FreKoo++ is a continuous spectral-dynamical framework designed for Temporal Domain Generalization (TDG). It unifies continuous Koopman modal dynamics with adaptive spectral disentanglement, mapping source-domain parameters into a latent space and modeling their evolution as a superposition of learnable continuous modes. The method handles irregular timestamps, supports arbitrary horizon extrapolation, and introduces an adaptive soft spectral weighting mechanism that isolates persistent dynamics from transient noise, achieving state‑of‑the‑art performance on discrete and continuous TDG benchmarks.
By En Yu, Xiaoyu Yang, Wei Duan, Guangquan Zhang, Jie Lu
arXiv:2606. 29679v1 Announce Type: new Abstract: Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \times N$ distance matrix $M(t)$ on a held set of $N$ inputs.
By Igor Halperin
arXiv:2608. 14716v1 Announce Type: cross Abstract: Abrupt transitions in complex systems are often preceded by early warning signals.
By Juan Nathaniel, Carla Roesch, Derek DeSantis, Parvathi Kooloth, Hang Fan, Valerio Lucarini, Anastasia Romanou, Pierre Gentine
arXiv:2607. 02050v1 Announce Type: new Abstract: Motivated by the challenge of stabilizing a general unknown linear dynamical system (LDS) from observations, we study the natural prerequisite of online prediction.
By Yuval Ran-Milo, Angelos Assos, Elad Hazan
arXiv:2308. 13380v3 Announce Type: replace-cross Abstract: Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class?
By Marco Forgione, Filippo Pura, Dario Piga
The paper challenges the common assumption that the successor measure in reinforcement learning is approximately low-rank, showing instead that a low-rank structure emerges in a shifted successor measure that ignores initial transitions. It provides finite-sample guarantees for estimating this low-rank approximation, introduces Type II Poincaré inequalities to bound spectral recoverability, and links the necessary shift to the decay of high-order singular values and local mixing properties. Experiments confirm that shifting the successor measure improves goal-conditioned RL performance.
By Bastien Dubail, Stefan Stojanovic, Alexandre Prouti\`ere
arXiv:2606. 28486v1 Announce Type: cross Abstract: The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem.
By Chanju Park, Dario Bocchi, Francesco D'Amico, Biagio Lucini, Gert Aarts
arXiv:2606. 03067v1 Announce Type: cross Abstract: A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior.
By Valentina Kuskova, Dmitry Zaytsev, Michael Coppedge
The paper introduces an in‑span adaptation technique for reduced‑order models, where the reduced subspace is continually updated using the model’s own predictions via an incremental singular‑value decomposition with a forgetting factor. This creates a trajectory‑informed spectral preconditioner that reweights and realigns the basis without changing the subspace, enabling the model to better absorb future out‑of‑span corrections. The authors demonstrate the method on a 3‑D spiral example and nonlinear PDEs such as viscous Burgers and Fisher–KPP, and relate the approach to in‑context learning in dynamical systems.
By Amirpasha Hedayat, Laura Balzano, Karthik Duraisamy
The paper introduces Regularized Emphatic Temporal‑Difference Learning (RETD), a modification of ETD that normalizes the post‑shock dynamics while preserving the emphatic TD signal and importance ratios. RETD achieves almost‑sure convergence under harmonic diminishing stepsizes and provides a conditional constant‑stepsize moment‑contraction guarantee, demonstrating negative Lyapunov exponents on a two‑state counterexample and the Baird point. Extensive experiments confirm RETD’s ability to recover the ETD fixed point, exhibit a non‑monotone stability region, and maintain task‑dependent performance.
By Xingguo Chen, Zhaohui Wu, Jinguo Ye, Chao Li, Shangdong Yang, Guang Yang, Skylar Liang, Wenhao Wang
Emphatic temporal-difference learning (ETD) stabilizes the expected off-policy TD update and changes its projection geometry, but neither property determines constant-stepsize sampled dynamics. We con...
arXiv:2407. 06312v2 Announce Type: replace-cross Abstract: Many systems resist analytical modeling, making data-driven inference of dynamics important.
By Matthew J. Colbrook, Igor Mezi\'c, Alexei Stepanenko