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Deep learning models are widely used in decision-making and recommendation systems, where they typically rely on the assumption of a static data distribution between training and deployment. However, real-world deployment environments often violate this assumption. Users who receive negative outcomes may adapt their features to meet model criteria, i.e., recourse action. These adaptive behaviors create shifts in the data distribution and when models are retrained on this shifted data, a feedback loop emerges: user behavior influences the model, and the updated model in turn reshapes future user behavior. Despite its importance, this bidirectional interaction between users and models has received limited attention. In this work, we develop a general framework to model user strategic behaviors and their interactions with decision-making systems under resource constraints and competitive dynamics. Both the theoretical and empirical analyses show that user recourse behavior tends to push logistic and MLP models toward increasingly higher decision standards, resulting in higher recourse costs and less reliable recourse actions over time. To mitigate these challenges, we propose two methods—Fair-top-k and Dynamic Continual Learning (DCL)—which significantly reduce recourse cost and improve model robustness. Our findings draw connections to economic theories, highlighting how algorithmic decision-making can unintentionally reinforce a higher standard and generate endogenous barriers to entry. 

Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood. We develop here an ab initio many-body method to study nonperturbative HHG based on the real-time propagation of the non-equilibrium Green’s function with the GW self energy. We calculate the HHG of monolayer MoS2 and obtain good agreement with experiment, including the reproduction of characteristic patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. Here, we show that many-body effects are especially important to accurately reproduce the spectral features in the perpendicular response, which reflect a complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization and Berry curvature of the independent quasiparticle bandstructure.