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This paper presents K2SVD, a principled method for learning Koopman operator representations with Kalman inference to achieve efficient and accurate time-series prediction, demonstrating superior performance over existing state-of-the-art approaches.
This paper presents a black-box method for LLM safety classification using dynamical systems and Koopman operators on prompt-response embedding dynamics to detect unsafe outputs.
This paper introduces a theoretical framework for identifying model-intrinsic structure in mechanistic interpretability using Koopman operator theory, proving the first identifiability theorem for a mechanistic-interpretability primitive with empirical validation on GPT-2, Gemma-2-2B, and Qwen3-8B-Base.
This paper introduces dynamics-aware preprocessing via Koopman-based upsampling (DMD/EDMD) to improve derivative estimation and equation discovery from sparse, noisy data, benchmarking on ODE and PDE systems.
Introduces Cluster-Weighted EDMD, a data-driven method that jointly learns a partition and per-cluster Koopman operators via expectation-maximization, improving prediction accuracy over standard EDMD on classical dynamical systems.
Proposes FedKAD, a federated Koopman anomaly detection framework for multivariate time series in IoT systems, using lightweight sliding-window Koopman representations and a Stiefel-ADMM algorithm for efficient communication and inference.
This paper introduces attention-free latent memory and dynamic re-encoding to improve long-horizon predictions in Koopman autoencoders, reducing error accumulation on benchmark dynamical systems.
Introduces Perron–Frobenius Operator Matching (PFOM), a generative framework that unifies flow, diffusion, and jump models via integral PF operator matching, proving KL divergence yields a practical loss equivalent to Koopman path matching, and develops Nesterov-accelerated training and sampling for improved efficiency.