Logarithmic warming curve of memory effects in CUA grounding

Determine whether the relationship between the number of prior application interactions stored in memory and the resulting increase in small-model confidence for CUA grounding follows a logarithmic pattern characterized by large initial gains and diminishing returns across subsequent interactions.

Background

The authors introduce a hypothetical warming curve describing how memory accumulation affects small-model confidence in GUI grounding, suggesting that initial interactions yield the largest benefits and later interactions contribute less. They explicitly characterize this as a conjecture rather than an established result.

Validating the functional form of this curve would inform how quickly memory reduces escalation to larger models and help calibrate routing thresholds and memory strategies in real deployments.