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We investigate finite-time Lyapunov exponents (FTLEs), a measure for exponential separation of input perturbations, of deep neural networks. Within the framework of neural ODEs, we demonstrate that FTLEs serve as a powerful organizer for input-to-output mappings, allowing the comparison of distinct model architectures. We establish a direct connection between Lyapunov exponents and adversarial vulnerability, and propose a novel training algorithm that improves robustness by FTLE regularization.

This thesis studies coevolutionary games on adaptive networks in which agents are equipped with bounded memory and the ability to rewire. We examine the emergence of cooperation, the evolution of network topology, and the reward disparities that arise across the different experimental scenarios. We depart from the classical well-mixed and memoryless populations used in Classical Game Theory by considering finite populations of heterogeneous agents whose behavior depends on their randomly assigned strategy type. The model is implemented as an agent-based simulation on three representative network topologies: Watts–Strogatz, Barabási–Albert, and Erdős–Rényi. Across all scenarios, the results consistently show that network adaptivity and rewiring promote cooperation and increase the rewards of cooperative agents relative to those who tend to defect, primarily by facilitating the formation of cooperative clusters. The findings highlight the joint importance of memory and adaptive network structure in sustaining cooperation and suggest extensions for future research, including heterogeneous memory capacities and endogenous strategy change.

TBA ______________________________ Invited by Prof. Phan Thành Nam

TBA