# Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning

arXiv: https://arxiv.org/abs/2405.12241 · HTML: https://mlsanity.com/paper/2405.12241/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 17 May 2024.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 14 of 14)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Causal Mediation Analysis for Interpreting Neural NLP: The Case of Gender Bias](https://mlsanity.com/paper/2004.12265/) (2020)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Causal Analysis of Syntactic Agreement Mechanisms in Neural Language Models](https://mlsanity.com/paper/2106.06087/) (2021)
- [Transformer visualization via dictionary learning: contextualized embedding as a linear superposition of transformer factors](https://mlsanity.com/paper/2103.15949/) (2021)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [SPINE: SParse Interpretable Neural Embeddings](https://mlsanity.com/paper/1711.08792/) (2017)
- [Codebook Features: Sparse and Discrete Interpretability for Neural Networks](https://mlsanity.com/paper/2310.17230/) (2023)
- [Sparse Overcomplete Word Vector Representations](https://mlsanity.com/paper/1506.02004/) (2015)

## Built on by (most cited first, 30 of 67)

- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)
- [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (2025)
- [Efficient Dictionary Learning with Switch Sparse Autoencoders](https://mlsanity.com/paper/2410.08201/) (2024)
- [Mathematical Models of Computation in Superposition](https://mlsanity.com/paper/2408.05451/) (2024)
- [Evaluating Open-Source Sparse Autoencoders on Disentangling Factual Knowledge in GPT-2 Small](https://mlsanity.com/paper/2409.04478/) (2024)
- [Interpreting the linear structure of vision-language model embedding spaces](https://mlsanity.com/paper/2504.11695/) (2025)
- [InterpBench: Semi-Synthetic Transformers for Evaluating Mechanistic Interpretability Techniques](https://mlsanity.com/paper/2407.14494/) (2024)
- [Mechanistic?](https://mlsanity.com/paper/2410.09087/) (2024)
- [The Quest for the Right Mediator: Surveying Mechanistic Interpretability Through the Lens of Causal Mediation Analysis](https://mlsanity.com/paper/2408.01416/) (2024)
- [Residual Stream Analysis with Multi-Layer SAEs](https://mlsanity.com/paper/2409.04185/) (2024)
- [Analyzing (In)Abilities of SAEs via Formal Languages](https://mlsanity.com/paper/2410.11767/) (2024)
- [Decoding Dark Matter: Specialized Sparse Autoencoders for Interpreting Rare Concepts in Foundation Models](https://mlsanity.com/paper/2411.00743/) (2024)
- [On the Limits of Sparse Autoencoders: A Theoretical Framework and Reweighted Remedy](https://mlsanity.com/paper/2506.15963/) (2025)
- [Monet: Mixture of Monosemantic Experts for Transformers](https://mlsanity.com/paper/2412.04139/) (2024)
- [I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?](https://mlsanity.com/paper/2503.08980/) (2025)
- [Diversity-driven Data Selection for Language Model Tuning through Sparse Autoencoder](https://mlsanity.com/paper/2502.14050/) (2025)
- [Predictive Concept Decoders: Training Scalable End-to-End Interpretability Assistants](https://mlsanity.com/paper/2512.15712/) (2025)
- [Jacobian Sparse Autoencoders: Sparsify Computations, Not Just Activations](https://mlsanity.com/paper/2502.18147/) (2025)
- [Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safety](https://mlsanity.com/paper/2506.05451/) (2025)
- [HyperDAS: Towards Automating Mechanistic Interpretability with Hypernetworks](https://mlsanity.com/paper/2503.10894/) (2025)
- [Low-Rank Adapting Models for Sparse Autoencoders](https://mlsanity.com/paper/2501.19406/) (2025)
- [Superposition as Lossy Compression: Measure with Sparse Autoencoders and Connect to Adversarial Vulnerability](https://mlsanity.com/paper/2512.13568/) (2025)
- [Sparse Feature Coactivation Reveals Causal Semantic Modules in Large Language Models](https://mlsanity.com/paper/2506.18141/) (2025)
- [Crosscoding Through Time: Tracking Emergence & Consolidation Of Linguistic Representations Throughout LLM Pretraining](https://mlsanity.com/paper/2509.05291/) (2025)

## Abstract (arXiv)

Identifying the features learned by neural networks is a core challenge in mechanistic interpretability. Sparse autoencoders (SAEs), which learn a sparse, overcomplete dictionary that reconstructs a network's internal activations, have been used to identify these features. However, SAEs may learn more about the structure of the datatset than the computational structure of the network. There is therefore only indirect reason to believe that the directions found in these dictionaries are functionally important to the network. We propose end-to-end (e2e) sparse dictionary learning, a method for training SAEs that ensures the features learned are functionally important by minimizing the KL divergence between the output distributions of the original model and the model with SAE activations inserted. Compared to standard SAEs, e2e SAEs offer a Pareto improvement: They explain more network performance, require fewer total features, and require fewer simultaneously active features per datapoint, all with no cost to interpretability. We explore geometric and qualitative differences between e2e SAE features and standard SAE features. E2e dictionary learning brings us closer to methods that can explain network behavior concisely and accurately. We release our library for training e2e SAEs and reproducing our analysis at https://github.com/ApolloResearch/e2e_sae