# Visualizing the Diversity of Representations Learned by Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2201.10859 · HTML: https://mlsanity.com/paper/2201.10859/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 65 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [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)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Understanding the Role of Individual Units in a Deep Neural Network](https://mlsanity.com/paper/2009.05041/) (2020)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Synthesizing the preferred inputs for neurons in neural networks via deep generator networks](https://mlsanity.com/paper/1605.09304/) (2016)

## Built on by (most cited first, 4 of 4)

- [Finding the right XAI method -- A Guide for the Evaluation and Ranking of Explainable AI Methods in Climate Science](https://mlsanity.com/paper/2303.00652/) (2023)
- [CoSy: Evaluating Textual Explanations of Neurons](https://mlsanity.com/paper/2405.20331/) (2024)
- [DORA: Exploring Outlier Representations in Deep Neural Networks](https://mlsanity.com/paper/2206.04530/) (2022)
- [Manipulating Feature Visualizations with Gradient Slingshots](https://mlsanity.com/paper/2401.06122/) (2024)

## Abstract (arXiv)

Explainable Artificial Intelligence (XAI) aims to make learning machines less opaque, and offers researchers and practitioners various tools to reveal the decision-making strategies of neural networks. In this work, we investigate how XAI methods can be used for exploring and visualizing the diversity of feature representations learned by Bayesian Neural Networks (BNNs). Our goal is to provide a global understanding of BNNs by making their decision-making strategies a) visible and tangible through feature visualizations and b) quantitatively measurable with a distance measure learned by contrastive learning. Our work provides new insights into the posterior distribution in terms of human-understandable feature information with regard to the underlying decision making strategies. The main findings of our work are the following: 1) global XAI methods can be applied to explain the diversity of decision-making strategies of BNN instances, 2) Monte Carlo dropout with commonly used Dropout rates exhibit increased diversity in feature representations compared to the multimodal posterior approximation of MultiSWAG, 3) the diversity of learned feature representations highly correlates with the uncertainty estimate for the output and 4) the inter-mode diversity of the multimodal posterior decreases as the network width increases, while the intra mode diversity increases. These findings are consistent with the recent Deep Neural Networks theory, providing additional intuitions about what the theory implies in terms of humanly understandable concepts.