# Emergent Linear Representations in World Models of Self-Supervised Sequence Models

arXiv: https://arxiv.org/abs/2309.00941 · HTML: https://mlsanity.com/paper/2309.00941/

## Key facts

- Cited by 319 papers in the map (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 36 of its 55 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [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)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Understanding the Role of Individual Units in a Deep Neural Network](https://mlsanity.com/paper/2009.05041/) (2020)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Information-Theoretic Probing for Linguistic Structure](https://mlsanity.com/paper/2004.03061/) (2020)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [Compositional Explanations of Neurons](https://mlsanity.com/paper/2006.14032/) (2020)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023)
- [Linearly Mapping from Image to Text Space](https://mlsanity.com/paper/2209.15162/) (2022)
- [Acquisition of Chess Knowledge in AlphaZero](https://mlsanity.com/paper/2111.09259/) (2021)
- [Under the Hood: Using Diagnostic Classifiers to Investigate and Improve how Language Models Track Agreement Information](https://mlsanity.com/paper/1808.08079/) (2018)
- [Residual Connections Encourage Iterative Inference](https://mlsanity.com/paper/1710.04773/) (2017)

## Built on by (most cited first, 30 of 319)

- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders](https://mlsanity.com/paper/2501.17148/) (2025)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicity](https://mlsanity.com/paper/2401.01967/) (2024)
- [Improving Instruction-Following in Language Models through Activation Steering](https://mlsanity.com/paper/2410.12877/) (2024)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [Analyzing the Generalization and Reliability of Steering Vectors](https://mlsanity.com/paper/2407.12404/) (2024)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [Mechanistically analyzing the effects of fine-tuning on procedurally defined tasks](https://mlsanity.com/paper/2311.12786/) (2023)
- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [Uncovering mesa-optimization algorithms in Transformers](https://mlsanity.com/paper/2309.05858/) (2023)
- [Model Organisms for Emergent Misalignment](https://mlsanity.com/paper/2506.11613/) (2025)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching](https://mlsanity.com/paper/2311.17030/) (2023)
- [On the Origins of Linear Representations in Large Language Models](https://mlsanity.com/paper/2403.03867/) (2024)
- [Transformers represent belief state geometry in their residual stream](https://mlsanity.com/paper/2405.15943/) (2024)
- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [The MASK Benchmark: Disentangling Honesty From Accuracy in AI Systems](https://mlsanity.com/paper/2503.03750/) (2025)
- [Convergent Linear Representations of Emergent Misalignment](https://mlsanity.com/paper/2506.11618/) (2025)
- [Improving Activation Steering in Language Models with Mean-Centring](https://mlsanity.com/paper/2312.03813/) (2023)
- [Mind's Eye of LLMs: Visualization-of-Thought Elicits Spatial Reasoning in Large Language Models](https://mlsanity.com/paper/2404.03622/) (2024)
- [Emergent World Models and Latent Variable Estimation in Chess-Playing Language Models](https://mlsanity.com/paper/2403.15498/) (2024)
- [JBShield: Defending Large Language Models from Jailbreak Attacks through Activated Concept Analysis and Manipulation](https://mlsanity.com/paper/2502.07557/) (2025)

## Abstract (arXiv)

How do sequence models represent their decision-making process? Prior work suggests that Othello-playing neural network learned nonlinear models of the board state (Li et al., 2023). In this work, we provide evidence of a closely related linear representation of the board. In particular, we show that probing for "my colour" vs. "opponent's colour" may be a simple yet powerful way to interpret the model's internal state. This precise understanding of the internal representations allows us to control the model's behaviour with simple vector arithmetic. Linear representations enable significant interpretability progress, which we demonstrate with further exploration of how the world model is computed.