# Language Models Implement Simple Word2Vec-style Vector Arithmetic

arXiv: https://arxiv.org/abs/2305.16130 · HTML: https://mlsanity.com/paper/2305.16130/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [The Bottom-up Evolution of Representations in the Transformer: A Study with Machine Translation and Language Modeling Objectives](https://mlsanity.com/paper/1909.01380/) (2019)
- [Knowledgeable or Educated Guess? Revisiting Language Models as Knowledge Bases](https://mlsanity.com/paper/2106.09231/) (2021)
- [Residual Connections Encourage Iterative Inference](https://mlsanity.com/paper/1710.04773/) (2017)
- [Inducing Relational Knowledge from BERT](https://mlsanity.com/paper/1911.12753/) (2019)
- [When Can Models Learn From Explanations? A Formal Framework for Understanding the Roles of Explanation Data](https://mlsanity.com/paper/2102.02201/) (2021)
- [Rethinking the Role of Scale for In-Context Learning: An Interpretability-based Case Study at 66 Billion Scale](https://mlsanity.com/paper/2212.09095/) (2022)
- [Discovering Latent Concepts Learned in BERT](https://mlsanity.com/paper/2205.07237/) (2022)
- [Towards falsifiable interpretability research](https://mlsanity.com/paper/2010.12016/) (2020)
- [Analyzing Commonsense Emergence in Few-shot Knowledge Models](https://mlsanity.com/paper/2101.00297/) (2021)
- [Static Embeddings as Efficient Knowledge Bases?](https://mlsanity.com/paper/2104.07094/) (2021)

## Built on by (most cited first, 30 of 98)

- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Circuit Component Reuse Across Tasks in Transformer Language Models](https://mlsanity.com/paper/2310.08744/) (2023)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries](https://mlsanity.com/paper/2406.12775/) (2024)
- [Successor Heads: Recurring, Interpretable Attention Heads In The Wild](https://mlsanity.com/paper/2312.09230/) (2023)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [The Semantic Hub Hypothesis: Language Models Share Semantic Representations Across Languages and Modalities](https://mlsanity.com/paper/2411.04986/) (2024)
- [Knowledge Circuits in Pretrained Transformers](https://mlsanity.com/paper/2405.17969/) (2024)
- [Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Models](https://mlsanity.com/paper/2310.14491/) (2023)
- [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)
- [From Tokens to Words: On the Inner Lexicon of LLMs](https://mlsanity.com/paper/2410.05864/) (2024)
- [Rigorously Assessing Natural Language Explanations of Neurons](https://mlsanity.com/paper/2309.10312/) (2023)
- [Pre-trained Large Language Models Use Fourier Features to Compute Addition](https://mlsanity.com/paper/2406.03445/) (2024)
- [Locate-then-edit for Multi-hop Factual Recall under Knowledge Editing](https://mlsanity.com/paper/2410.06331/) (2024)
- [Finding and Editing Multi-Modal Neurons in Pre-Trained Transformers](https://mlsanity.com/paper/2311.07470/) (2023)
- [Answer, Assemble, Ace: Understanding How LMs Answer Multiple Choice Questions](https://mlsanity.com/paper/2407.15018/) (2024)
- [M2IV: Towards Efficient and Fine-grained Multimodal In-Context Learning via Representation Engineering](https://mlsanity.com/paper/2504.04633/) (2025)
- [The Same But Different: Structural Similarities and Differences in Multilingual Language Modeling](https://mlsanity.com/paper/2410.09223/) (2024)
- [LLMs as Hackers: Autonomous Linux Privilege Escalation Attacks](https://mlsanity.com/paper/2310.11409/) (2023)
- [Optimal ablation for interpretability](https://mlsanity.com/paper/2409.09951/) (2024)
- [On Linear Representations and Pretraining Data Frequency in Language Models](https://mlsanity.com/paper/2504.12459/) (2025)
- [DecoderLens: Layerwise Interpretation of Encoder-Decoder Transformers](https://mlsanity.com/paper/2310.03686/) (2023)
- [Position: Understanding LLMs Requires More Than Statistical Generalization](https://mlsanity.com/paper/2405.01964/) (2024)
- [Paths Not Taken: Understanding and Mending the Multilingual Factual Recall Pipeline](https://mlsanity.com/paper/2505.20546/) (2025)
- [BiasEdit: Debiasing Stereotyped Language Models via Model Editing](https://mlsanity.com/paper/2503.08588/) (2025)

## Abstract (arXiv)

A primary criticism towards language models (LMs) is their inscrutability. This paper presents evidence that, despite their size and complexity, LMs sometimes exploit a simple vector arithmetic style mechanism to solve some relational tasks using regularities encoded in the hidden space of the model (e.g., Poland:Warsaw::China:Beijing). We investigate a range of language model sizes (from 124M parameters to 176B parameters) in an in-context learning setting, and find that for a variety of tasks (involving capital cities, uppercasing, and past-tensing) a key part of the mechanism reduces to a simple additive update typically applied by the feedforward (FFN) networks. We further show that this mechanism is specific to tasks that require retrieval from pretraining memory, rather than retrieval from local context. Our results contribute to a growing body of work on the interpretability of LMs, and offer reason to be optimistic that, despite the massive and non-linear nature of the models, the strategies they ultimately use to solve tasks can sometimes reduce to familiar and even intuitive algorithms.