How Much Consistency Is Your Accuracy Worth? (2023)

Abstract: Contrast set consistency is a robustness measurement that evaluates the rate at which a model correctly responds to all instances in a bundle of minimally different examples relying on the same knowledge. To draw additional insights, we propose to complement consistency with relative consistency—the probability that an equally accurate model would surpass the consistency of the proposed model, given a distribution over possible consistencies. Models with 100% relative consistency have reached a consistency peak for their accuracy. We reflect on prior work that reports consistency in contrast sets and observe that relative consistency can alter the assessment of a model’s consistency compared to another. We anticipate that our proposed measurement and insights will influence future studies aiming to promote consistent behavior in models.

## introduction annotators introduce data shortcuts that allow models to solve tasks in unintended ways @xcite . in response, it has been proposed to measure whether a model correctly responds to a bundle (or a contrast set) of slightly modified instances that rely on the same knowledge @xcite . the rate at which a model accomplishes this is termed consistency. we propose an additional measurementrelative consistency -that facilitates discussion about achievable consistency scores, enabling a more nuanced comparison. to demonstrate why this is desired, consider situations that are illustrated in the same accuracy. this analysis sheds light on an upside of 1a and a limitation of 1b that might go unnoticed if we solely compare accuracy/consistency. let us turn to examples 1d. although it represents a model with an improved consistency relative to 1a, we could have achieved better consistency for the same accuracy (see 1e). 1 relative consistency ( §2) measures whether the consistency of our model would likely be outper-formed by an equally accurate model, relative to the distribution of possible consistencies; see eq. ( 5 ). specifically, it is the probability that our model's consistency is (in most cases) higher or equal to the consistency scores that are achievable with the same accuracy. if relative consistency is 100% then our model is the most consistent it can be given its accuracy, as a more consistent, equally accurate model exists only with near-zero probability. in practice, the goal should be to increase the "standard consistency" while also achieving 100% relative consistency. in light of this additional consistency metric, in §4 we revisit the findings of three publications that report consistency as a metric for their evaluations and point out some additional conclusions we might draw from these reported consistencies. our code is available at https://github.com/ jacobkj314/relative-consistency . ## relative consistency we first introduce background terminology ( §2.1), then derive elements we need for defining relative consistency: (i) achievable consistency scores for a given accuracy ( §2.2) and (ii) a distribution over achievable consistency scores (2.3). ## analysis with simulated contrastive set suppose you evaluate a model on a contrastive test set containing 100 bundles of 2 instances. the distribution of consistencies for this dataset is shown in figure 1a , with the cdf of that distribution (corresponding to the rc score) in figure 1b . note that the highest-density region of the distribution moves upward as accuracy increases, and takes up only a very thin band. this means that, for a given accuracy, there is generally little room for improvement in consistency. this can be useful when discussing results: if a particular training approach yields a 5% improvement in consistency for an equally accurate model, that represents a substantial change in how the model tends to respond to inputs. it can still happen that improving accuracy and consistency decreases relative consistency. as an example, consider comparing a model m 1 , which achieves @xmath0, @xmath1, 45% consistency) against a model m 2 with @xmath2, @xmath3, 55% consistency). clearly, model m 2 is more desirable for practical uses, if we are just comparing one model to another, but if we are comparing two different training approaches, and want to know which induces a stronger tendency for consistent responses, then we would be interested to know that m 1 has @xmath4.0%, while m 2 has @xmath5.1%. this insight, that one model is below chance consistency, while another is well above, is made possible by the probabilistic interpretation of rc. ## meta-analysis of prior work in this section, we discuss results reported by prior works that conduct evaluation with contrast sets under the light of relative consistency. ## conclusion we introduce relative consistency, which complements standard contrast consistency by allowing an accuracy and consistency score pair to be examined to determine whether a higher consistency was possible with that accuracy. this facilitates the comparison of consistencies achieved by models that achieved different levels of accuracy. we show that relative consistency enriches conclusions we make about whether a model is more consistent than another, and occasionally even leads us to different takeaways.