# Compute Optimal Inference and Provable Amortisation Gap in Sparse Autoencoders

arXiv: https://arxiv.org/abs/2411.13117 · HTML: https://mlsanity.com/paper/2411.13117/

## Key facts

- Cited by 18 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 38 references that are in the map.
- First posted on arXiv 20 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)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [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)
- [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)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networks](https://mlsanity.com/paper/2207.13243/) (2022)
- [Iterative Amortized Inference](https://mlsanity.com/paper/1807.09356/) (2018)
- [On Interpretability of Artificial Neural Networks: A Survey](https://mlsanity.com/paper/2001.02522/) (2020)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [Interpreting Attention Layer Outputs with Sparse Autoencoders](https://mlsanity.com/paper/2406.17759/) (2024)
- [The Missing Curve Detectors of InceptionV1: Applying Sparse Autoencoders to InceptionV1 Early Vision](https://mlsanity.com/paper/2406.03662/) (2024)
- [A Survey on Understanding, Visualizations, and Explanation of Deep Neural Networks](https://mlsanity.com/paper/2102.01792/) (2021)
- [Identifying Interpretable Visual Features in Artificial and Biological Neural Systems](https://mlsanity.com/paper/2310.11431/) (2023)

## Built on by (most cited first, 18 of 18)

- [From superposition to sparse codes: interpretable representations in neural networks](https://mlsanity.com/paper/2503.01824/) (2025)
- [Position: Mechanistic Interpretability Should Prioritize Feature Consistency in SAEs](https://mlsanity.com/paper/2505.20254/) (2025)
- [SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data](https://mlsanity.com/paper/2602.14687/) (2026)
- [AbsTopK: Rethinking Sparse Autoencoders For Bidirectional Features](https://mlsanity.com/paper/2510.00404/) (2025)
- [Stop Probing, Start Coding: Why Linear Probes and Sparse Autoencoders Fail at Compositional Generalisation](https://mlsanity.com/paper/2603.28744/) (2026)
- [Superposition disentanglement of neural representations reveals hidden alignment](https://mlsanity.com/paper/2510.03186/) (2025)
- [Are Sparse Autoencoder Benchmarks Reliable?](https://mlsanity.com/paper/2605.18229/) (2026)
- [Resurrecting the Salmon: Rethinking Mechanistic Interpretability with Domain-Specific Sparse Autoencoders](https://mlsanity.com/paper/2508.09363/) (2025)
- [The Rate-Distortion-Polysemanticity Tradeoff in SAEs](https://mlsanity.com/paper/2605.14694/) (2026)
- [MedSAE: Dissecting MedCLIP Representations with Sparse Autoencoders](https://mlsanity.com/paper/2510.26411/) (2025)
- [Kronecker Factorization Improves Efficiency and Interpretability of Sparse Autoencoders](https://mlsanity.com/paper/2505.22255/) (2025)
- [Towards Atoms of Large Language Models](https://mlsanity.com/paper/2509.20784/) (2025)
- [Equivariant Sparse Autoencoders: Mechanistic Interpretability of Neural Networks on Symmetric Data](https://mlsanity.com/paper/2511.09432/) (2025)
- [Similarity of Neural Network Representations in Superposition](https://mlsanity.com/paper/2604.00208/) (2026)
- [Sign-Aware Gated Sparse Autoencoders: Modeling Anticorrelated Features with Bi-Jump-ReLU Activations](https://mlsanity.com/paper/2605.28149/) (2026)
- [How Optimality Structures Sparse Dictionaries: Theory for Interpreting SAE Representations](https://mlsanity.com/paper/2606.02385/) (2026)
- [Interference Beyond Geometry in Concept Extraction](https://mlsanity.com/paper/2609.35351/) (2026)
- [The Independence Prior of SAEs Fragments Visual Concepts](https://mlsanity.com/paper/2610.04112/) (2026)

## Abstract (arXiv)

A recent line of work has shown promise in using sparse autoencoders (SAEs) to uncover interpretable features in neural network representations. However, the simple linear-nonlinear encoding mechanism in SAEs limits their ability to perform accurate sparse inference. Using compressed sensing theory, we prove that an SAE encoder is inherently insufficient for accurate sparse inference, even in solvable cases. We then decouple encoding and decoding processes to empirically explore conditions where more sophisticated sparse inference methods outperform traditional SAE encoders. Our results reveal substantial performance gains with minimal compute increases in correct inference of sparse codes. We demonstrate this generalises to SAEs applied to large language models, where more expressive encoders achieve greater interpretability. This work opens new avenues for understanding neural network representations and analysing large language model activations.