# Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning

arXiv: https://arxiv.org/abs/2411.10397 · HTML: https://mlsanity.com/paper/2411.10397/

## Key facts

- Cited by 5 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 11 of its 23 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Placed in

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

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

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Models](https://mlsanity.com/paper/2408.00113/) (2024)
- [Evaluating Synthetic Activations composed of SAE Latents in GPT-2](https://mlsanity.com/paper/2409.15019/) (2024)
- [Investigating Sensitive Directions in GPT-2: An Improved Baseline and Comparative Analysis of SAEs](https://mlsanity.com/paper/2410.12555/) (2024)

## Built on by (most cited first, 5 of 5)

- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [Dialogue Is Not Enough to Make a Communicative BabyLM (But Neither Is Developmentally Inspired Reinforcement Learning)](https://mlsanity.com/paper/2510.20358/) (2025)
- [Low-Rank Adapting Models for Sparse Autoencoders](https://mlsanity.com/paper/2501.19406/) (2025)
- [When Do Concepts Become Functionally Sufficient During Language-Model Training?](https://mlsanity.com/paper/2608.15323/) (2026)
- [Gradient Atoms: Unsupervised Discovery, Attribution and Steering of Model Behaviors via Sparse Decomposition of Training Gradients](https://mlsanity.com/paper/2603.14665/) (2026)

## Abstract (arXiv)

Sparse Autoencoders (SAEs) are a promising approach for extracting neural network representations by learning a sparse and overcomplete decomposition of the network's internal activations. However, SAEs are traditionally trained considering only activation values and not the effect those activations have on downstream computations. This limits the information available to learn features, and biases the autoencoder towards neglecting features which are represented with small activation values but strongly influence model outputs. To address this, we introduce Gradient SAEs (g-SAEs), which modify the k-sparse autoencoder architecture by augmenting the TopK activation function to rely on the gradients of the input activation when selecting the k elements. For a given sparsity level, g-SAEs produce reconstructions that are more faithful to original network performance when propagated through the network. Additionally, we find evidence that g-SAEs learn latents that are on average more effective at steering models in arbitrary contexts. By considering the downstream effects of activations, our approach leverages the dual nature of neural network features as both textitrepresentations, retrospectively, and textitactions, prospectively. While previous methods have approached the problem of feature discovery primarily focused on the former aspect, g-SAEs represent a step towards accounting for the latter as well.