Clustered alpha-smoothing mixture wrapper

(1) Exact integration point: place this module after any stochastic predictor that can be queried repeatedly, such as a trajectory policy, diffusion denoiser, probabilistic world model, or multimodal regression network. At inference time, draw N perturbations epsilon_i around input x, run the existing model once per perturbation, and aggregate its output trajectories or actions. Do not change the neural network initially. (2) Pseudocode: sample H_i=h_w(x+epsilon_i) for i=1,...,N; cluster {H_i} into K clusters using k-means, a Gaussian mixture model, or a cheap farthest-point algorithm; for each cluster C_j, set n_j=|C_j| and k_j=floor(alpha*n_j); sort each output coordinate within C_j, retain indices R_j after removing the lowest and highest k_j values, compute m_j=mean(H_i for i in R_j), and compute Sigma_j from the retained samples; return mixture weights pi_j=n_j/N and components Normal(m_j,Sigma_j+lambda I). If the downstream controller needs one action, select the component with maximum pi_j, sample from the mixture, or use a risk-sensitive rule that rejects components with high predicted collision probability. (3) The mathematical quantities are N, alpha, local trimmed means, mixture weights, and covariance estimates. The clustering algorithm, K, perturbation distribution, and covariance floor lambda are empirical design choices. Require n_j>2*k_j; merge small clusters into their nearest larger cluster. For vector trajectories, cluster on a learned low-dimensional embedding or endpoint features, then trim coordinates in the original output space. (4) First cheap experiment: use a small stochastic MLP or diffusion trajectory predictor on a synthetic two-mode 2-D regression dataset with adversarial input perturbations, comparing ordinary Monte Carlo averaging, global alpha-smoothing, and clustered alpha-smoothing at equal N. Then test a compact trajectory model on a driving or quadrotor benchmark. Measure Wasserstein distance to the target distribution, mode coverage, collision rate, and runtime. Success is lower Wasserstein error and fewer unsafe averaged trajectories at the same sample budget, without a large increase in inference latency.