# Gaussian Latent Representations for Uncertainty Estimation using Mahalanobis Distance in Deep Classifiers

arXiv: https://arxiv.org/abs/2305.13849 · HTML: https://mlsanity.com/paper/2305.13849/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [Why is the Mahalanobis Distance Effective for Anomaly Detection?](https://mlsanity.com/paper/2003.00402/) (2020)

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

- [Probabilistic Embeddings for Frozen Vision-Language Models: Uncertainty Quantification with Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2505.05163/) (2025)
- [Adversarially Robust Out-of-Distribution Detection Using Lyapunov-Stabilized Embeddings](https://mlsanity.com/paper/2410.10744/) (2024)
- [Leveraging Intermediate Representations for Better Out-of-Distribution Detection](https://mlsanity.com/paper/2502.12849/) (2025)
- [Distance-informed Neural Processes](https://mlsanity.com/paper/2508.18903/) (2025)
- [ZClassifier: Temperature Tuning and Manifold Approximation via KL Divergence on Logit Space](https://mlsanity.com/paper/2507.10638/) (2025)
- [Towards Robust Artificial Intelligence: Self-Supervised Learning Approach for Out-of-Distribution Detection](https://mlsanity.com/paper/2510.12713/) (2025)
- [Uncertainty-aware Physics-informed Neural Networks for Robust CARS-to-Raman Signal Reconstruction](https://mlsanity.com/paper/2511.13185/) (2025)
- [From Calibration to Refinement: Seeking Certainty via Probabilistic Evidence Propagation for Noisy-Label Person Re-Identification](https://mlsanity.com/paper/2602.23133/) (2026)
- [Ranked Activation Shift for Post-Hoc Out-of-Distribution Detection](https://mlsanity.com/paper/2604.08572/) (2026)
- [ADAPTOOD: Uncertainty-Aware Fine-Tuning for Out-of-Distribution ECG Time Series Models](https://mlsanity.com/paper/2606.04164/) (2026)

## Abstract (arXiv)

Recent works show that the data distribution in a network's latent space is useful for estimating classification uncertainty and detecting Out-of-distribution (OOD) samples. To obtain a well-regularized latent space that is conducive for uncertainty estimation, existing methods bring in significant changes to model architectures and training procedures. In this paper, we present a lightweight, fast, and high-performance regularization method for Mahalanobis distance-based uncertainty prediction, and that requires minimal changes to the network's architecture. To derive Gaussian latent representation favourable for Mahalanobis Distance calculation, we introduce a self-supervised representation learning method that separates in-class representations into multiple Gaussians. Classes with non-Gaussian representations are automatically identified and dynamically clustered into multiple new classes that are approximately Gaussian. Evaluation on standard OOD benchmarks shows that our method achieves state-of-the-art results on OOD detection with minimal inference time, and is very competitive on predictive probability calibration. Finally, we show the applicability of our method to a real-life computer vision use case on microorganism classification.