# Measuring Feature Sparsity in Language Models

arXiv: https://arxiv.org/abs/2310.07837 · HTML: https://mlsanity.com/paper/2310.07837/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 11 Oct 2023.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [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)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [YOLOv7: Trainable bag-of-freebies sets new state-of-the-art for real-time object detectors](https://mlsanity.com/paper/2207.02696/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [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)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [CLIP-Dissect: Automatic Description of Neuron Representations in Deep Vision Networks](https://mlsanity.com/paper/2204.10965/) (2022)
- [Well-Read Students Learn Better: On the Importance of Pre-training Compact Models](https://mlsanity.com/paper/1908.08962/) (2019)
- [Transformer visualization via dictionary learning: contextualized embedding as a linear superposition of transformer factors](https://mlsanity.com/paper/2103.15949/) (2021)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Interpreting Language Models with Contrastive Explanations](https://mlsanity.com/paper/2202.10419/) (2022)
- [Understanding and Improving Interpolation in Autoencoders via an Adversarial Regularizer](https://mlsanity.com/paper/1807.07543/) (2018)
- [Polysemanticity and Capacity in Neural Networks](https://mlsanity.com/paper/2210.01892/) (2022)
- [Generalization in NLI: Ways (Not) To Go Beyond Simple Heuristics](https://mlsanity.com/paper/2110.01518/) (2021)
- [Sparse Overcomplete Word Vector Representations](https://mlsanity.com/paper/1506.02004/) (2015)
- [Interpreting the Latent Space of Generative Adversarial Networks using Supervised Learning](https://mlsanity.com/paper/2102.12139/) (2021)

## Built on by (most cited first, 3 of 3)

- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Unboxing the Black Box: Mechanistic Interpretability for Algorithmic Understanding of Neural Networks](https://mlsanity.com/paper/2511.19265/) (2025)
- [Correcting Influence: Unboxing LLM Outputs with Orthogonal Latent Spaces](https://mlsanity.com/paper/2605.12809/) (2026)

## Abstract (arXiv)

Recent works have proposed that activations in language models can be modelled as sparse linear combinations of vectors corresponding to features of input text. Under this assumption, these works aimed to reconstruct feature directions using sparse coding. We develop metrics to assess the success of these sparse coding techniques and test the validity of the linearity and sparsity assumptions. We show our metrics can predict the level of sparsity on synthetic sparse linear activations, and can distinguish between sparse linear data and several other distributions. We use our metrics to measure levels of sparsity in several language models. We find evidence that language model activations can be accurately modelled by sparse linear combinations of features, significantly more so than control datasets. We also show that model activations appear to be sparsest in the first and final layers.