# Contribution Weights: A Geometrical Analysis of Self-Attention Transformers

arXiv: https://arxiv.org/abs/2606.07604 · HTML: https://mlsanity.com/paper/2606.07604/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 33 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Vision Transformers Need Registers](https://mlsanity.com/paper/2309.16588/) (2023)
- [ERASER: A Benchmark to Evaluate Rationalized NLP Models](https://mlsanity.com/paper/1911.03429/) (2019)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [The Unreasonable Ineffectiveness of the Deeper Layers](https://mlsanity.com/paper/2403.17887/) (2024)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [Why do LLMs attend to the first token?](https://mlsanity.com/paper/2504.02732/) (2025)
- [The elephant in the interpretability room: Why use attention as explanation when we have saliency methods?](https://mlsanity.com/paper/2010.05607/) (2020)
- [A Simple and Effective L2 Norm-Based Strategy for KV Cache Compression](https://mlsanity.com/paper/2406.11430/) (2024)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [Attention Score is not All You Need for Token Importance Indicator in KV Cache Reduction: Value Also Matters](https://mlsanity.com/paper/2406.12335/) (2024)
- [Spectral Filters, Dark Signals, and Attention Sinks](https://mlsanity.com/paper/2402.09221/) (2024)
- [Active-Dormant Attention Heads: Mechanistically Demystifying Extreme-Token Phenomena in LLMs](https://mlsanity.com/paper/2410.13835/) (2024)
- [Incorporating Residual and Normalization Layers into Analysis of Masked Language Models](https://mlsanity.com/paper/2109.07152/) (2021)
- [Understanding the Skill Gap in Recurrent Language Models: The Role of the Gather-and-Aggregate Mechanism](https://mlsanity.com/paper/2504.18574/) (2025)
- [Attention Meets Post-hoc Interpretability: A Mathematical Perspective](https://mlsanity.com/paper/2402.03485/) (2024)
- [OrthoRank: Token Selection via Sink Token Orthogonality for Efficient LLM inference](https://mlsanity.com/paper/2507.03865/) (2025)
- [From Memorization to Reasoning in the Spectrum of Loss Curvature](https://mlsanity.com/paper/2510.24256/) (2025)

## Abstract (arXiv)

Analyzing attention weights has become a standard approach for interpreting the information flow of Large Language Models (LLMs). However, this approach has significant limitations as it neglects the geometric properties of the value vectors being aggregated. To address this gap, we introduce Contribution Weights, a projection-based metric that quantifies a token's influence by accounting for it's attention weight, value magnitude, and directional alignment with the layer output. We demonstrate that contribution weights provide a more faithful measure of token importance, consistently outperforming attention-based metrics in identifying semantically critical tokens across different decoder-only models, tasks, and datasets. Further, our metric enables novel mechanistic analysis of attention sinks. While previous work characterized sinks as passive repositories for excess attention, we reveal they serve an active functional role, suppressing information through a convex relationship between sink rate and output norm, stabilizing representations by opposing the semantic drift of low-confidence tokens.