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Path Dependence under Adaptive AI Delegation
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Proposes a two-state ODE model (latent skill and AI-delegation level) with error-driven learning, decay under delegation, and performance-driven reliance, showing bistability with a saddle separatrix, path dependence, and short-run gains masking long-run skill loss.
Problem
How adaptive reliance on AI assistance co-evolves with human skill over repeated tasks, and when small differences in initial skill or reliance lead to different long-run outcomes.
Approach
Couples a natural-gradient skill-learning/decay flow with a delegation flow driven by the performance gap between independent and AI-assisted work, yielding two attracting regimes (high skill/low delegation and low skill/high delegation) separated by the stable manifold of an interior saddle.
Key results
- With adaptive delegation the system has two attracting equilibria (1,0) and (0,1) separated by the stable manifold of an interior saddle at (theta_a, (1-theta_a)/(1-(1-Delta)theta_a)).
- Increasing AI skill theta_a shifts the basin boundary monotonically downward, enlarging the low-skill basin.
- AI assistance can give lower instantaneous loss initially but higher loss than no-AI after a finite final crossing time t_c, with theta(t_c; no-AI) <= theta_a.
Surprising findings
- Sufficiently heavy reliance can place even high-skill learners in the low-skill basin.
- Learning from AI during delegation lifts the low-skill equilibrium but does not eliminate the low-skill, high-delegation regime.
Limitations
- Model is theoretical and not calibrated to human behavior; functional forms chosen for tractability.
- Robustness variants are supported mainly by simulations and local analysis rather than full proofs.
- Stochastic and multi-skill results are simulation-supported.
Experimental setup
Metrics: basin membership performance gap G_ell(t) crossing time t_c
Baselines: fixed delegation no-AI baseline
Builds on: performative prediction item response theory natural gradient
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