Model Utility Law: Evaluating LLMs beyond Performance through Mechanism Interpretable Metric
Yixin Cao, Jiahao Ying, Yaoning Wang, Xipeng Qiu, Xuanjing Huang, Yugang Jiang
TL;DR
This work addresses the evaluation generalization gap for large language models by introducing Model Utilization Index (MUI), a mechanism interpretability metric that quantifies the fraction of a model's activated capabilities during inference to complement traditional performance metrics. It formalizes MUI via neuron-based and sparse autoencoder (SAE) based interpretations, and demonstrates a near-logarithmic inverse relationship—the Utility Law—between MUI and performance across diverse datasets and models. From this law, four corollaries are derived to guide training diagnostics, data contamination detection, fair model comparisons, and data diversity evaluation, with empirical validation on multiple benchmarks and open-source LLMs. The framework enables better interpretation of model capabilities, provides practical guidance for training and data curation, and supports more robust cross-model rankings beyond raw accuracy. The authors also provide code to reproduce their analyses, highlighting practical impact for researchers and practitioners in model evaluation and development.
Abstract
Large Language Models (LLMs) have become indispensable across academia, industry, and daily applications, yet current evaluation methods struggle to keep pace with their rapid development. One core challenge of evaluation in the large language model (LLM) era is the generalization issue: how to infer a model's near-unbounded abilities from inevitably bounded benchmarks. We address this challenge by proposing Model Utilization Index (MUI), a mechanism interpretability enhanced metric that complements traditional performance scores. MUI quantifies the effort a model expends on a task, defined as the proportion of activated neurons or features during inference. Intuitively, a truly capable model should achieve higher performance with lower effort. Extensive experiments across popular LLMs reveal a consistent inverse logarithmic relationship between MUI and performance, which we formulate as the Utility Law. From this law we derive four practical corollaries that (i) guide training diagnostics, (ii) expose data contamination issue, (iii) enable fairer model comparisons, and (iv) design model-specific dataset diversity. Our code can be found at https://github.com/ALEX-nlp/MUI-Eva.