STEP: Learning STructured Embeddings for Progressive Time Series

2026-05-29

AI Summary

This work addresses time series characterized by irreversible state evolution—such as equipment degradation, task completion, or neural dynamics—and proposes a novel “latent compass” representation. By leveraging self-supervised contrastive learning, the method constructs a structured latent space in which each time series is mapped onto a manifold trajectory between two orthogonal prototype vectors. State progression and operational mode are disentangled via polar coordinates (θ, r), enabling transparent and interpretable modeling without requiring labeled data. Evaluated on industrial degradation, robotic tasks, and neural activity datasets, the approach achieves performance on par with or superior to black-box deep models in endpoint prediction, multi-step forecasting, and phase separation tasks—even when paired with simple linear regression—while substantially enhancing model interpretability and computational efficiency.

Abstract

We present a novel method for learning interpretable representations of progressive time series, that is, data capturing irreversible state transitions such as degradation or task completion. Our approach uses a self-supervised contrastive objective to learn a low-dimensional latent space whose geometry is itself the interpretation: each observation becomes a point on a manifold anchored between two fixed orthogonal prototype vectors, and a trajectory becomes a path across that manifold. From this structure we read a latent compass, the polar coordinates (θ, r) of the latent vector, in which θ tracks the progression of the underlying state (e.g., from healthy to failed) and r identifies the active mode (e.g., the operating condition), without any proxy labels. We evaluate the approach against the state of the art on diverse domains, including industrial degradation, robotic tasks, and neural activity, validating three key capabilities: (1) end-state prediction, (2) multi-step forecasting, and (3) interpretable phase separation. Our method matches or improves over black-box counterparts on all of these while providing transparency about the underlying mechanisms. A simple linear regressor on top of the latent compass coordinates is competitive with deep architectures, direct quantitative evidence that the underlying state is encoded in a geometrically accessible form.

Problem

• progressive time series
• interpretable representations
• irreversible state transitions
• latent geometry
• self-supervised learning

Innovation

• structured embeddings
• progressive time series
• self-supervised contrastive learning
• latent compass
• interpretable representation