# STEP: Learning STructured Embeddings for Progressive Time Series

arXiv: https://arxiv.org/abs/2605.31061 · HTML: https://mlsanity.com/paper/2605.31061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 23 of 23)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Time-Series Representation Learning via Temporal and Contextual Contrasting](https://mlsanity.com/paper/2106.14112/) (2021)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency](https://mlsanity.com/paper/2206.08496/) (2022)
- [LIV: Language-Image Representations and Rewards for Robotic Control](https://mlsanity.com/paper/2306.00958/) (2023)
- [Potential, Challenges and Future Directions for Deep Learning in Prognostics and Health Management Applications](https://mlsanity.com/paper/2005.02144/) (2020)
- [Deep Speaker: an End-to-End Neural Speaker Embedding System](https://mlsanity.com/paper/1705.02304/) (2017)
- [TimesURL: Self-supervised Contrastive Learning for Universal Time Series Representation Learning](https://mlsanity.com/paper/2312.15709/) (2023)
- [Soft Contrastive Learning for Time Series](https://mlsanity.com/paper/2312.16424/) (2023)
- [SARM: Stage-Aware Reward Modeling for Long Horizon Robot Manipulation](https://mlsanity.com/paper/2509.25358/) (2025)
- [Temporal Straightening for Latent Planning](https://mlsanity.com/paper/2603.12231/) (2026)
- [Learning Local Image Descriptors with Deep Siamese and Triplet Convolutional Networks by Minimising Global Loss Functions](https://mlsanity.com/paper/1512.09272/) (2015)
- [Self-Supervised Contrastive Learning for Long-term Forecasting](https://mlsanity.com/paper/2402.02023/) (2024)
- [Degradation Modeling and Prognostic Analysis Under Unknown Failure Modes](https://mlsanity.com/paper/2402.19294/) (2024)
- [SING: SDE Inference via Natural Gradients](https://mlsanity.com/paper/2506.17796/) (2025)
- [Learning Informative Health Indicators Through Unsupervised Contrastive Learning](https://mlsanity.com/paper/2208.13288/) (2022)
- [Semi-Supervised End-To-End Contrastive Learning For Time Series Classification](https://mlsanity.com/paper/2310.08848/) (2023)
- [I-GLIDE: Input Groups for Latent Health Indicators in Degradation Estimation](https://mlsanity.com/paper/2511.21208/) (2025)
- [A Machine Learning Framework for Turbofan Health Estimation via Inverse Problem Formulation](https://mlsanity.com/paper/2604.08460/) (2026)

## Abstract (arXiv)

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.