# Performance Law of Large Language Models

arXiv: https://arxiv.org/abs/2408.09895 · HTML: https://mlsanity.com/paper/2408.09895/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [LLaMA-MoE: Building Mixture-of-Experts from LLaMA with Continual Pre-training](https://mlsanity.com/paper/2406.16554/) (2024)
- [Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabularies](https://mlsanity.com/paper/2407.13623/) (2024)
- [Understanding Emergent Abilities of Language Models from the Loss Perspective](https://mlsanity.com/paper/2403.15796/) (2024)
- [How predictable is language model benchmark performance?](https://mlsanity.com/paper/2401.04757/) (2024)
- [How Predictable Are Large Language Model Capabilities? A Case Study on BIG-bench](https://mlsanity.com/paper/2305.14947/) (2023)

## Built on by (most cited first, 6 of 6)

- [Sparsing Law: Towards Large Language Models with Greater Activation Sparsity](https://mlsanity.com/paper/2411.02335/) (2024)
- [From Prompts to Power: Measuring the Energy Footprint of LLM Inference](https://mlsanity.com/paper/2511.05597/) (2025)
- [Research Superalignment Should Advance Now with Alternating Competence and Conformity Optimization](https://mlsanity.com/paper/2503.07660/) (2025)
- [Model Hemorrhage and the Robustness Limits of Large Language Models](https://mlsanity.com/paper/2503.23924/) (2025)
- [FormuLLA: A Large Language Model Approach to Generating Novel 3D Printable Formulations](https://mlsanity.com/paper/2601.02071/) (2026)
- [The Chicken and Egg Dilemma: Co-optimizing Data and Model Configurations for LLMs](https://mlsanity.com/paper/2602.08351/) (2026)

## Abstract (arXiv)

Guided by the belief of the scaling law, large language models (LLMs) have achieved impressive performance in recent years. However, scaling law only gives a qualitative estimation of loss, which is influenced by various factors such as model architectures, data distributions, tokenizers, and computation precision. Thus, estimating the real performance of LLMs with different training settings rather than loss may be quite useful in practical development. In this article, we present an empirical equation named "Performance Law" to directly predict the MMLU score of an LLM, which is a widely used metric to indicate the general capability of LLMs in real-world conversations and applications. Based on only a few key hyperparameters of the LLM architecture and the size of training data, we obtain a quite accurate MMLU prediction of various LLMs with diverse sizes and architectures developed by different organizations in different years. Performance law can be used to guide the choice of LLM architecture and the effective allocation of computational resources without extensive experiments.