# Demystifying Disagreement-on-the-Line in High Dimensions

arXiv: https://arxiv.org/abs/2301.13371 · HTML: https://mlsanity.com/paper/2301.13371/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 128 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 30 of 41)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)
- [Hidden Stratification Causes Clinically Meaningful Failures in Machine Learning for Medical Imaging](https://mlsanity.com/paper/1909.12475/) (2019)
- [Linearized two-layers neural networks in high dimension](https://mlsanity.com/paper/1904.12191/) (2019)
- [High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation](https://mlsanity.com/paper/2205.01445/) (2022)
- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [Leveraging Unlabeled Data to Predict Out-of-Distribution Performance](https://mlsanity.com/paper/2201.04234/) (2022)
- [Learning curves of generic features maps for realistic datasets with a teacher-student model](https://mlsanity.com/paper/2102.08127/) (2021)
- [Assessing Generalization of SGD via Disagreement](https://mlsanity.com/paper/2106.13799/) (2021)
- [Predicting with Confidence on Unseen Distributions](https://mlsanity.com/paper/2107.03315/) (2021)
- [The Gaussian equivalence of generative models for learning with shallow neural networks](https://mlsanity.com/paper/2006.14709/) (2020)
- [Are Labels Always Necessary for Classifier Accuracy Evaluation?](https://mlsanity.com/paper/2007.02915/) (2020)
- [The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalization](https://mlsanity.com/paper/2008.06786/) (2020)
- [On the Optimal Weighted ℓ2 Regularization in Overparameterized Linear Regression](https://mlsanity.com/paper/2006.05800/) (2020)
- [Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift](https://mlsanity.com/paper/2206.13089/) (2022)
- [Understanding Double Descent Requires a Fine-Grained Bias-Variance Decomposition](https://mlsanity.com/paper/2011.03321/) (2020)
- [Universality of empirical risk minimization](https://mlsanity.com/paper/2202.08832/) (2022)
- [Let's Agree to Agree: Neural Networks Share Classification Order on Real Datasets](https://mlsanity.com/paper/1905.10854/) (2019)
- [Detecting Errors and Estimating Accuracy on Unlabeled Data with Self-training Ensembles](https://mlsanity.com/paper/2106.15728/) (2021)
- [Distributional Generalization: A New Kind of Generalization](https://mlsanity.com/paper/2009.08092/) (2020)
- [Near-Optimal Linear Regression under Distribution Shift](https://mlsanity.com/paper/2106.12108/) (2021)

## Built on by (most cited first, 12 of 12)

- [Strong Model Collapse](https://mlsanity.com/paper/2410.04840/) (2024)
- [A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networks](https://mlsanity.com/paper/2310.07891/) (2023)
- [Test-Time Adaptation Induces Stronger Accuracy and Agreement-on-the-Line](https://mlsanity.com/paper/2310.04941/) (2023)
- [Monitoring Risks in Test-Time Adaptation](https://mlsanity.com/paper/2507.08721/) (2025)
- [Accuracy on the wrong line: On the pitfalls of noisy data for out-of-distribution generalisation](https://mlsanity.com/paper/2406.19049/) (2024)
- [Spurious Correlations in High Dimensional Regression: The Roles of Regularization, Simplicity Bias and Over-Parameterization](https://mlsanity.com/paper/2502.01347/) (2025)
- [Asymptotic Analysis of Two-Layer Neural Networks after One Gradient Step under Gaussian Mixtures Data with Structure](https://mlsanity.com/paper/2503.00856/) (2025)
- [A Law of Data Reconstruction for Random Features (and Beyond)](https://mlsanity.com/paper/2509.22214/) (2025)
- [Signal-Plus-Noise Decomposition of Nonlinear Spiked Random Matrix Models](https://mlsanity.com/paper/2405.18274/) (2024)
- [Implicit Regularization Paths of Weighted Neural Representations](https://mlsanity.com/paper/2408.15784/) (2024)
- [auto-fpt: Automating Free Probability Theory Calculations for Machine Learning Theory](https://mlsanity.com/paper/2504.10754/) (2025)
- [Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent](https://mlsanity.com/paper/2605.17767/) (2026)

## Abstract (arXiv)

Evaluating the performance of machine learning models under distribution shift is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackle this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain; and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression; and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings.