# Understanding out-of-distribution accuracies through quantifying difficulty of test samples

arXiv: https://arxiv.org/abs/2203.15100 · HTML: https://mlsanity.com/paper/2203.15100/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 29 of 29)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [Gradient Starvation: A Learning Proclivity in Neural Networks](https://mlsanity.com/paper/2011.09468/) (2020)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [Do CIFAR-10 Classifiers Generalize to CIFAR-10?](https://mlsanity.com/paper/1806.00451/) (2018)
- [Partial success in closing the gap between human and machine vision](https://mlsanity.com/paper/2106.07411/) (2021)
- [Deep Learning Through the Lens of Example Difficulty](https://mlsanity.com/paper/2106.09647/) (2021)
- [Assessing Generalization of SGD via Disagreement](https://mlsanity.com/paper/2106.13799/) (2021)
- [Are Convolutional Neural Networks or Transformers more like human vision?](https://mlsanity.com/paper/2105.07197/) (2021)
- [Estimating Example Difficulty Using Variance of Gradients](https://mlsanity.com/paper/2008.11600/) (2020)
- [Scaling description of generalization with number of parameters in deep learning](https://mlsanity.com/paper/1901.01608/) (2019)
- [The Evolution of Out-of-Distribution Robustness Throughout Fine-Tuning](https://mlsanity.com/paper/2106.15831/) (2021)
- [Comparing Dynamics: Deep Neural Networks versus Glassy Systems](https://mlsanity.com/paper/1803.06969/) (2018)
- [Why do classifier accuracies show linear trends under distribution shift?](https://mlsanity.com/paper/2012.15483/) (2020)
- [What classifiers know what they don't?](https://mlsanity.com/paper/2107.06217/) (2021)

## Built on by (most cited first, 3 of 3)

- [Feedback-guided Data Synthesis for Imbalanced Classification](https://mlsanity.com/paper/2310.00158/) (2023)
- [Simplicity Bias Leads to Amplified Performance Disparities](https://mlsanity.com/paper/2212.06641/) (2022)
- [Error Discovery by Clustering Influence Embeddings](https://mlsanity.com/paper/2312.04712/) (2023)

## Abstract (arXiv)

Existing works show that although modern neural networks achieve remarkable generalization performance on the in-distribution (ID) dataset, the accuracy drops significantly on the out-of-distribution (OOD) datasets citerecht2018cifar, recht2019imagenet. To understand why a variety of models consistently make more mistakes in the OOD datasets, we propose a new metric to quantify the difficulty of the test images (either ID or OOD) that depends on the interaction of the training dataset and the model. In particular, we introduce textitconfusion score as a label-free measure of image difficulty which quantifies the amount of disagreement on a given test image based on the class conditional probabilities estimated by an ensemble of trained models. Using the confusion score, we investigate CIFAR-10 and its OOD derivatives. Next, by partitioning test and OOD datasets via their confusion scores, we predict the relationship between ID and OOD accuracies for various architectures. This allows us to obtain an estimator of the OOD accuracy of a given model only using ID test labels. Our observations indicate that the biggest contribution to the accuracy drop comes from images with high confusion scores. Upon further inspection, we report on the nature of the misclassified images grouped by their confusion scores: textit(i) images with high confusion scores contain textitweak spurious correlations that appear in multiple classes in the training data and lack clear textitclass-specific features, and textit(ii) images with low confusion scores exhibit spurious correlations that belong to another class, namely textitclass-specific spurious correlations.