arXiv:2606. 20443v1 Announce Type: cross Abstract: Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data.
arXiv:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.
arXiv:2606. 07385v1 Announce Type: cross Abstract: Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics.
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.
arXiv:2606. 14284v1 Announce Type: cross Abstract: Time series prototype learning is fundamentally challenged by observational ambiguity.
arXiv:2608.22044v1 Announce Type: new Abstract: Modern machine learning (ML) methods are highly effective for prediction tasks, but many commonly used representations reduce complex data to fixed dim...
arXiv:2606. 21295v2 Announce Type: replace-cross Abstract: Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently.
The operational integrity of complex industrial systems relies on precise anomaly detection and diagnosis. The vast majority of existing methods narrowly focus on capturing temporal similarities of representations, often overlooking the disruption of internal causal relationships, which characterizes system failures and latent anomalies.
The paper proposes using concepts from low‑dimensional topology—specifically Morse theory and cobordism—to enhance graph diffusion models, introducing the MG‑Diff pipeline. It provides theoretical guarantees that the Morse‑theoretic guidance remains stable under small perturbations when a positive decision‑gap exists. The authors demonstrate the approach on spatio‑temporal graph forecasting and graph regeneration, suggesting broader potential for topology in machine learning.
arXiv:2603. 23746v2 Announce Type: replace Abstract: Events in spatiotemporal domains arise in numerous real-world applications, where uncovering event relationships and enabling accurate prediction are central challenges.
arXiv:2609.39792v2 Announce Type: new Abstract: Distinguishing periodic from chaotic dynamics in a time series is a fundamental challenge in both physics and engineering. Yet, end-to-end learned arch...
The paper introduces a unified pipeline that classifies univariate time series by first converting them into graphs using one of five constructions from three families (visibility, transition, proximity). The resulting graph is turned into a dissimilarity matrix, from which a Vietoris–Rips filtration produces persistence diagrams that are vectorized via persistence landscapes and topological summary statistics. Experiments on twelve UCR benchmarks reveal that no single graph construction dominates, diffusion distance consistently outperforms shortest-path metrics, and persistence-based features remain robust to noise.
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.