Residual bayesian attention networks for uncertainty quantification in regression tasks.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Deep Learning

Background:

• Modern sequence modeling demands robust uncertainty quantification.
• Existing Bayesian inference and Transformer integrations face engineering challenges.
• Key issues include attention probabilization, uncertainty propagation in residual connections, and decoupling epistemic-aleatoric uncertainty.

Purpose of the Study:

• To propose the Residual Bayesian Attention (RBA) framework for end-to-end probabilistic inference.
• To address systematic engineering challenges in integrating Bayesian methods with Transformer architectures.
• To provide principled uncertainty quantification for deep sequence modeling.

Main Methods:

• Developed Bayesian feedforward layers for differentiable parameter-level uncertainty propagation.
• Embedded radial basis function kernels and adaptive Beta-distributed weights in multi-layer residual Bayesian attention.
• Utilized Bayesian covariance construction with outer products and eigenvalue correction for rigorous covariance representations.

Main Results:

• RBA demonstrated stable uncertainty quantification on benchmark datasets across six domains.
• Achieved technical advantages in prediction interval calibration quality for structured data.
• Identified technical limitations of current deep learning in multi-physics coupled system modeling.

Conclusions:

• RBA offers a systematic engineering framework for Bayesian inference and Transformer integration.
• Provides methodological contributions for principled uncertainty quantification in deep sequence modeling.
• Highlights applicability boundaries and empirical insights for future research directions.