# Linear Algebraic Structure of Word Senses, with Applications to Polysemy

arXiv: https://arxiv.org/abs/1601.03764 · HTML: https://mlsanity.com/paper/1601.03764/

## Key facts

- Cited by 165 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2016.

## Built on by (most cited first, 30 of 165)

- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders](https://mlsanity.com/paper/2410.20526/) (2024)
- [Modality Competition: What Makes Joint Training of Multi-modal Network Fail in Deep Learning? (Provably)](https://mlsanity.com/paper/2203.12221/) (2022)
- [Toward Understanding the Feature Learning Process of Self-supervised Contrastive Learning](https://mlsanity.com/paper/2105.15134/) (2021)
- [Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)](https://mlsanity.com/paper/2402.10376/) (2024)
- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [Automatically Interpreting Millions of Features in Large Language Models](https://mlsanity.com/paper/2410.13928/) (2024)
- [Transformer visualization via dictionary learning: contextualized embedding as a linear superposition of transformer factors](https://mlsanity.com/paper/2103.15949/) (2021)
- [LLM Social Simulations Are a Promising Research Method](https://mlsanity.com/paper/2504.02234/) (2025)
- [Improving Steering Vectors by Targeting Sparse Autoencoder Features](https://mlsanity.com/paper/2411.02193/) (2024)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [Persona Features Control Emergent Misalignment](https://mlsanity.com/paper/2506.19823/) (2025)
- [Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching](https://mlsanity.com/paper/2311.17030/) (2023)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [On the Origins of Linear Representations in Large Language Models](https://mlsanity.com/paper/2403.03867/) (2024)
- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [Sparse Autoencoders Learn Monosemantic Features in Vision-Language Models](https://mlsanity.com/paper/2504.02821/) (2025)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [InterPLM: Discovering Interpretable Features in Protein Language Models via Sparse Autoencoders](https://mlsanity.com/paper/2412.12101/) (2024)
- [Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometry](https://mlsanity.com/paper/2503.01822/) (2025)
- [From Language Modeling to Instruction Following: Understanding the Behavior Shift in LLMs after Instruction Tuning](https://mlsanity.com/paper/2310.00492/) (2023)
- [Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Models](https://mlsanity.com/paper/2408.00113/) (2024)
- [The Origins of Representation Manifolds in Large Language Models](https://mlsanity.com/paper/2505.18235/) (2025)
- [From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit](https://mlsanity.com/paper/2506.03093/) (2025)
- [Codebook Features: Sparse and Discrete Interpretability for Neural Networks](https://mlsanity.com/paper/2310.17230/) (2023)
- [Usable XAI: 10 Strategies Towards Exploiting Explainability in the LLM Era](https://mlsanity.com/paper/2403.08946/) (2024)
- [Exploring Memorization in Fine-tuned Language Models](https://mlsanity.com/paper/2310.06714/) (2023)

## Abstract (arXiv)

Word embeddings are ubiquitous in NLP and information retrieval, but it is unclear what they represent when the word is polysemous. Here it is shown that multiple word senses reside in linear superposition within the word embedding and simple sparse coding can recover vectors that approximately capture the senses. The success of our approach, which applies to several embedding methods, is mathematically explained using a variant of the random walk on discourses model (Arora et al., 2016). A novel aspect of our technique is that each extracted word sense is accompanied by one of about 2000 "discourse atoms" that gives a succinct description of which other words co-occur with that word sense. Discourse atoms can be of independent interest, and make the method potentially more useful. Empirical tests are used to verify and support the theory.