Data to 13 Oct 2026

Bayesian Layers: A Module for Neural Network Uncertainty

arXiv 1812.03973 ↗First posted 10 Dec 2018cs.LG cs.PL stat.MLcited by 57

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Abstract (arXiv)

We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction over deterministic and stochastic functions and allows for scalability via the underlying system. These layers capture uncertainty over weights (Bayesian neural nets), pre-activation units (dropout), activations ("stochastic output layers"), or the function itself (Gaussian processes). They can also be reversible to propagate uncertainty from input to output. We include code examples for common architectures such as Bayesian LSTMs, deep GPs, and flow-based models. As demonstration, we fit a 5-billion parameter "Bayesian Transformer" on 512 TPUv2 cores for uncertainty in machine translation and a Bayesian dynamics model for model-based planning. Finally, we show how Bayesian Layers can be used within the Edward2 probabilistic programming language for probabilistic programs with stochastic processes.

Key facts. Cited by 57 papers in the map (data through 13 Oct 2026). First posted on arXiv 10 Dec 2018.

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Citing papers per year: 2021: 16; 2022: 10; 2023: 8; 2024: 10; 2025: 7; 2026: 6.

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2023Bayesian Low-rank Adaptation for Large Language Modelscited by 114
2021Priors in Bayesian Deep Learning: A Reviewcited by 101
2022Hyperbolic Image Segmentationcited by 101
2021Towards a Science of Human-AI Decision Making: A Survey of Empirical Studiescited by 86
2021Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representationscited by 81
2024BLoB: Bayesian Low-Rank Adaptation by Backpropagation for Large Language Modelscited by 50
2023A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methodscited by 39
2024Uncertainty quantification in fine-tuned LLMs using LoRA ensemblescited by 37
2021Uncertainty-Aware Machine Translation Evaluationcited by 35
2021Bayesian Attention Belief Networkscited by 25
2024BlackJAX: Composable Bayesian inference in JAXcited by 25
2021Bayesian Transformer Language Models for Speech Recognitioncited by 22

38 more

2021RecSim NG: Toward Principled Uncertainty Modeling for Recommender Ecosystemscited by 21
2023Calibrating Transformers via Sparse Gaussian Processescited by 21
2024Gaussian Stochastic Weight Averaging for Bayesian Low-Rank Adaptation of Large Language Modelscited by 20
2025Evaluating Uncertainty and Quality of Vision-Language-Action-enabled Robotscited by 17
2021A Bayesian neural network predicts the dissolution of compact planetary systemscited by 15
2023Fortuna: A Library for Uncertainty Quantification in Deep Learningcited by 14
2021deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regressioncited by 13
2021Pathologies in priors and inference for Bayesian transformerscited by 13
2022Lymphoma segmentation from 3D PET-CT images using a deep evidential networkcited by 12
2021Applications of the Free Energy Principle to Machine Learning and Neurosciencecited by 9
2025Revisiting Kernel Attention with Correlated Gaussian Process Representationcited by 9
2022Confidence estimation of classification based on the distribution of the neural network output layercited by 8
2024Uncertainty Quantification for Forward and Inverse Problems of PDEs via Latent Global Evolutioncited by 8
2021TyXe: Pyro-based Bayesian neural nets for Pytorchcited by 6
2023Block-local learning with probabilistic latent representationscited by 6
2023Flexible Visual Recognition by Evidential Modeling of Confusion and Ignorancecited by 6
2024Boundary Exploration for Bayesian Optimization With Unknown Physical Constraintscited by 6
2024Improving Interpretability of Deep Active Learning for Flood Inundation Mapping Through Class Ambiguity Indices Using Multi-spectral Satellite Imagerycited by 6
2024Self-Attention through Kernel-Eigen Pair Sparse Variational Gaussian Processescited by 5
2021Probabilistic Deep Learning with Probabilistic Neural Networks and Deep Probabilistic Modelscited by 4
2022Application of belief functions to medical image segmentation: A reviewcited by 4
2021The Bayesian Method of Tensor Networkscited by 3
2022Sample-Efficient Optimisation with Probabilistic Transformer Surrogatescited by 3
2022Methods for Estimating and Improving Robustness of Language Modelscited by 3
2022Bayesian Neural Network Language Modeling for Speech Recognitioncited by 3
2023DiffLoad: Uncertainty Quantification in Electrical Load Forecasting with the Diffusion Modelcited by 3
2025Comparing Uncertainty Measurement and Mitigation Methods for Large Language Models: A Systematic Reviewcited by 3
2025Towards Unveiling Predictive Uncertainty Vulnerabilities in the Context of the Right to Be Forgottencited by 3
2022Mitigating Closed-model Adversarial Examples with Bayesian Neural Modeling for Enhanced End-to-End Speech Recognitioncited by 2
2024Multi-Fidelity Bayesian Neural Network for Uncertainty Quantification in Transonic Aerodynamic Loadscited by 2
2025CLAPS: Aleatoric-Epistemic Scaling via Last-Layer Laplace for Conformal Regressioncited by 2
2021Estimating the Uncertainty of Neural Network Forecasts for Influenza Prevalence Using Web Search Activitycited by 1
2022Optimal Lighting Control in Greenhouses Using Bayesian Neural Networks for Sunlight Predictioncited by 1
2024Assessing the Uncertainty and Robustness of the Laptop Refurbishing Softwarecited by 1
2026Provably Robust Bayesian Counterfactual Explanations under Model Changescited by 1
2021Graceful Degradation and Related Fieldscited by 0
2022A Deep Learning Approach to Dst Index Predictioncited by 0
2023Bayesian Neural Networks for 2D MRI Segmentationcited by 0

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