A Gradient Framework for Communication Cost and Calibration Mismatch in Human–LLM Interaction

Aversion and disengagement in human–LLM interaction follow the dynamics of a calibration loop between user expectations and model behaviour. Modelling the gap Δ(t) = C(t) − E(t) between interpreted communication cost C and expected cost E as a prediction-error quantity within the user's model of the interaction, the time derivatives Δ̇ and Δ̈ become the load-bearing quantities. Under specified conditions, aversion correlates with |Δ̇| rather than with |Δ| alone, and disengagement correlates with derivative information dominating the static gap, with the second derivative gating reset under restricted assumptions on the per-period cost function and accelerating reset more generally. Communication cost is jointly paid but asymmetrically measurable under current alignment instrumentation. Model-side cost is approximated by token-derived measures, while human-side cost requires multi-modal measurement (tokens, timing, affect, trait-expectation gaps, behavioural signals) and resists scalar reduction. The asymmetry has direct alignment implications: where the standard pipeline collapses the multi-modal human-side signal to scalar reward before learning, an alternative organised around a learned cost encoder (structurally analogous to JEPA-style joint embedding architectures) preserves the structure. Three derivative-driven dynamics organise empirical investigation: a disillusionment trajectory under candidate mechanisms (asymmetric prior updating, case-distribution shift, capability stagnation against rising ambition; the list is illustrative, not exhaustive), cost-shifting equilibria under partial-observability scalar optimisation, and reset behaviour governed by second-derivative thresholds. Sycophancy and default-condescension are reframed as candidate manifestations of the same calibration failure, with a directional trade-off prediction across mitigations; the user preference prompt is identified as a partial diagnostic of default-prior mismatch in high-capability subpopulations. The proposed alignment-target rewrite is conditional on three open technical problems: a constructed cost encoder, a constrained endogenous-E update law, and a fixed-point existence proof on the resulting policy. Identifying this technical agenda is the paper's primary contribution; solving it is future work.