# Linearity of Relation Decoding in Transformer Language Models

arXiv: https://arxiv.org/abs/2308.09124 · HTML: https://mlsanity.com/paper/2308.09124/

## Key facts

- Cited by 200 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [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)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [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)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [How Much Knowledge Can You Pack Into the Parameters of a Language Model?](https://mlsanity.com/paper/2002.08910/) (2020)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [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)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [Analysis Methods in Neural Language Processing: A Survey](https://mlsanity.com/paper/1812.08951/) (2018)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Information-Theoretic Probing with Minimum Description Length](https://mlsanity.com/paper/2003.12298/) (2020)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [What do Neural Machine Translation Models Learn about Morphology?](https://mlsanity.com/paper/1704.03471/) (2017)
- [Inspecting and Editing Knowledge Representations in Language Models](https://mlsanity.com/paper/2304.00740/) (2023)
- [Language Models Implement Simple Word2Vec-style Vector Arithmetic](https://mlsanity.com/paper/2305.16130/) (2023)
- [Jump to Conclusions: Short-Cutting Transformers With Linear Transformations](https://mlsanity.com/paper/2303.09435/) (2023)
- [Crawling the Internal Knowledge-Base of Language Models](https://mlsanity.com/paper/2301.12810/) (2023)

## Built on by (most cited first, 30 of 200)

- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicity](https://mlsanity.com/paper/2401.01967/) (2024)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [A Comprehensive Study of Knowledge Editing for Large Language Models](https://mlsanity.com/paper/2401.01286/) (2024)
- [Future Lens: Anticipating Subsequent Tokens from a Single Hidden State](https://mlsanity.com/paper/2311.04897/) (2023)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [How do Language Models Bind Entities in Context?](https://mlsanity.com/paper/2310.17191/) (2023)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [Attention Satisfies: A Constraint-Satisfaction Lens on Factual Errors of Language Models](https://mlsanity.com/paper/2309.15098/) (2023)
- [SelfIE: Self-Interpretation of Large Language Model Embeddings](https://mlsanity.com/paper/2403.10949/) (2024)
- [Attention Heads of Large Language Models: A Survey](https://mlsanity.com/paper/2409.03752/) (2024)
- [Knowledge Circuits in Pretrained Transformers](https://mlsanity.com/paper/2405.17969/) (2024)
- [Activation Oracles: Training and Evaluating LLMs as General-Purpose Activation Explainers](https://mlsanity.com/paper/2512.15674/) (2025)
- [LatentQA: Teaching LLMs to Decode Activations Into Natural Language](https://mlsanity.com/paper/2412.08686/) (2024)
- [Do language models plan ahead for future tokens?](https://mlsanity.com/paper/2404.00859/) (2024)
- [From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit](https://mlsanity.com/paper/2506.03093/) (2025)
- [Lost in Multilinguality: Dissecting Cross-lingual Factual Inconsistency in Transformer Language Models](https://mlsanity.com/paper/2504.04264/) (2025)
- [On Large Language Models' Hallucination with Regard to Known Facts](https://mlsanity.com/paper/2403.20009/) (2024)
- [Monitoring Latent World States in Language Models with Propositional Probes](https://mlsanity.com/paper/2406.19501/) (2024)
- [Summing Up the Facts: Additive Mechanisms Behind Factual Recall in LLMs](https://mlsanity.com/paper/2402.07321/) (2024)
- [Who's asking? User personas and the mechanics of latent misalignment](https://mlsanity.com/paper/2406.12094/) (2024)
- [Estimating Knowledge in Large Language Models Without Generating a Single Token](https://mlsanity.com/paper/2406.12673/) (2024)
- [Mechanistic Understanding and Mitigation of Language Model Non-Factual Hallucinations](https://mlsanity.com/paper/2403.18167/) (2024)

## Abstract (arXiv)

Much of the knowledge encoded in transformer language models (LMs) may be expressed in terms of relations: relations between words and their synonyms, entities and their attributes, etc. We show that, for a subset of relations, this computation is well-approximated by a single linear transformation on the subject representation. Linear relation representations may be obtained by constructing a first-order approximation to the LM from a single prompt, and they exist for a variety of factual, commonsense, and linguistic relations. However, we also identify many cases in which LM predictions capture relational knowledge accurately, but this knowledge is not linearly encoded in their representations. Our results thus reveal a simple, interpretable, but heterogeneously deployed knowledge representation strategy in transformer LMs.