# On the Performance of Direct Loss Minimization for Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2211.08393 · HTML: https://mlsanity.com/paper/2211.08393/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 15 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [PACm-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime](https://mlsanity.com/paper/2010.09629/) (2020)
- [Direct loss minimization algorithms for sparse Gaussian processes](https://mlsanity.com/paper/2004.03083/) (2020)

## Built on by (most cited first, 3 of 3)

- [Variational Inference on the Final-Layer Output of Neural Networks](https://mlsanity.com/paper/2302.02420/) (2023)
- [A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks](https://mlsanity.com/paper/2402.18729/) (2024)
- [Stability-based Generalization Bounds for Variational Inference](https://mlsanity.com/paper/2502.12353/) (2025)

## Abstract (arXiv)

Direct Loss Minimization (DLM) has been proposed as a pseudo-Bayesian method motivated as regularized loss minimization. Compared to variational inference, it replaces the loss term in the evidence lower bound (ELBO) with the predictive log loss, which is the same loss function used in evaluation. A number of theoretical and empirical results in prior work suggest that DLM can significantly improve over ELBO optimization for some models. However, as we point out in this paper, this is not the case for Bayesian neural networks (BNNs). The paper explores the practical performance of DLM for BNN, the reasons for its failure and its relationship to optimizing the ELBO, uncovering some interesting facts about both algorithms.