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: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.
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:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
arXiv:2608. 15388v1 Announce Type: new Abstract: Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs.
arXiv:2607. 08555v1 Announce Type: new Abstract: The operational integrity of complex industrial systems relies on precise anomaly detection and diagnosis.
arXiv:2606. 15452v1 Announce Type: new Abstract: Rare events in time series are critical to model but hard to learn due to data scarcity.
arXiv:2606. 15897v1 Announce Type: cross Abstract: Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance.