# Bayesian Metric Learning for Uncertainty Quantification in Image Retrieval

arXiv: https://arxiv.org/abs/2302.01332 · HTML: https://mlsanity.com/paper/2302.01332/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 53 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Fine-tuning CNN Image Retrieval with No Human Annotation](https://mlsanity.com/paper/1711.02512/) (2017)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Deep Face Recognition: A Survey](https://mlsanity.com/paper/1804.06655/) (2018)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Probabilistic Embeddings for Cross-Modal Retrieval](https://mlsanity.com/paper/2101.05068/) (2021)
- [Data Uncertainty Learning in Face Recognition](https://mlsanity.com/paper/2003.11339/) (2020)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [Polysemous Visual-Semantic Embedding for Cross-Modal Retrieval](https://mlsanity.com/paper/1906.04402/) (2019)
- [BackPACK: Packing more into backprop](https://mlsanity.com/paper/1912.10985/) (2019)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [Modeling Uncertainty with Hedged Instance Embedding](https://mlsanity.com/paper/1810.00319/) (2018)
- [View-Invariant Probabilistic Embedding for Human Pose](https://mlsanity.com/paper/1912.01001/) (2019)
- [Bayesian Triplet Loss: Uncertainty Quantification in Image Retrieval](https://mlsanity.com/paper/2011.12663/) (2020)
- [Hotels-50K: A Global Hotel Recognition Dataset](https://mlsanity.com/paper/1901.11397/) (2019)
- [Laplacian Autoencoders for Learning Stochastic Representations](https://mlsanity.com/paper/2206.15078/) (2022)
- [Unsupervised Data Uncertainty Learning in Visual Retrieval Systems](https://mlsanity.com/paper/1902.02586/) (2019)
- [Learning Concept Embeddings with Combined Human-Machine Expertise](https://mlsanity.com/paper/1509.07479/) (2015)

## Built on by (most cited first, 10 of 10)

- [Improved Probabilistic Image-Text Representations](https://mlsanity.com/paper/2305.18171/) (2023)
- [Reparameterization invariance in approximate Bayesian inference](https://mlsanity.com/paper/2406.03334/) (2024)
- [VIKING: Deep variational inference with stochastic projections](https://mlsanity.com/paper/2510.23684/) (2025)
- [Towards certifiable AI in aviation: landscape, challenges, and opportunities](https://mlsanity.com/paper/2409.08666/) (2024)
- [Corpus-informed Retrieval Augmented Generation of Clarifying Questions](https://mlsanity.com/paper/2409.18575/) (2024)
- [Quantifying the uncertainty of model-based synthetic image quality metrics](https://mlsanity.com/paper/2504.03623/) (2025)
- [UncertainGen: Uncertainty-Aware Representations of DNA Sequences for Metagenomic Binning](https://mlsanity.com/paper/2509.26116/) (2025)
- [PEdger++: Practical Edge Detection via Assembling Cross Information](https://mlsanity.com/paper/2508.11961/) (2025)
- [Uncertainty-Aware Subset Selection for Robust Visual Explainability under Distribution Shifts](https://mlsanity.com/paper/2512.08445/) (2025)
- [Contrastive Linearized Laplace: Loss Geometry, Valid Repairs, and Reliable Cores](https://mlsanity.com/paper/2610.14875/) (2026)

## Abstract (arXiv)

We propose the first Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We actualize this by first proving that the contrastive loss is a valid log-posterior. We then propose three methods that ensure a positive definite Hessian. Lastly, we present a novel decomposition of the Generalized Gauss-Newton approximation. Empirically, we show that our Laplacian Metric Learner (LAM) estimates well-calibrated uncertainties, reliably detects out-of-distribution examples, and yields state-of-the-art predictive performance.