# Shaken, and Stirred: Long-Range Dependencies Enable Robust Outlier Detection with PixelCNN++

arXiv: https://arxiv.org/abs/2208.13579 · HTML: https://mlsanity.com/paper/2208.13579/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 29 Aug 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (2020)
- [A Large-Scale Car Dataset for Fine-Grained Categorization and Verification](https://mlsanity.com/paper/1506.08959/) (2015)
- [Detecting Out-of-Distribution Inputs to Deep Generative Models Using Typicality](https://mlsanity.com/paper/1906.02994/) (2019)
- [The Image Local Autoregressive Transformer](https://mlsanity.com/paper/2106.02514/) (2021)
- [Robust outlier detection by de-biasing VAE likelihoods](https://mlsanity.com/paper/2108.08760/) (2021)

## Built on by (most cited first, 1 of 1)

- [Spatial Autoregressive Modeling of DINOv3 Embeddings for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2603.02974/) (2026)

## Abstract (arXiv)

Reliable outlier detection is critical for real-world deployment of deep learning models. Although extensively studied, likelihoods produced by deep generative models have been largely dismissed as being impractical for outlier detection. First, deep generative model likelihoods are readily biased by low-level input statistics. Second, many recent solutions for correcting these biases are computationally expensive, or do not generalize well to complex, natural datasets. Here, we explore outlier detection with a state-of-the-art deep autoregressive model: PixelCNN++. We show that biases in PixelCNN++ likelihoods arise primarily from predictions based on local dependencies. We propose two families of bijective transformations -- ``stirring'' and ``shaking'' -- which ameliorate low-level biases and isolate the contribution of long-range dependencies to PixelCNN++ likelihoods. These transformations are inexpensive and readily computed at evaluation time. We test our approaches extensively with five grayscale and six natural image datasets and show that they achieve or exceed state-of-the-art outlier detection, particularly on datasets with complex, natural images. We also show that our solutions work well with other types of generative models (generative flows and variational autoencoders) and that their efficacy is governed by each model's reliance on local dependencies. In sum, lightweight remedies suffice to achieve robust outlier detection on image data with deep generative models.