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.
Figures & tables
Figure 1: Overview of the repeated-task adaptation model. In each short time window t , the learner faces many comparable tasks and delegates a fraction p(t) of them. Evaluator feedback is aggregated across tasks and enters the skill-update and delegation-update mechanisms. The former combines error-driven learning under practice with non-use decay, while the latter updates reliance through relative performance feedback.
Figure 2: Phase portraits for the adaptive-delegation dynamics. (a) Fixed delegation has a single attracting skill level, while adaptive delegation creates competing attracting regimes. (b) The stable manifold of the interior saddle separates the high-skill and low-skill basins. (c) Increasing AI skill shifts the basin boundary downward, expanding the low-skill basin. Default parameters are (θa,κ,Δ)=(0.5,3,2) unless varied.
Figure 3: Plots illustrating the instantaneous performance loss over time with and without AI, and how the crossing point varies with respect to AI skill θa , with default settings (θa,κ,Δ,θ0,p0)=(0.5,3,2,0.4,0.3) .
Symbol
Domain
Description
θd
[0,1]
Default skill
θa
[0,1]
AI skill
θ0
[0,1]
Initial skill of learner
θ(t)
[0,1]
Learner skill at time t
θ(t;θ0,p0)
[0,1]
Learner skill at time t with initial state (θ0,p0)
p0
[0,1]
Initial delegation level of learner
Table 1: Used notations
Figure 4: Heatmap of the probability of converging to the high-skill equilibrium (1,0) for SDEs ( 13 ) and ( 14 ) as a function of the initial state (θ0,p0) , with default settings of (θa,κ,Δ,σ)=(0.5,3,2,0.1) . Green indicates probability 0 , and red indicates probability 1 .
Figure 5: Plots illustrating the closeness between the stable manifold ψ(⋅) and its approximation ψ , with default parameter settings (θa,κ,Δ)=(0.5,3,2) .
Figure 6: Plots illustrating the relationship between the basin boundary ψ(⋅) and model parameters θa,κ,Δ , with default setting (θa,κ,Δ)=(0.5,3,2) .
Figure 7: Plots illustrating how the basins of attraction change under learner- and teacher-side interventions, with default parameter settings (θa,κ,Δ)=(0.5,3,2) .
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Variant
Status
Jagged AI performance
Exact reduction via effective loss
Biased perceived AI skill
Analytically characterized
Power- z loss
Analytic nullcline deformation and simulations
Stochastic delegation updates
Simulation-supported
Multiple skills
Simulation-supported
Learning from AI during delegation
Analytic equilibrium shift and simulations
Appendix
Table 2: Status of robustness variants.
Figure 8: Plots illustrating z -th power loss with default setings (θa,κ,Δ)=(0.5,3,2) ; and the two-skill extension ( 26 ), with default settings (θa,κ,Δ1,Δ2,w1,w2)=(0.5,3,1,3,0.5,0.5) . Skill trajectories can still diverge from nearby initial conditions, while θ1(t)>θ2(t) holds for all t≥0 because the decay rate satisfies Δ1<Δ2 .
Figure 9: Plots illustrating how the basins of attraction vary under learner- and AI-side extensions, with default settings (θa,κ,Δ)=(0.5,3,2) .
Window t
Delegation fraction pt
Avg. independent loss LtH
Skill estimate θt
1
0.20
0.09
0.70
2
0.24
0.1024
0.68
3
0.30
0.1296
0.64
4
0.38
0.16
0.60
Appendix
Table 3: Synthetic repeated-task data used only to illustrate the calibration procedure.
People often optimize for long-term goals in collaboration: A mentor or companion doesn't just answer questions, but also scaffolds learning, tracks progress, and prioritizes the other person's growth over immediate results. In contrast, current AI systems are fundamentally short-sighted collaborators - optimized for providing instant and complete responses, without ever saying no (unless for safety reasons). What are the consequences of this dynamic? Here, through a series of randomized controlled trials on human-AI interactions (N = 1,222), we provide causal evidence for two key consequences of AI assistance: reduced persistence and impairment of unassisted performance. Across a variety of tasks, including mathematical reasoning and reading comprehension, we find that although AI assistance improves performance in the short-term, people perform significantly worse without AI and are more likely to give up. Notably, these effects emerge after only brief interactions with AI (approximately 10 minutes). These findings are particularly concerning because persistence is foundational to skill acquisition and is one of the strongest predictors of long-term learning. We posit that persistence is reduced because AI conditions people to expect immediate answers, thereby denying them the experience of working through challenges on their own. These results suggest the need for AI model development to prioritize scaffolding long-term competence alongside immediate task completion.
Grace Liu, Brian Christian, Tsvetomira Dumbalska +2
Carnegie Mellon University · UC Berkeley · University of Oxford +2
While AI assistance can improve human task performance in the short term, it may also undermine the development of skills in the longer term. We examine this tension in a controlled logic-puzzle experiment involving on-demand AI assistance, where participants complete tasks before, during, and after AI is available. By experimentally varying AI request costs, we find that lower-cost assistance induces more frequent AI use. We also find that participants who request AI assistance during the AI-access phase perform worse at the task after assistance is removed, and their subsequent unassisted performance is overestimated when predicted from earlier AI-assisted performance. We use a Bayesian latent ability model to separate initial ability, post-AI ability, and participant-specific skill change, while estimating how independent reasoning during the AI-access phase relates to skill development. The results show that greater independent problem-solving effort is associated with larger gains in latent ability, consistent with the interpretation that skill development is weaker when AI assistance substitutes for independent reasoning.
Generative Artificial Intelligence (AI) tools are rapidly adopted in the workplace and in education, yet the empirical evidence on AI's impact remains mixed. We propose a model of human-AI interaction to better understand and analyze several mechanisms by which AI affects productivity. In our setup, human agents with varying skill levels exert utility-maximizing effort to produce certain task outcomes with AI assistance. We find that incorporating either endogeneity in skill development or in AI unreliability can induce a productivity paradox: increased levels of AI assistance may degrade productivity, leading to potentially significant shortfalls. Moreover, we examine the long-term distributional effect of AI on skill, and demonstrate that skill polarization can emerge in steady state when accounting for heterogeneity in AI literacy -- the agent's capability to identify and adapt to inaccurate AI outputs. Our results elucidate several mechanisms that may explain the emergence of human-AI productivity paradoxes and skill polarization, and identify simple measures that characterize when they arise.