# Identifying Linear Relational Concepts in Large Language Models

arXiv: https://arxiv.org/abs/2311.08968 · HTML: https://mlsanity.com/paper/2311.08968/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Understanding Neural Networks Through Deep Visualization](https://mlsanity.com/paper/1506.06579/) (2015)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [Causal Analysis of Syntactic Agreement Mechanisms in Neural Language Models](https://mlsanity.com/paper/2106.06087/) (2021)

## Built on by (most cited first, 12 of 12)

- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Understanding and Patching Compositional Reasoning in LLMs](https://mlsanity.com/paper/2402.14328/) (2024)
- [On Linear Representations and Pretraining Data Frequency in Language Models](https://mlsanity.com/paper/2504.12459/) (2025)
- [Linear Representations of Hierarchical Concepts in Language Models](https://mlsanity.com/paper/2604.07886/) (2026)
- [From Tokens to Lattices: Emergent Lattice Structures in Language Models](https://mlsanity.com/paper/2504.08778/) (2025)
- [Geospatial Mechanistic Interpretability of Large Language Models](https://mlsanity.com/paper/2505.03368/) (2025)
- [A Comprehensive Evaluation of Semantic Relation Knowledge of Pretrained Language Models and Humans](https://mlsanity.com/paper/2412.01131/) (2024)
- [The Structure of Relation Decoding Linear Operators in Large Language Models](https://mlsanity.com/paper/2510.26543/) (2025)
- [Behavior and Representation in Open-Weight Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selection](https://mlsanity.com/paper/2512.13374/) (2025)
- [Correcting Influence: Unboxing LLM Outputs with Orthogonal Latent Spaces](https://mlsanity.com/paper/2605.12809/) (2026)
- [Task Matrices: Linear Maps for Cross-Model Finetuning Transfer](https://mlsanity.com/paper/2512.14880/) (2025)
- [Relational Linear Properties in Language Models: An Empirical Investigation](https://mlsanity.com/paper/2605.22532/) (2026)

## Abstract (arXiv)

Transformer language models (LMs) have been shown to represent concepts as directions in the latent space of hidden activations. However, for any human-interpretable concept, how can we find its direction in the latent space? We present a technique called linear relational concepts (LRC) for finding concept directions corresponding to human-interpretable concepts by first modeling the relation between subject and object as a linear relational embedding (LRE). We find that inverting the LRE and using earlier object layers results in a powerful technique for finding concept directions that outperforms standard black-box probing classifiers. We evaluate LRCs on their performance as concept classifiers as well as their ability to causally change model output.