# Entropy Meets Importance: A Unified Head Importance-Entropy Score for Stable and Efficient Transformer Pruning

arXiv: https://arxiv.org/abs/2510.13832 · HTML: https://mlsanity.com/paper/2510.13832/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 81 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 30 of 61)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [MM-Vet: Evaluating Large Multimodal Models for Integrated Capabilities](https://mlsanity.com/paper/2308.02490/) (2023)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)

## Built on by (most cited first, 1 of 1)

- [Sparse Growing Transformer: Training-Time Sparse Depth Allocation via Progressive Attention Looping](https://mlsanity.com/paper/2603.23998/) (2026)

## Abstract (arXiv)

Transformer-based models have achieved remarkable performance in NLP tasks. However, their structural characteristics-multiple layers and attention heads-introduce efficiency challenges in inference and deployment. To address these challenges, various pruning methods have recently been proposed. Notably, gradient-based methods using Head Importance Scores (HIS) have gained traction for interpretability, efficiency, and ability to identify redundant heads. However, HIS alone has limitations as it captures only the gradient-driven contribution, overlooking the diversity of attention patterns. To overcome these limitations, we introduce a novel pruning criterion, HIES (Head Importance-Entropy Score), which integrates head importance scores with attention entropy, providing complementary evidence on per-head contribution. Empirically, HIES-based pruning yields up to 15.2% improvement in model quality and 2.04x improvement in stability over HIS-only methods, enabling substantial model compression without sacrificing either accuracy or stability. Code will be released upon publication.