Count-Aware IPW Estimator

Without clipping, the count-aware IPW estimator is unbiased because the expected normalized draw count equals one. The ablation results support a bias-variance tradeoff for clipping thresholds. The count-aware IPW estimator multiplies the scalar finite difference by an IPW factor, the layer draw count, and the layer perturbation. Layer multiplicity increases the update assigned to layers sampled multiple times. Sampling with replacement is central because it creates multiplicities and enables the count-aware IPW correction. Clipping introduces finite bias but bounds the effect of very small sampling probabilities.