# Jacobian Sparse Autoencoders: Sparsify Computations, Not Just Activations

arXiv: https://arxiv.org/abs/2502.18147 · HTML: https://mlsanity.com/paper/2502.18147/

## Key facts

- Cited by 10 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 31 of its 44 references that are in the map.
- First posted on arXiv 25 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [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)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model](https://mlsanity.com/paper/2305.00586/) (2023)
- [Transcoders Find Interpretable LLM Feature Circuits](https://mlsanity.com/paper/2406.11944/) (2024)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [Automatically Interpreting Millions of Features in Large Language Models](https://mlsanity.com/paper/2410.13928/) (2024)
- [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024)
- [Transformer visualization via dictionary learning: contextualized embedding as a linear superposition of transformer factors](https://mlsanity.com/paper/2103.15949/) (2021)
- [Steering Language Model Refusal with Sparse Autoencoders](https://mlsanity.com/paper/2411.11296/) (2024)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [Applying sparse autoencoders to unlearn knowledge in language models](https://mlsanity.com/paper/2410.19278/) (2024)
- [Large Language Models Share Representations of Latent Grammatical Concepts Across Typologically Diverse Languages](https://mlsanity.com/paper/2501.06346/) (2025)
- [Interpreting Attention Layer Outputs with Sparse Autoencoders](https://mlsanity.com/paper/2406.17759/) (2024)
- [Automated Interpretability Metrics Do Not Distinguish Trained and Random Transformers](https://mlsanity.com/paper/2501.17727/) (2025)
- [Quantifying Feature Space Universality Across Large Language Models via Sparse Autoencoders](https://mlsanity.com/paper/2410.06981/) (2024)
- [Residual Stream Analysis with Multi-Layer SAEs](https://mlsanity.com/paper/2409.04185/) (2024)
- [JumpReLU: A Retrofit Defense Strategy for Adversarial Attacks](https://mlsanity.com/paper/1904.03750/) (2019)
- [Evolution of SAE Features Across Layers in LLMs](https://mlsanity.com/paper/2410.08869/) (2024)

## Built on by (most cited first, 10 of 10)

- [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (2025)
- [Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safety](https://mlsanity.com/paper/2506.05451/) (2025)
- [Transformers Don't Need LayerNorm at Inference Time: Scaling LayerNorm Removal to GPT-2 XL and the Implications for Mechanistic Interpretability](https://mlsanity.com/paper/2507.02559/) (2025)
- [Towards Interpretability Without Sacrifice: Faithful Dense Layer Decomposition with Mixture of Decoders](https://mlsanity.com/paper/2505.21364/) (2025)
- [Rhetorical Questions in LLM Representations: A Linear Probing Study](https://mlsanity.com/paper/2604.14128/) (2026)
- [WriteSAE: Sparse Autoencoders for Recurrent State](https://mlsanity.com/paper/2605.12770/) (2026)
- [SCALAR: Benchmarking SAE Interaction Sparsity in Toy LLMs](https://mlsanity.com/paper/2511.07572/) (2025)
- [Hierarchical Sparse Circuit Extraction from Billion-Parameter Language Models through Scalable Attribution Graph Decomposition](https://mlsanity.com/paper/2601.12879/) (2026)
- [Diverse Dictionary Learning](https://mlsanity.com/paper/2604.17568/) (2026)
- [From Latent Space to Jacobian Space: Measuring, Evading, and Training Against Safety-Content Accessibility](https://mlsanity.com/paper/2610.04316/) (2026)

## Abstract (arXiv)

Sparse autoencoders (SAEs) have been successfully used to discover sparse and human-interpretable representations of the latent activations of LLMs. However, we would ultimately like to understand the computations performed by LLMs and not just their representations. The extent to which SAEs can help us understand computations is unclear because they are not designed to "sparsify" computations in any sense, only latent activations. To solve this, we propose Jacobian SAEs (JSAEs), which yield not only sparsity in the input and output activations of a given model component but also sparsity in the computation (formally, the Jacobian) connecting them. With a na"ive implementation, the Jacobians in LLMs would be computationally intractable due to their size. One key technical contribution is thus finding an efficient way of computing Jacobians in this setup. We find that JSAEs extract a relatively large degree of computational sparsity while preserving downstream LLM performance approximately as well as traditional SAEs. We also show that Jacobians are a reasonable proxy for computational sparsity because MLPs are approximately linear when rewritten in the JSAE basis. Lastly, we show that JSAEs achieve a greater degree of computational sparsity on pre-trained LLMs than on the equivalent randomized LLM. This shows that the sparsity of the computational graph appears to be a property that LLMs learn through training, and suggests that JSAEs might be more suitable for understanding learned transformer computations than standard SAEs.