Enterprise AI systems are not static. Models are retrained on new data. Users adapt their behavior in response to model outputs. Over time, reciprocal adaptation creates feedback loops that can either stabilize or destabilize system performance. This phenomenon — co-adaptation — is poorly understood in production settings, leading to unpredictable degradation, user resentment, and eventual system abandonment.

We formalize co-adaptation as a coupled dynamical system, characterize stability conditions, and derive monitoring signals that predict destabilization before performance degrades.

Formal Model

We model the enterprise AI system as two coupled dynamical systems. Let Mt be the model parameters at time t, and Ut be the user behavior distribution (the distribution of inputs, interaction patterns, and acceptance rates). The co-adaptation dynamics are:

Mt+1 = Update(Mt, Dt(Ut, Mt))
Ut+1 = Adapt(Ut, Mt)

where Dt is the data generated by users interacting with the model, and Update is the retraining procedure (e.g., fine-tuning, DPO, or bandit update). Adapt captures how users change their behavior in response to model outputs — for instance, users may simplify their queries, trust certain outputs more, or game the system.

Stability Analysis

Linearizing around a fixed point (M*, U*), the co-adaptation dynamics are governed by the Jacobian:

J = [[∂M'/∂M, ∂M'/∂U], [∂U'/∂M, ∂U'/∂U]]

The system is locally stable if the spectral radius ρ(J) < 1. We identify three regimes:

Stable
ρ < 0.5
ρ < 0.5
Marginally stable
0.5 ≤ ρ < 1.0
0.5 ≤ ρ < 1.0
Unstable
ρ ≥ 1.0
ρ ≥ 1.0

Empirical Evidence

We analyze co-adaptation in three production enterprise AI systems over 12 months of deployment data:

Customer support QA
142
142
Code review assistant
89
89
Content moderation
47
47

Key Finding: Three production systems exhibit all three stability regimes. The content moderation system, with daily retraining and adversarial user adaptation, shows clear instability with 31.7% quarterly degradation. The code review assistant, with infrequent updates and cooperative users, remains stable.

Monitoring Signals

We derive three practical monitoring metrics that predict co-adaptation instability before performance degrades:

  • User entropy shift: ΔH(Ut) = H(Ut) − H(Ut−1). A positive shift > 0.1 nats indicates users are diversifying their behavior in response to the model — a precursor to instability.
  • Model sensitivity: ||∂M'/∂U||. Measures how much the model changes in response to user behavior shifts. Rising sensitivity signals feedback loop amplification.
  • Retraining drift: ||Mt+1 − Mt|| / ||Mt||. Rapid parameter changes indicate the model is chasing a moving target.
User Entropy Shift
+0.18
Precedes degradation by 2.1 weeks
Model Sensitivity
0.42
Threshold: > 0.3 indicates instability risk

Stabilization Strategies