# Output-Constrained Bayesian Neural Networks

arXiv: https://arxiv.org/abs/1905.06287 · HTML: https://mlsanity.com/paper/1905.06287/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 4 of 4)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Deep Classifiers with Label Noise Modeling and Distance Awareness](https://mlsanity.com/paper/2110.02609/) (2021)
- [Bayesian neural networks with interpretable priors from Mercer kernels](https://mlsanity.com/paper/2510.23745/) (2025)
- [Soft Checksums to Flag Untrustworthy Machine Learning Surrogate Predictions and Application to Atomic Physics Simulations](https://mlsanity.com/paper/2412.03497/) (2024)

## Abstract (arXiv)

Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be in regions of the input space. Output-Constrained BNNs (OC-BNN) represent an interpretable approach of enforcing a range of constraints, fully consistent with the Bayesian framework and amenable to black-box inference. We demonstrate how OC-BNNs improve model robustness and prevent the prediction of infeasible outputs in two real-world applications of healthcare and robotics.