Pointwise complexity-gated inference

Integrate this at inference for a stochastic predictor: a dropout transformer, ensemble, stochastic-depth network, or diffusion model using repeated denoising trajectories. Let x be the input, f_ξ(x) the output under random seed ξ, and x_0 a validation-set medoid. Collect n calibration inputs and Q stochastic outputs per input. Estimate the robust empirical metric \widehat d(x,x') as a high quantile or median of ||f_{ξ_q}(x)−f_{ξ_q}(x')||, using logits or compact embeddings rather than full generated outputs. Approximate μ(B_d(x,r)) with k-nearest-neighbor counts in the calibration set. Evaluate the displayed Φ integral on a logarithmic radius grid from a small positive floor to 4\widehat d(x,x_0). Fit α and the multiplicative constant C on a held-out calibration split so M_δ covers observed high-sample output error at the desired rate. At inference, run K_min stochastic samples, estimate M_δ(x), then allocate K(x) additional samples; stop when the running mean's empirical confidence radius is below ε. The paper supplies the envelope structure, while metric estimation, C, α, and the mapping from M_δ to Monte Carlo error are empirical. First test a 10-member dropout ResNet-18 on CIFAR-10 and a small dropout language model. Compare fixed-K inference and global variance gating at equal error and equal compute. Success is lower average sample count at matched accuracy, empirical failure probability near δ, and positive correlation between M_δ(x) and actual stochastic prediction error.