LLM-as-a-judge methods are widely used for evaluating the quality of generated open-ended text. Such evaluations are generally multi-dimensional, since the error patterns in texts can be different for different dimensions. Therefore, reliable LLM judges should evaluate each target dimension independently. To quantify the extent to which LLM judges depend on non-target dimensions when evaluating a target dimension, i.e., inter-dimension dependence, we propose CorrGap. To measure this, CorrGap uses the difference in correlations between LLM-predicted scores and ground truth scores across different groups of texts. Using CorrGap, we show that inter-dimension dependence is pervasive across LLM judges in open-ended text evaluation tasks. To mitigate inter-dimension dependence, we propose DimCheck, a method that iteratively removes unrelated evidence from COTs generated by LLM judges in a step-wise way. We show that DimCheck mitigates inter-dimension dependence and outperforms strong baselines across three LLMs and four tasks. We also show that smaller trained LLMs can approximate larger LLMs in DimCheck, with much lower inference costs.

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