Information-Theoretic Evaluation of Free-Text Rationales with Conditional $\mathcal{V}$-Information

Free-text rationales are a promising step towards explainable AI, yet their evaluation remains an open research problem. While existing metrics have mostly focused on measuring the direct association between the rationale and a given label, we argue that an ideal metric should also be able to focus on the new information uniquely provided in the rationale that is otherwise not provided in the input or the label. We investigate this research problem from an information-theoretic perspective using the conditional $\mathcal{V}$-information \citep{hewitt-etal-2021-conditional}. More concretely, we propose a metric called REV (Rationale Evaluation with conditional $\mathcal{V}$-information), that can quantify the new information in a rationale supporting a given label beyond the information already available in the input or the label. Experiments on reasoning tasks across four benchmarks, including few-shot prompting with GPT-3, demonstrate the effectiveness of REV in evaluating different types of rationale-label pairs, compared to existing metrics. Through several quantitative comparisons, we demonstrate the capability of REV in providing more sensitive measurements of new information in free-text rationales with respect to a label. Furthermore, REV is consistent with human judgments on rationale evaluations. Overall, when used alongside traditional performance metrics, REV provides deeper insights into a models' reasoning and prediction processes.