STEP: Learning STructured Embeddings for Progressive Time Series

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.

Subspace-Decomposed JEPAs: Disentangling Progression and Content in Latent World Models

Joint-Embedding Predictive Architectures (JEPAs) learn compact latent world models by predicting future embeddings, but no single coordinate of the latent is designated to encode task progression. We carve the JEPA latent into two orthogonal subspaces with disjoint roles: a low-dimensional progression subspace shaped by a cosine-margin triplet loss, and a high-dimensional content subspace regularised by the existing SIGReg objective of LeWM. We prove that the two anti-collapse forces act on disjoint coordinates, so they compose additively rather than competing on the same dimensions. Our method, SD-JEPA improves over the LeWM baseline on the majority of its control benchmarks at matched compute, and outperforms the strongest non-LeWM JEPA baseline on Push-T; a subspace-ablation falsifier confirms the split is the load-bearing ingredient. Beyond planning, the resulting 1-D angular progression coordinate functions as a scene-aware compass on the latent. It advances with task progress, regresses when the agent backtracks, and under controlled perturbations both spikes and relocalises to a semantically appropriate new task-phase sector, separating the moment of surprise from its meaning in a way that prediction-error scalars cannot. Three quantitative tests back this up: $|Δθ_t|$ outperforms the standard latent-prediction-error surprise at localising semantic events on 40 held-out cube episodes by up to +0.18 pooled AUROC (97.5% per-episode win rate at $\pm 1$-step tolerance); a within-episode linear probe across all four environments (40 episodes per env) shows the 8-dimensional progression subspace (4.2% of the latent) explains 72-95% of task-progress variance..

A Machine Learning Framework for Turbofan Health Estimation via Inverse Problem Formulation

Estimating the health state of turbofan engines is a challenging ill-posed inverse problem, hindered by sparse sensing and complex nonlinear thermodynamics. Research in this area remains fragmented, with comparisons limited by the use of unrealistic datasets and insufficient exploration of the exploitation of temporal information. This work investigates how to recover component-level health indicators from operational sensor data under realistic degradation and maintenance patterns. To support this study, we introduce a new dataset that incorporates industry-oriented complexities such as maintenance events and usage changes. Using this dataset, we establish an initial benchmark that compares steady-state and nonstationary data-driven models, and Bayesian filters, classic families of methods used to solve this problem. In addition to this benchmark, we introduce self-supervised learning (SSL) approaches that learn latent representations without access to true health labels, a scenario reflective of real-world operational constraints. By comparing the downstream estimation performance of these unsupervised representations against the direct prediction baselines, we establish a practical lower bound on the difficulty of solving this inverse problem. Our results reveal that traditional filters remain strong baselines, while SSL methods reveal the intrinsic complexity of health estimation and highlight the need for more advanced and interpretable inference strategies. For reproducibility, both the generated dataset and the implementation used in this work are made accessible.