# Linear Predictability of Attention Heads in Large Language Models

arXiv: https://arxiv.org/abs/2603.13314 · HTML: https://mlsanity.com/paper/2603.13314/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [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)
- [Taming Throughput-Latency Tradeoff in LLM Inference with Sarathi-Serve](https://mlsanity.com/paper/2403.02310/) (2024)
- [Cache Me If You Must: Adaptive Key-Value Quantization for Large Language Models](https://mlsanity.com/paper/2501.19392/) (2025)
- [Lexico: Extreme KV Cache Compression via Sparse Coding over Universal Dictionaries](https://mlsanity.com/paper/2412.08890/) (2024)
- [Layer-wise Pruning of Transformer Attention Heads for Efficient Language Modeling](https://mlsanity.com/paper/2110.03252/) (2021)
- [CHAI: Clustered Head Attention for Efficient LLM Inference](https://mlsanity.com/paper/2403.08058/) (2024)

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

- [Autonomy-of-Heads: Data-Free Sparse Attention from Frozen Query-Key Geometry](https://mlsanity.com/paper/2608.06849/) (2026)

## Abstract (arXiv)

Large language model (LLM) inference is increasingly bottlenecked by the Key-Value (KV) cache, yet the fine-grained structure of attention-head activations remains poorly understood. We show that pretrained Transformers exhibit a pervasive inter-head linear structure: for a given token, the Query, Key, and Value (QKV) vectors of an attention head can often be reconstructed as a linear combination of a small number of peer heads, typically within the same layer. Across Llama-3.1-8B, Falcon3-10B, OLMo-2-7B, and Qwen3-32B, just 2-5 reference heads recover many target heads with high fidelity (e.g., mean R^2 approx 0.76 for Keys on C4 with five references, and frequently R^2 > 0.85 on GSM8K). This predictability is learned rather than architectural: it is largely absent at random initialization, rises rapidly during pretraining as we track through OLMo-2 checkpoints, and is supported by a theoretical lower bound showing high mean-squared error for linear prediction at initialization. We further connect this emergence to increasing intra-layer alignment of Key projection subspaces. Finally, we exploit this redundancy for efficiency by caching only reference-head KV states and reconstructing the remaining heads on the fly via lightweight linear maps, achieving 2x KV-cache reduction with model-dependent accuracy trade-offs (4.5-5.5 percentage point average drop on Falcon3-10B and Qwen3-32B across five benchmarks, and larger drops on Llama-3.1-8B), and we find that reconstructing Keys is substantially less harmful than reconstructing Values.