# Emergent Structure in the Marginal Attention Space of Language Models

arXiv: https://arxiv.org/abs/2610.03109 · HTML: https://mlsanity.com/paper/2610.03109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 62 of its 72 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 30 of 62)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [DuoAttention: Efficient Long-Context LLM Inference with Retrieval and Streaming Heads](https://mlsanity.com/paper/2410.10819/) (2024)
- [InfiniGen: Efficient Generative Inference of Large Language Models with Dynamic KV Cache Management](https://mlsanity.com/paper/2406.19707/) (2024)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Ada-KV: Optimizing KV Cache Eviction by Adaptive Budget Allocation for Efficient LLM Inference](https://mlsanity.com/paper/2407.11550/) (2024)
- [Retrieval Head Mechanistically Explains Long-Context Factuality](https://mlsanity.com/paper/2404.15574/) (2024)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Interpreting CLIP's Image Representation via Text-Based Decomposition](https://mlsanity.com/paper/2310.05916/) (2023)

## Abstract (arXiv)

While representation similarity across independently trained language models is well-documented, how internal mechanics such as attention behave across models remains far less characterized. Inspired by this gap, we examine the structure of post-softmax attention weights by marginalizing over query positions, mapping them into a joint token-head "marginal attention space". Evaluating across 60+ diverse LLMs, we find that different properties emerge when reducing this space along its token and head axes. When reduced token-wise, marginal attention yields a text-intrinsic signal robustly conserved across models. To explain this property, we empirically connect marginal attention to the input-output Jacobian of the network, and prove theoretically that under a smoothness assumption, models with similar next-token distributions are guaranteed to have similar input-output Jacobian statistics. When reduced head-wise, it forms a model-private signature conserved across documents. Practically, this provides a natural way to estimate a per-head budget for key-value (KV) cache eviction, effectively decoupling model-specific budget allocation from text-intrinsic token scoring. On standard eviction benchmarks, a per-head budget precomputed offline on pretraining text, combined with a training-free token score, shows competitive performance with methods that recompute the budget on every document or train it per target. Code available at https://github.com/Flegyas/marginal-attention