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.
arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.
arXiv:2608. 08689v1 Announce Type: new Abstract: The state evolution of a complex system arises jointly from object laws, relational propagation, domain conservation, and unmodeled error.
arXiv:2606. 30789v1 Announce Type: new Abstract: Group Relative Policy Optimization (GRPO) has become a standard tool for improving the reasoning ability of large language models, yet its training dynamics are still described empirically: reward trajectories are fit with low-parameter functional forms whose constants carry no mechanistic meaning, and hyperparameter choices remain a matter of trial and error.
arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
arXiv:2607. 03671v1 Announce Type: cross Abstract: Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes.
arXiv:2608. 00852v1 Announce Type: new Abstract: Understanding and controlling complex dynamical systems often requires executing thousands of numerical simulations across vast parametric landscapes, which is time-consuming.
arXiv:2606. 24958v1 Announce Type: new Abstract: Collective behavior arises when locally interacting units produce coordinated global organization, from synchronization in dynamical systems to task-relevant information flow on graphs.
arXiv:2606. 18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate.
arXiv:2606. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
arXiv:2607. 21421v1 Announce Type: new Abstract: Generative models can support decision-making under uncertainty by producing ensembles of plausible future system trajectories, but statistical plausibility does not ensure structural feasibility.
arXiv:2604. 13213v2 Announce Type: replace-cross Abstract: Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased simulations seldom produce them.
arXiv:2606. 05326v1 Announce Type: cross Abstract: We study the dynamics of gradient descent in the Edge of Stability regime, where the learning rate is large enough to induce persistent oscillations in the loss and the sharpness.