Recently, Miller et al. showed that a model's in-distribution (ID) accuracy has a strong linear correlation with its out-of-distribution (OOD) accuracy, on several OOD benchmarks, a phenomenon they dubbed ``accuracy-on-the-line''. While a useful tool for model selection (i.e., the model most likely to perform the best OOD is the one with highest ID accuracy), this fact does not help to estimate the actual OOD performance of models without access to a labeled OOD validation set. In this paper, we show a similar surprising phenomena also holds for the agreement between pairs of neural network classifiers: whenever accuracy-on-the-line holds, we observe that the OOD agreement between the predictions of any two pairs of neural networks (with potentially different architectures) also observes a strong linear correlation with their ID agreement. Furthermore, we observe that the slope and bias of OOD vs ID agreement closely matches that of OOD vs ID accuracy. This phenomenon which we call agreement-on-the-line, has important practical applications: without any labeled data, we can predict the OOD accuracy of classifiers, since OOD agreement can be estimated with just unlabeled data. Our prediction algorithm outperforms previous methods both in shifts where agreement-on-the-line holds and, surprisingly, when accuracy is not on the line. This phenomenon also provides new insights into neural networks: unlike accuracy-on-the-line, agreement-on-the-line only appears to hold for neural network classifiers.

Estimating the out-of-distribution performance in regimes where labels are scarce is critical to safely deploy foundation models. Recently, it was shown that ensembles of neural networks observe the phenomena "agreement-on-the-line", which can be leveraged to reliably predict OOD performance without labels. However, in contrast to classical neural networks that are trained on in-distribution data from scratch for numerous epochs, foundation models undergo minimal finetuning from heavily pretrained weights, which may reduce the ensemble diversity needed to observe agreement-on-the-line. In our work, we demonstrate that when lightly finetuning multiple runs from a \textit{single} foundation model, the choice of randomness during training (linear head initialization, data ordering, and data subsetting) can lead to drastically different levels of agreement-on-the-line in the resulting ensemble. Surprisingly, only random head initialization is able to reliably induce agreement-on-the-line in finetuned foundation models across vision and language benchmarks. Second, we demonstrate that ensembles of \textit{multiple} foundation models pretrained on different datasets but finetuned on the same task can also show agreement-on-the-line.

Recently, Miller et al. showed that a model's in-distribution (ID) accuracy has a strong linear correlation with its out-of-distribution (OOD) accuracy, on several OOD benchmarks, a phenomenon they dubbed accuracy-on-the-line''. While a useful tool for model selection (i.e., the model most likely to perform the best OOD is the one with highest ID accuracy), this fact does not help to estimate the actual OOD performance of models without access to a labeled OOD validation set. In this paper, we show a similar surprising phenomena also holds for the agreement between pairs of neural network classifiers: whenever accuracy-on-the-line holds, we observe that the OOD agreement between the predictions of any two pairs of neural networks (with potentially different architectures) also observes a strong linear correlation with their ID agreement. Furthermore, we observe that the slope and bias of OOD vs ID agreement closely matches that of OOD vs ID accuracy. This phenomenon which we call agreement-on-the-line, has important practical applications: without any labeled data, we can predict the OOD accuracy of classifiers, since OOD agreement can be estimated with just unlabeled data.

Test-time adaptation (TTA) methods aim to improve robustness to distribution shifts by adapting models using unlabeled data from the shifted test distribution. However, there remain unresolved challenges that undermine the reliability of TTA, which include difficulties in evaluating TTA performance, miscalibration after TTA, and unreliable hyperparameter tuning for adaptation. In this work, we make a notable and surprising observation that TTAed models strongly show the agreement-on-the-line phenomenon (Baek et al., 2022) across a wide range of distribution shifts. We find such linear trends occur consistently in a wide range of models adapted with various hyperparameters, and persist in distributions where the phenomenon fails to hold in vanilla models (i.e., before adaptation). We leverage these observations to make TTA methods more reliable in three perspectives: (i) estimating OOD accuracy (without labeled data) to determine when TTA helps and when it hurts, (ii) calibrating TTAed models without label information, and (iii) reliably determining hyperparameters for TTA without any labeled validation data. Through extensive experiments, we demonstrate that various TTA methods can be precisely evaluated, both in terms of their improvements and degradations. Moreover, our proposed methods on unsupervised calibration and hyperparameters tuning for TTA achieve results close to the ones assuming access to ground-truth labels, in terms of both OOD accuracy and calibration error.