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.
By Lennart Bastian, Samuel Leventhal, Mustafa Hajij, Tolga Birdal
arXiv:2606. 07385v1 Announce Type: cross Abstract: Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics.
By S. V. Manivelan, Andrei Velichko, I. Manimehan
arXiv:2511. 10841v3 Announce Type: replace-cross Abstract: Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge.
By YongKyung Oh, Dong-Young Lim, Sungil Kim
arXiv:2606. 14284v1 Announce Type: cross Abstract: Time series prototype learning is fundamentally challenged by observational ambiguity.
By Jiaen Lv, Leran Qi, Shaowei Wang
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.
By Borui Cai, Yao Zhao
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.