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Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs

NeurIPS 2026 · Time series › Causal and generative time series · approach: Irregular series and imputation · 0 citations (OpenAlex)

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Proves that continuous injective (faithful) embeddings transfer compact-set universality from model input space to data space, and uses this to build an interpolation-free, online log-signature embedding of irregular asynchronous observations for Log-NCDEs.

Problem

How to embed discrete, irregular, asynchronous observations into continuous time for NCDE/Log-NCDE models without reconstructing (interpolating or imputing) unobserved behaviour between measurements.

Approach

Replace interpolation with a faithful (continuous, injective) embedding that records observations as increments with observation-count coordinates and composes event and gap tensor factors over arbitrary query intervals; a universality-transfer lemma guarantees compact-set universality is preserved from the model input space to the data space.

Key results

• Log-ODE with a SLiCE raises EigenWorms test accuracy by 11.1 points over standard NCDE (85.6 to 86.1 for BD-SLiCE vs 75.0 NCDE) while cutting time per training step by almost 3,000x (26.02 s to 0.009 s for BD-SLiCE).
• BD-SLiCE reaches 64.0% average accuracy with no dropping and 62.5% at 95% input dropping on six UEA datasets, with the best average rank at most dropping levels.
• Log-NCDE gives the best macro-average accuracy at no drop (64.3%), 30% drop (64.2%) and 70% drop (62.7%).

Surprising findings

• A model trained on synchronous regular sinusoidal data generalises poorly to asynchronous sparse data, suggesting it learns shortcuts from regular sampling.
• Including second-level Levy area information lowers MSE on the Brownian controlled system, with the gap shrinking as the number of query intervals grows.

Limitations

• Universality is a compact-set approximation result and does not give sample efficiency or optimisation guarantees.
• Dropping count coordinates identifies streams differing only by value-preserving observations; dropping time identifies streams with different event timings.

Experimental setup

Datasets: EigenWorms UEA multivariate time-series archive (six datasets) synthetic sinusoidal coupled system synthetic Brownian controlled linear system

Benchmarks: EigenWorms six UEA classification datasets with input dropping (30%, 70%, 95%) synthetic sinusoidal coupled data across sampling regimes Brownian controlled linear system MSE

Metrics: test accuracy average rank time per training step GPU memory MSE

Baselines: S5 LRU S6 Mamba NCDE Log-NCDE D-SLiCE BD-SLiCE

Builds on: Neural controlled differential equations Log-ODE method Structured Linear CDEs (SLiCEs) rectilinear control path signature universality

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