mlsanityData to 7 Oct 2026

Function Space Particle Optimization for Bayesian Neural Networks

arXiv 1902.09754 ↗First posted 26 Feb 2019stat.ML cs.LGcited by 41

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Abstract (arXiv)

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable variational inference procedures based on the idea of particle optimization have been proposed. These methods directly optimize a set of particles to approximate the target posterior. However, their application to BNNs often yields sub-optimal performance, as such methods have a particular failure mode on over-parameterized models. In this paper, we propose to solve this issue by performing particle optimization directly in the space of regression functions. We demonstrate through extensive experiments that our method successfully overcomes this issue, and outperforms strong baselines in a variety of tasks including prediction, defense against adversarial examples, and reinforcement learning.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Feb 2019.

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Citing papers per year: 2021: 7; 2022: 5; 2023: 12; 2024: 8; 2025: 4; 2026: 5.

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  1. 2023ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillationcited by 1,207
  2. 2021Repulsive Deep Ensembles are Bayesiancited by 103
  3. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  4. 2023Tractable Function-Space Variational Inference in Bayesian Neural Networkscited by 41
  5. 2021On Stein Variational Neural Network Ensemblescited by 21
  6. 2023Function-Space Regularization in Neural Networks: A Probabilistic Perspectivecited by 20
  7. 2024Gaussian Stochastic Weight Averaging for Bayesian Low-Rank Adaptation of Large Language Modelscited by 20
  8. 2021Neural Variational Gradient Descentcited by 19
  9. 2021NOMU: Neural Optimization-based Model Uncertaintycited by 16
  10. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16
  11. 2023Improving Neural Additive Models with Bayesian Principlescited by 15
  12. 2024Retrieval-Augmented Score Distillation for Text-to-3D Generationcited by 14
29 more
  1. 2023Promises and Pitfalls of the Linearized Laplace in Bayesian Optimizationcited by 10
  2. 2023A Scalable Walsh-Hadamard Regularizer to Overcome the Low-degree Spectral Bias of Neural Networkscited by 10
  3. 2022Feature Space Particle Inference for Neural Network Ensemblescited by 9
  4. 2022On the detrimental effect of invariances in the likelihood for variational inferencecited by 8
  5. 2024Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensemblescited by 8
  6. 2023Input-gradient space particle inference for neural network ensemblescited by 7
  7. 2023Guided Deep Kernel Learningcited by 6
  8. 2024Bridging the Sim-to-Real Gap with Bayesian Inferencecited by 6
  9. 2025CLEAR: Calibrated Learning for Epistemic and Aleatoric Riskcited by 6
  10. 2022MARS: Meta-Learning as Score Matching in the Function Spacecited by 5
  11. 2021Greedy Bayesian Posterior Approximation with Deep Ensemblescited by 3
  12. 2021Loss function based second-order Jensen inequality and its application to particle variational inferencecited by 3
  13. 2024On Uncertainty Quantification for Near-Bayes Optimal Algorithmscited by 3
  14. 2023Function Space Bayesian Pseudocoreset for Bayesian Neural Networkscited by 2
  15. 2024Scientific Machine Learning Seismologycited by 2
  16. 2024Perturb-and-Revise: Flexible 3D Editing with Generative Trajectoriescited by 2
  17. 2022Deep Ensemble as a Gaussian Process Approximate Posteriorcited by 1
  18. 2023Long-tailed Classification from a Bayesian-decision-theory Perspectivecited by 1
  19. 2025Repulsive Ensembles for Bayesian Inference in Physics-informed Neural Networkscited by 1
  20. 2022Excess risk analysis for epistemic uncertainty with application to variational inferencecited by 0
  21. 2023Function-Space Regularization for Deep Bayesian Classificationcited by 0
  22. 2023Uncertainty in Graph Contrastive Learning with Bayesian Neural Networkscited by 0
  23. 2025Simulation Priors for Data-Efficient Deep Learningcited by 0
  24. 2025BOCO: Bayesian Online Contextual Optimization for Decision-Focused Online Learningcited by 0
  25. 2026Function-Space Empirical Bayes Regularisation with Large Vision-Language Model Priorscited by 0
  26. 2026Function-Space Empirical Bayes Regularisation with Student's t Priorscited by 0
  27. 2026Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networkscited by 0
  28. 2026Bayesian three-dimensional seismic travel-time tomography for active- and passive-source seismic data using physics-informed neural networkcited by 0
  29. 2026A Distributional Optimisation Perspective on Combining Models in Deep Learningcited by 0