Optimal Transport Dropout for Structured Predictive Uncertainty

Giacomo Lorenzon, Francesco Regazzoni

Deterministic neural networks and neural operators provide point predictions with no intrinsic measure of reliability. Yet, predictive uncertainty may stem from irreducible outcome variability, finite data, or limitations of the chosen model class. Monte Carlo dropout offers a computationally convenient way to construct a predictive distribution through stochastic feature masking, without training multiple independent networks or explicitly inferring a posterior over model parameters. However, its perturbation law is largely prescribed a priori and typically factorised across latent coordinates. We introduce Optimal Transport Dropout (OTD), which instead learns the predictive mapping and the law of its latent perturbations jointly. Starting from a simple independent reference distribution, OTD transports latent perturbations through a learnable flow and propagates them through the predictive neural network, thereby inducing a structured predictive law. Training uses the strictly proper Energy Score, while a kinetic-action term geometrically regularises the transport. Synthetic benchmarks show that OTD captures multimodal predictive distributions, generates meaningful dispersion…