# Model Utility Law: Evaluating LLMs beyond Performance through Mechanism Interpretable Metric

arXiv: https://arxiv.org/abs/2504.07440 · HTML: https://mlsanity.com/paper/2504.07440/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 33 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Builds on (most cited first, 26 of 26)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [How do Large Language Models Handle Multilingualism?](https://mlsanity.com/paper/2402.18815/) (2024)
- [Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders](https://mlsanity.com/paper/2410.20526/) (2024)
- [Finding Skill Neurons in Pre-trained Transformer-based Language Models](https://mlsanity.com/paper/2211.07349/) (2022)
- [Towards Understanding Safety Alignment: A Mechanistic Perspective from Safety Neurons](https://mlsanity.com/paper/2406.14144/) (2024)
- [Finding and Editing Multi-Modal Neurons in Pre-Trained Transformers](https://mlsanity.com/paper/2311.07470/) (2023)
- [Automating Dataset Updates Towards Reliable and Timely Evaluation of Large Language Models](https://mlsanity.com/paper/2402.11894/) (2024)

## Built on by (most cited first, 11 of 11)

- [Toward Generalizable Evaluation in the LLM Era: A Survey Beyond Benchmarks](https://mlsanity.com/paper/2504.18838/) (2025)
- [Disentangling Language and Culture for Evaluating Multilingual Large Language Models](https://mlsanity.com/paper/2505.24635/) (2025)
- [Do LLMs Signal When They're Right? Evidence from Neuron Agreement](https://mlsanity.com/paper/2510.26277/) (2025)
- [EffiEval: Efficient and Generalizable Model Evaluation via Capability Coverage Maximization](https://mlsanity.com/paper/2508.09662/) (2025)
- [Beyond Benchmarks: Understanding Mixture-of-Experts Models through Internal Mechanisms](https://mlsanity.com/paper/2509.23933/) (2025)
- [NEX: Neuron Explore-Exploit Scoring for Label-Free Chain-of-Thought Selection and Model Ranking](https://mlsanity.com/paper/2602.05805/) (2026)
- [Does the Same Token Mean the Same State? MoE Routing as Signal for Reasoning Control](https://mlsanity.com/paper/2606.22798/) (2026)
- [Opening the Black Box: A Survey on the Mechanisms of Multi-Step Reasoning in Large Language Models](https://mlsanity.com/paper/2601.14270/) (2026)
- [Neuron-Aware Data Selection for Annotation-Free LLM Self-Distillation](https://mlsanity.com/paper/2607.02460/) (2026)
- [Demographic Prompting at Scale: When More Attributes Hurt LLM--Human Agreement](https://mlsanity.com/paper/2607.10590/) (2026)
- [Belief-Trajectory Energy: Measuring the Path to a Prediction](https://mlsanity.com/paper/2610.05114/) (2026)

## Abstract (arXiv)

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.