Test-Time Adaptation Induces Stronger Accuracy and Agreement-on-the-Line

TL;DR

Test-time adaptation significantly enhances the correlation between in-distribution and out-of-distribution accuracy and agreement, enabling more reliable OOD performance estimation and model selection without labeled data.

Contribution

This paper demonstrates that recent TTA methods strengthen accuracy-on-the-line and agreement-on-the-line trends, even under challenging distribution shifts, and explains the underlying theoretical conditions.

Findings

TTA improves OOD performance and strengthens ACL and AGL trends.

TTA causes data distribution to collapse into a single scaling variable in feature space.

Combining TTA with AGL allows high-precision OOD performance estimation.

Abstract

Recently, Miller et al. (2021) and Baek et al. (2022) empirically demonstrated strong linear correlations between in-distribution (ID) versus out-of-distribution (OOD) accuracy and agreement. These trends, coined accuracy-on-the-line (ACL) and agreement-on-the-line (AGL), enable OOD model selection and performance estimation without labeled data. However, these phenomena also break for certain shifts, such as CIFAR10-C Gaussian Noise, posing a critical bottleneck. In this paper, we make a key finding that recent test-time adaptation (TTA) methods not only improve OOD performance, but drastically strengthen the ACL and AGL trends in models, even in shifts where models showed very weak correlations before. To analyze this, we revisit the theoretical conditions from Miller et al. (2021) that outline the types of distribution shifts needed for perfect ACL in linear models. Surprisingly, these conditions are satisfied after applying TTA to deep models in the penultimate feature embedding space. In particular, TTA causes the data distribution to collapse complex shifts into those can be expressed by a singular scaling variable in the feature space. Our results show that by combining TTA with AGL-based estimation methods, we can estimate the OOD performance of models with high precision for a broader set of distribution shifts. This lends us a simple system for selecting the best hyperparameters and adaptation strategy without any OOD labeled data.