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arxiv: 2603.02950 · v2 · submitted 2026-03-03 · 💻 cs.CY · cs.AI· cs.GT

Path Dependence under Adaptive AI Delegation

Lingxiao Huang , Nisheeth K. Vishnoi This is my paper

Pith reviewed 2026-05-15 17:07 UTC · model grok-4.3

classification 💻 cs.CY cs.AIcs.GT
keywords path dependenceadaptive delegationskill dynamicshuman-AI interactiondynamical systemsbistabilityequilibrium analysis
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The pith

Adaptive delegation to AI produces path-dependent skill dynamics with two attracting equilibria separated by a separatrix.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a dynamical model in which human skill improves through error-driven practice but decays when tasks are delegated to AI, while the level of delegation itself adjusts upward or downward according to whether AI-assisted performance exceeds independent performance. Analysis of the resulting two-dimensional system shows that adaptive delegation yields bistability: trajectories converge to either a high-skill low-delegation equilibrium or a low-skill high-delegation equilibrium, depending on which side of an interior saddle's stable manifold the initial conditions lie. Because the separatrix divides the phase plane, even small differences in starting skill or initial reliance can produce permanently different long-run outcomes. The same structure implies that AI assistance can raise short-term output yet leave final skill below the level achieved by a no-AI baseline. Raising AI capability enlarges the basin of the low-skill equilibrium, increasing the chance that delegation appears beneficial for longer before skill erosion becomes irreversible.

Core claim

With adaptive delegation the coupled system possesses two attracting equilibria separated by the stable manifold of an interior saddle; the resulting path dependence means that performance-driven adjustments in reliance can trap the user in a low-skill steady state even when AI assistance improves immediate results relative to independent work.

What carries the argument

The two-dimensional dynamical system whose state variables are latent human skill (governing expected independent performance) and delegation level (the evolving tendency to rely on AI), with skill evolving by error-driven improvement under practice and decay under delegation, and delegation evolving by a performance-based rule that increases reliance when AI-assisted output exceeds independent output.

If this is right

  • Small initial differences in skill or reliance can produce permanently different long-run skill levels.
  • AI assistance can improve short-run performance while producing worse long-run performance than a no-AI baseline.
  • Higher AI capability enlarges the basin of attraction of the low-skill equilibrium.
  • The source of long-run risk is the coupling between performance-driven reliance and use-dependent skill change rather than AI assistance in isolation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Deployment protocols could deliberately restrict early delegation to keep trajectories on the high-skill side of the separatrix.
  • Empirical studies might measure the width of the separatrix by varying initial conditions in controlled repeated-task experiments.
  • The same bistable structure may appear in other feedback systems where capability and usage co-evolve, such as tool-assisted learning or automated decision support.

Load-bearing premise

The specific functional forms chosen for error-driven skill improvement, skill decay under delegation, and the performance-comparison rule that updates delegation level are what produce the two-equilibrium structure and the separating manifold.

What would settle it

Longitudinal tracking of individual users performing repeated tasks under adaptive AI, recording both measured skill on independent trials and observed delegation rates, to test whether trajectories cluster into two distinct long-run attractors rather than converging to a single outcome regardless of small initial differences.

Figures

Figures reproduced from arXiv: 2603.02950 by Lingxiao Huang, Nisheeth K. Vishnoi.

Figure 1
Figure 1. Figure 1: Plots illustrating the outcomes of ODE (3) and effects of AI skill, with default settings of (θa, κ, ∆) = (0.5, 3, 2). A complete derivation and an analysis of the stochastic trajectories are provided in Section 5. Importantly, both θ and p evolve to locally minimize the same instantaneous performance loss, so the system exhibits no incentive misalignment. Despite this local alignment, the resulting global… view at source ↗
Figure 2
Figure 2. Figure 2: Plots illustrating the instantaneous performance loss across time with and with AI, and [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Heatmap of the probability of converging to the high-skill equilibrium (1 [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plots illustrating the closeness between the stable manifold [PITH_FULL_IMAGE:figures/full_fig_p026_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Plots illustrating the relationship between the basin boundary [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Plots illustrating how the basins vary under different model extensions, with default [PITH_FULL_IMAGE:figures/full_fig_p031_6.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper develops a two-dimensional dynamical system tracking latent human skill s and delegation level d. Skill evolves via error-driven improvement under independent practice and decay under delegation; delegation updates based on observed performance comparison between AI-assisted and independent work. With fixed delegation the system reduces to a one-dimensional process with a unique stable equilibrium. With adaptive delegation the coupled flow possesses two attracting equilibria separated by the stable manifold of an interior saddle, producing path dependence: trajectories starting near the separatrix converge to either a high-skill/low-delegation or low-skill/high-delegation attractor. The analysis shows that short-run performance gains from AI can place the system in the basin of the inferior long-run equilibrium, and that higher AI capability enlarges that basin. The qualitative structure is reported to survive changes in the functional forms of the update rules.

Significance. If the phase-plane results hold, the paper supplies a clean, falsifiable mechanism for the long-run skill-atrophy risk of performance-driven AI delegation. The global analysis, explicit contrast with fixed delegation, and robustness statements across functional forms constitute a genuine contribution to the formal modeling of human-AI interaction. The framework is simple enough to be extended empirically yet rich enough to generate testable predictions about basin boundaries and the effect of AI capability.

major comments (2)
  1. [§3.2] §3.2, Eq. (11)–(12): the claim that the interior equilibrium is a saddle whose stable manifold forms the separatrix is supported only by a qualitative sign argument on the Jacobian; an explicit computation of the eigenvalues (or at least their signs) at the equilibrium point would make the saddle classification and the geometry of the basins rigorous rather than heuristic.
  2. [§4.3] §4.3: the statement that the two-equilibrium structure 'persists across alternative specifications' is illustrated with only two variants of the skill-update rule; because the existence of the interior saddle and the separatrix are sensitive to the relative curvatures of the learning and decay functions, the robustness section should either enumerate the precise class of functions for which the result holds or provide a general proof that does not rely on the specific forms chosen in the main text.
minor comments (3)
  1. [§2.1] §2.1: the performance function P(s,d) used to drive the delegation update is described verbally but never written explicitly; inserting the functional form immediately after its introduction would remove ambiguity about how the comparison between assisted and unassisted performance is operationalized.
  2. [Figure 2] Figure 2: the phase portrait would be clearer if the stable manifold of the saddle were drawn as a distinct curve (rather than inferred from the flow arrows) and if the no-AI baseline trajectory were overlaid for direct visual comparison.
  3. [§5] §5: the discussion of policy implications is brief; a short paragraph indicating how the separatrix location could be estimated from observable data (initial skill and delegation levels) would strengthen the bridge to empirical work.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the thoughtful review and the recommendation for minor revision. The comments help strengthen the rigor of our analysis, and we address them point by point below.

read point-by-point responses

  1. Referee: [§3.2] §3.2, Eq. (11)–(12): the claim that the interior equilibrium is a saddle whose stable manifold forms the separatrix is supported only by a qualitative sign argument on the Jacobian; an explicit computation of the eigenvalues (or at least their signs) at the equilibrium point would make the saddle classification and the geometry of the basins rigorous rather than heuristic.

    Authors: We concur that the qualitative sign argument on the Jacobian can be made more rigorous with explicit eigenvalue computation. We will add this calculation in the revised manuscript, explicitly solving for the eigenvalues at the interior equilibrium point given by Eqs. (11)–(12) and verifying that they are real and of opposite signs, thereby confirming the saddle nature and the role of its stable manifold as the separatrix. revision: yes

  2. Referee: [§4.3] §4.3: the statement that the two-equilibrium structure 'persists across alternative specifications' is illustrated with only two variants of the skill-update rule; because the existence of the interior saddle and the separatrix are sensitive to the relative curvatures of the learning and decay functions, the robustness section should either enumerate the precise class of functions for which the result holds or provide a general proof that does not rely on the specific forms chosen in the main text.

    Authors: We acknowledge that the current robustness checks are limited to two variants. To address the concern about sensitivity to curvatures, we will revise §4.3 to provide a general argument under the assumption that the skill update functions satisfy certain monotonicity and concavity conditions (specifically, positive but decreasing marginal learning and non-increasing marginal decay). This will delineate the precise class of functions for which the two-attractor structure holds, without relying on the specific forms in the main text. We will also include an additional functional form in the illustrations. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines a two-dimensional dynamical system from explicit first-principles functional forms for error-driven skill improvement, skill decay under delegation, and performance-based delegation adjustment. The two attracting equilibria, interior saddle, and separating stable manifold are derived via global phase-plane analysis of the resulting ODEs; they are not presupposed, fitted to data, or imported via self-citation. The path-dependence and short-run vs. long-run tradeoff statements follow directly from the geometry of the vector field and are shown to be robust under alternative specifications of the update rules. No load-bearing step reduces to a definition, a fitted parameter renamed as prediction, or an unverified self-citation chain. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on domain assumptions about how skill evolves and how delegation is chosen; no free parameters are explicitly fitted in the abstract, and no new physical entities are postulated.

axioms (2)
  • domain assumption Skill changes through error-driven learning under practice and decay under delegation
    Stated directly in the model description as the mechanism for skill evolution.
  • domain assumption Delegation level increases when AI-assisted performance appears to outperform independent performance
    Core rule for the adaptive component of the model.

pith-pipeline@v0.9.0 · 5549 in / 1396 out tokens · 49126 ms · 2026-05-15T17:07:46.897098+00:00 · methodology

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