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STEP: Learning STructured Embeddings for Progressive Time Series

NeurIPS 2026 · Time series › Causal and generative time series · approach: Dynamical system reconstruction · 0 citations (OpenAlex)

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Proposes STEP, a self-supervised contrastive autoencoder that anchors progressive time-series latents to two orthogonal prototypes so polar coordinates (θ, r) act as an interpretable "latent compass" for progression and mode.

Problem

Learning interpretable, label-free representations of progressive time series (irreversible degradation or task completion) for RUL prediction, forecasting, and phase separation, where the latent state is unobserved and only time is a weak supervision signal.

Approach

Combine a cosine triplet loss, a prototype loss pulling start/end windows to fixed orthogonal basis vectors e1 and e2, and an MLP-decoder reconstruction term, so that polar angle θ = arctan2 of the prototype projections tracks progression and radius r tracks operating/failure mode.

Key results

• STEP with transformer head reaches 12.52 RMSE on FD002 at z=2 and 12.10 on FD004 at z=4, the best reported in the comparison table.
• A linear regressor on STEP latent compass coordinates (LR.STEP z=4) reaches 12.94 RMSE on FD002, competitive with deep baselines.
• Ablating the prototype loss raises FD004 RMSE from 12.10 to 19.01.

Surprising findings

• A simple linear regressor on the latent compass coordinates matches or beats several deep RUL models on FD002 and FD004.
• Removing the prototype loss barely changes homogeneous FD003 (13.35 to 11.59 RMSE, which is actually better without it).

Limitations

• Designed only for progressive (non-regressive) sequences; cannot handle reversible states such as post-maintenance reversion.
• Forecasting degrades on longer horizons relative to latent SDE baselines (SING-GP, VDP-GP).
• Prototype anchoring assumes identifiable trajectory extremes in training data.

Experimental setup

Datasets: C-MAPSS Can2Drawer (GR00T) LeRobot mouse brain activity recording

Benchmarks: C-MAPSS FD001-FD004 RUL RMSE mouse brain multi-step forecasting R2

Metrics: RMSE R2 silhouette score prognosability trendability monotonicity Spearman correlation KS statistic

Baselines: SoftCLT AE I-GLIDE SING-GP VDP-GP MS-DCNN RVE Prob. CNN MLE4X+CCF

Builds on: SoftCLT SimCLR BYOL LeJEPA

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