windowed truncated log-signatures and feeds them to a selective Mamba-style SSM, reporting accuracy gains and large speed/memory savings over Mamba on UEA, PPG-DaLiA, weather, and PhysioNet Sepsis.

Problem

Long, irregularly sampled high-frequency multivariate time series are hard to model: continuous-time NCDE/NRDE models scale poorly, and diagonal selective SSMs like Mamba degrade on very long sequences and cannot mix cross-channel higher-order information within a block.

Approach

Compress the input sequence into a shorter token stream of multi-scale windowed truncated log-signatures (capturing cross-channel iterated integrals such as Lévy areas and invariant to monotone reparameterisation), then apply a diagonal selective SSM; the model admits an NRDE-style linear CDE interpretation with input-dependent time rescaling.

Key results

• On UEA, LogSig-SSM reaches 71.7% average accuracy, the best across the compared models, versus 58.6% for raw Mamba.
• On EigenWorms, LogSig-SSM trains 30x faster than Mamba (4 s vs 122 s per 1000 steps) using 37x less GPU memory (362 MB vs 13,486 MB).
• On PPG-DaLiA, LogSig-SSM achieves MSE 4.46e-2, versus 6.16e-2 for D-LinOSS and 10.65e-2 for Mamba.

Surprising findings

• Forcing log-signature depth one instead of two costs 2.3 points on average on UEA, with the largest losses on datasets with few channels.
• A search-free tokeniser rule based only on sequence length still reaches 64.0% average UEA accuracy, above S5, LRU and Mamba.

Limitations

• For single-channel paths, log-signature tokens reduce to increments and the cross-channel structure degenerates unless time is added as a channel.
• Token width grows as O(d_x^m / m), so tokenisation cost and input embedding size grow rapidly with channel count.
• Window lengths and stride are still selected per dataset via hyperparameter search.

Experimental setup

Datasets: UEA Archive (EigenWorms, SCP1, SCP2, EthanolConcentration, Heartbeat, MotorImagery) PPG-DaLiA weather forecasting benchmark PhysioNet 2019 Sepsis

Benchmarks: UEA PPG-DaLiA weather forecasting PhysioNet Sepsis

Metrics: accuracy MSE MAE AUROC GPU memory training time

Baselines: Mamba S5 LRU LinOSS-IM D-LinOSS PD-SSM NRDE Neural LSDE

Builds on: Mamba Neural Rough Differential Equations Log-NCDE LinOSS signature transform

Closest papers by meaning

• Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching (NeurIPS 2024 · similarity 0.86)
• SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings (ICLR 2025 · similarity 0.86)
• Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models (NeurIPS 2024 · similarity 0.86)
• Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs (NeurIPS 2026 · similarity 0.86)
• From Generalization Analysis to Optimization Designs for State Space Models (ICML 2024 · similarity 0.86)
• Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Series (ICLR 2025 · similarity 0.85)