# Adversarial Examples, Uncertainty, and Transfer Testing Robustness in Gaussian Process Hybrid Deep Networks

arXiv: https://arxiv.org/abs/1707.02476 · HTML: https://mlsanity.com/paper/1707.02476/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2017.

## Built on by (most cited first, 30 of 48)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
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- [Sparse Uncertainty Representation in Deep Learning with Inducing Weights](https://mlsanity.com/paper/2105.14594/) (2021)
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- [Mitigating Transformer Overconfidence via Lipschitz Regularization](https://mlsanity.com/paper/2306.06849/) (2023)
- [DeepAdversaries: Examining the Robustness of Deep Learning Models for Galaxy Morphology Classification](https://mlsanity.com/paper/2112.14299/) (2021)
- [Uncertainty Estimation for Multi-view Data: The Power of Seeing the Whole Picture](https://mlsanity.com/paper/2210.02676/) (2022)
- [A Hierarchical Spatial Transformer for Massive Point Samples in Continuous Space](https://mlsanity.com/paper/2311.04434/) (2023)
- [Revisiting Kernel Attention with Correlated Gaussian Process Representation](https://mlsanity.com/paper/2502.20525/) (2025)
- [Interpretable Uncertainty Quantification in AI for HEP](https://mlsanity.com/paper/2208.03284/) (2022)
- [Probabilistic Circuits That Know What They Don't Know](https://mlsanity.com/paper/2302.06544/) (2023)
- [Key Technology Considerations in Developing and Deploying Machine Learning Models in Clinical Radiology Practice](https://mlsanity.com/paper/2102.01979/) (2021)
- [Towards Adversarial Patch Analysis and Certified Defense against Crowd Counting](https://mlsanity.com/paper/2104.10868/) (2021)
- [Deep Kernel Learning of Dynamical Models from High-Dimensional Noisy Data](https://mlsanity.com/paper/2208.12975/) (2022)
- [Guided Deep Kernel Learning](https://mlsanity.com/paper/2302.09574/) (2023)
- [Adversarial Robustness Guarantees for Gaussian Processes](https://mlsanity.com/paper/2104.03180/) (2021)
- [Stochastic-Shield: A Probabilistic Approach Towards Training-Free Adversarial Defense in Quantized CNNs](https://mlsanity.com/paper/2105.06512/) (2021)
- [Uncertainty-Aware Time-to-Event Prediction using Deep Kernel Accelerated Failure Time Models](https://mlsanity.com/paper/2107.12250/) (2021)
- [Adversarial Attack for Uncertainty Estimation: Identifying Critical Regions in Neural Networks](https://mlsanity.com/paper/2107.07618/) (2021)
- [On Attacking Out-Domain Uncertainty Estimation in Deep Neural Networks](https://mlsanity.com/paper/2210.02191/) (2022)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Calibrated simplex-mapping classification](https://mlsanity.com/paper/2103.02926/) (2021)

## Abstract (arXiv)

Deep neural networks (DNNs) have excellent representative power and are state of the art classifiers on many tasks. However, they often do not capture their own uncertainties well making them less robust in the real world as they overconfidently extrapolate and do not notice domain shift. Gaussian processes (GPs) with RBF kernels on the other hand have better calibrated uncertainties and do not overconfidently extrapolate far from data in their training set. However, GPs have poor representational power and do not perform as well as DNNs on complex domains. In this paper we show that GP hybrid deep networks, GPDNNs, (GPs on top of DNNs and trained end-to-end) inherit the nice properties of both GPs and DNNs and are much more robust to adversarial examples. When extrapolating to adversarial examples and testing in domain shift settings, GPDNNs frequently output high entropy class probabilities corresponding to essentially "don't know". GPDNNs are therefore promising as deep architectures that know when they don't know.