Hybrid Probabilistic Zonotopes Enhance Neural Network Uncertainty Prediction.

Traditional neural network prediction heads often struggle to differentiate between various sources of uncertainty, typically outputting either a Gaussian mixture or a single conformal region. This limitation makes it difficult to understand the specific nature of prediction errors in real-world tasks. The proposed Hybrid Probabilistic Zonotope (HProbZ) addresses this by representing uncertainty through three distinct generators: binary for discrete choices, bounded for systematic drift, and stochastic for noise. This structure allows for a closed-form likelihood and ensures that these three uncertainty sources are identifiable. A key advantage of HProbZ is its ability to refine future predictions. By sharing the bounded generator across prediction steps, observing one step algebraically updates the predictive distribution for all remaining steps in a single forward pass. This design offers structural properties not jointly provided by existing mixture or convex-conformal predictors, demonstrating effectiveness on prediction benchmarks.