# Adaptive Sparse Allocation with Mutual Choice & Feature Choice Sparse Autoencoders

arXiv: https://arxiv.org/abs/2411.02124 · HTML: https://mlsanity.com/paper/2411.02124/

## Key facts

- Cited by 9 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 15 of its 34 references that are in the map.
- First posted on arXiv 4 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, 15 of 15)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Models](https://mlsanity.com/paper/2408.00113/) (2024)
- [Sparse Modeling for Image and Vision Processing](https://mlsanity.com/paper/1411.3230/) (2014)
- [Routers in Vision Mixture of Experts: An Empirical Study](https://mlsanity.com/paper/2401.15969/) (2024)
- [Rethinking Conventional Wisdom in Machine Learning: From Generalization to Scaling](https://mlsanity.com/paper/2409.15156/) (2024)
- [Interpretability as Compression: Reconsidering SAE Explanations of Neural Activations with MDL-SAEs](https://mlsanity.com/paper/2410.11179/) (2024)
- [Adaptive Computation with Elastic Input Sequence](https://mlsanity.com/paper/2301.13195/) (2023)
- [JumpReLU: A Retrofit Defense Strategy for Adversarial Attacks](https://mlsanity.com/paper/1904.03750/) (2019)

## Built on by (most cited first, 9 of 9)

- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data](https://mlsanity.com/paper/2602.14687/) (2026)
- [LLM Interpretability with Identifiable Temporal-Instantaneous Representation](https://mlsanity.com/paper/2509.23323/) (2025)
- [Revisiting End-To-End Sparse Autoencoder Training: A Short Finetune Is All You Need](https://mlsanity.com/paper/2503.17272/) (2025)
- [Beyond Input Activations: Identifying Influential Latents by Gradient Sparse Autoencoders](https://mlsanity.com/paper/2505.08080/) (2025)
- [Unveiling Decision-Making in LLMs for Text Classification : Extraction of influential and interpretable concepts with Sparse Autoencoders](https://mlsanity.com/paper/2506.23951/) (2025)
- [Sparsification and Reconstruction from the Perspective of Representation Geometry](https://mlsanity.com/paper/2505.22506/) (2025)
- [Feature Starvation as Geometric Instability in Sparse Autoencoders](https://mlsanity.com/paper/2605.05341/) (2026)

## Abstract (arXiv)

Sparse autoencoders (SAEs) are a promising approach to extracting features from neural networks, enabling model interpretability as well as causal interventions on model internals. SAEs generate sparse feature representations using a sparsifying activation function that implicitly defines a set of token-feature matches. We frame the token-feature matching as a resource allocation problem constrained by a total sparsity upper bound. For example, TopK SAEs solve this allocation problem with the additional constraint that each token matches with at most k features. In TopK SAEs, the k active features per token constraint is the same across tokens, despite some tokens being more difficult to reconstruct than others. To address this limitation, we propose two novel SAE variants, Feature Choice SAEs and Mutual Choice SAEs, which each allow for a variable number of active features per token. Feature Choice SAEs solve the sparsity allocation problem under the additional constraint that each feature matches with at most m tokens. Mutual Choice SAEs solve the unrestricted allocation problem where the total sparsity budget can be allocated freely between tokens and features. Additionally, we introduce a new auxiliary loss function, mathttauxzipfloss, which generalises the mathttauxkloss to mitigate dead and underutilised features. Our methods result in SAEs with fewer dead features and improved reconstruction loss at equivalent sparsity levels as a result of the inherent adaptive computation. More accurate and scalable feature extraction methods provide a path towards better understanding and more precise control of foundation models.