arXiv subjects

Chaoyang Luo

Publications and source records attributed to Chaoyang Luo.

3 recordsLinked to original sources

arXiv2025

Evolutionary Cooperation with Game Transitions via Markov Decision Chain in Networked Population

Individual cooperative strategy influences the surrounding dynamic population, which in turn affects cooperative strategy. To better model this phenomenon, we develop a Markov decision chain based game transitions model and examine the dynamic transitions in game states of individuals within a network and their impact on the strategy's evolution. Additionally, we extend single-round strategy imitation to multiple rounds to better capture players' potential non-rational behavior. Using intensive simulations, we explore the effects of transition probabilities and game parameters on game transitions and cooperation. Our study finds that strategy-driven game transitions promote cooperation, and increasing the transition rates of Markov decision chains can significantly accelerate this process. By designing different Markov decision chains, these results provide simulation based guidance for practical applications in swarm intelligence, such as strategic collaboration.

physics.soc-ph↗

arXiv2025

Learning Aligned Stability in Neural ODEs Reconciling Accuracy with Robustness

Despite Neural Ordinary Differential Equations (Neural ODEs) exhibiting intrinsic robustness, existing methods often impose Lyapunov stability for formal guarantees. However, these methods still face a fundamental accuracy-robustness trade-off, which stems from a core limitation: their applied stability conditions are rigid and inappropriate, creating a mismatch between the model's regions of attraction (RoAs) and its decision boundaries. To resolve this, we propose Zubov-Net, a novel framework that unifies dynamics and decision-making. We first employ learnable Lyapunov functions directly as the multi-class classifier, ensuring the prescribed RoAs (PRoAs, defined by the Lyapunov functions) inherently align with a classification objective. Then, for aligning prescribed and true regions of attraction (PRoAs-RoAs), we establish a Zubov-driven stability region matching mechanism by reformulating Zubov's equation into a differentiable consistency loss. Building on this alignment, we introduce a new paradigm for actively controlling the geometry of RoAs by directly optimizing PRoAs to reconcile accuracy and robustness. Theoretically, we prove that minimizing the tripartite loss guarantees consistency alignment of PRoAs-RoAs, non-overlapping PRoAs, trajectory stability, and a certified robustness margin. Moreover, we establish stochastic convex separability with tighter probability bounds and lower dimensionality requirements to justify the convex design in Lyapunov functions.

cs.LG↗

arXiv2024

FxTS-Net: Fixed-Time Stable Learning Framework for Neural ODEs

Neural Ordinary Differential Equations (Neural ODEs), as a novel category of modeling big data methods, cleverly link traditional neural networks and dynamical systems. However, it is challenging to ensure the dynamics system reaches a correctly predicted state within a user-defined fixed time. To address this problem, we propose a new method for training Neural ODEs using fixed-time stability (FxTS) Lyapunov conditions. Our framework, called FxTS-Net, is based on the novel FxTS loss (FxTS-Loss) designed on Lyapunov functions, which aims to encourage convergence to accurate predictions in a user-defined fixed time. We also provide an innovative approach for constructing Lyapunov functions to meet various tasks and network architecture requirements, achieved by leveraging supervised information during training. By developing a more precise time upper bound estimation for bounded non-vanishingly perturbed systems, we demonstrate that minimizing FxTS-Loss not only guarantees FxTS behavior of the dynamics but also input perturbation robustness. For optimising FxTS-Loss, we also propose a learning algorithm, in which the simulated perturbation sampling method can capture sample points in critical regions to approximate FxTS-Loss. Experimentally, we find that FxTS-Net provides better prediction performance and better robustness under input perturbation.

math.OC↗