analiza aiqbench
Optimal Transport Dropout introduces a novel method for learning structured predictive uncertainty by jointly optimizing the mapping and perturbation laws within neural networks, moving beyond the factorized assumptions of standard Monte Carlo dropout. This approach enables deterministic models to capture multimodal distributions and better-calibrated error intervals without requiring computationally expensive ensembles or explicit posterior inference. The technique demonstrates improved accuracy and spatial alignment with prediction errors on partial differential equation surrogates, offering a more efficient path to reliable uncertainty quantification in advanced machine learning applications.
Optimal Transport Dropout for Structured Predictive Uncertainty
arXiv:2609.33377v1 Announce Type: new Abstract: 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 when the model is misspecified, and exhibits contracting dispersion as more training data or greater model capacity are provided. For a field-valued partial differential equation surrogate, predictive dispersion strongly aligns with the spatial pattern of prediction errors. On this task, compared with Monte Carlo dropout, OTD yields more accurate predictions and better-calibrated, substantially narrower intervals. On real-world regression benchmarks, it further shows competitive accuracy and better probabilistic predictions compared to established baselines. OTD therefore offers a way to learn structured predictive uncertainty without explicit posterior inference or ensembles of independently trained predictors.
Abstract: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 when the model is misspecified, and exhibits contracting dispersion as more training data or greater model capacity are provided. For a field-valued partial differential equation surrogate, predictive dispersion strongly aligns with the spatial pattern of prediction errors. On this task, compared with Monte Carlo dropout, OTD yields more accurate predictions and better-calibrated, substantially narrower intervals. On real-world regression benchmarks, it further shows competitive accuracy and better probabilistic predictions compared to established baselines. OTD therefore offers a way to learn structured predictive uncertainty without explicit posterior inference or ensembles of independently trained predictors.
Machine Learning (cs.LG); Numerical Analysis (math.NA)
arXiv:2609.33377 [cs.LG]
(or arXiv:2609.33377v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.33377 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 343 cuvinte
Subiecte conexe
RadOT-Eval: Auditable Structured-Evidence Transport for Radiology Report Evaluation
arXiv · 9 iun. 2026
Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
arXiv · 3 iun. 2026
Geometry-Aware Bayesian Parameter-Efficient Fine-Tuning on the Stiefel Manifold via Stein Variational Gradient Descent
arXiv · 9 sept. 2026
Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization
arXiv · 9 oct. 2026