Repeated AI assistance can improve immediate task performance while reducing the skill available for future independent work. We develop a mathematical framework for this long-run tradeoff. The model tracks two state variables: a latent human skill level governing expected independent performance, and a delegation level representing the learner's evolving tendency to rely on AI. Skill changes through error-driven learning under practice and decay under delegation; delegation responds to observed performance, increasing when AI-assisted work appears to outperform independent work. We analyze the resulting dynamics and contrast them with fixed delegation. With fixed delegation, skill follows a one-dimensional learning-decay process with a single stable equilibrium. With adaptive delegation, the coupled system has two attracting equilibria separated by the stable manifold of an interior saddle. The existence and geometry of this separatrix require a global phase-plane analysis of the coupled dynamics. The system is path-dependent: small differences in initial skill or reliance can lead to different long-run outcomes. We use this characterization to show that AI assistance can improve short-run performance while producing worse long-run performance than a no-AI baseline. Increasing AI capability can enlarge the basin of attraction of the low-skill equilibrium, making delegation appear beneficial for longer while increasing the risk of eventual skill loss. The qualitative picture is observed to persist across alternative specifications. Together, these results show that the risk is not AI assistance itself, but the coupling between performance-driven reliance and use-dependent skill change.

翻译：重复的AI辅助可以提升即时任务表现，但会削弱未来独立工作所需的能力。我们为此长期权衡建立了一个数学框架。该模型追踪两个状态变量：一个决定预期独立表现的潜在人类技能水平，以及一个代表学习者对AI依赖程度演变趋势的委派水平。技能通过实践中的错误驱动学习得以提升，在委派状态下发生衰退；委派行为则根据观察到的表现进行调整——当AI辅助工作表现优于独立工作时，委派程度增加。我们分析了由此产生的动态过程，并将其与固定委派模式进行对比。在固定委派模式下，技能遵循一维学习-衰退过程，存在单一稳定均衡点。而在自适应委派模式下，耦合系统存在两个吸引性均衡点，它们被内部鞍点的稳定流形分隔。该分隔线的存在性与几何特性需要对耦合动态进行全局相平面分析。该系统具有路径依赖性：初始技能或依赖程度的微小差异可能导致截然不同的长期结果。基于这一特征，我们证明：与无AI基线相比，AI辅助虽然能提升短期表现，却可能导致更差的长期绩效。增强AI能力会扩大低技能均衡点的吸引域，使委派行为看似更长时间保持有利，实则增加了最终技能丧失的风险。该定性结论在多种替代设定下依然成立。这些结果共同表明：风险并非源于AI辅助本身，而在于绩效驱动的依赖行为与使用相关的技能改变之间的耦合关系。