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Main Authors: Budd, Jeremy, Ideami, Javier, Rynne, Benjamin Macdowall, Duggar, Keith, Balestriero, Randall
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.11836
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author Budd, Jeremy
Ideami, Javier
Rynne, Benjamin Macdowall
Duggar, Keith
Balestriero, Randall
author_facet Budd, Jeremy
Ideami, Javier
Rynne, Benjamin Macdowall
Duggar, Keith
Balestriero, Randall
contents Sparse autoencoders (SAEs) have received considerable recent attention as tools for mechanistic interpretability, showing success at extracting interpretable features even from very large LLMs. However, this research has been largely empirical, and there have been recent doubts about the true utility of SAEs. In this work, we seek to enhance the theoretical understanding of SAEs, using the spline theory of deep learning. By situating SAEs in this framework: we discover that SAEs generalise ``$k$-means autoencoders'' to be piecewise affine, but sacrifice accuracy for interpretability vs. the optimal ``$k$-means-esque plus local principal component analysis (PCA)'' piecewise affine autoencoder. We characterise the underlying geometry of (TopK) SAEs using power diagrams. And we develop a novel proximal alternating method SGD (PAM-SGD) algorithm for training SAEs, with both solid theoretical foundations and promising empirical results in MNIST and LLM experiments, particularly in sample efficiency and (in the LLM setting) improved sparsity of codes. All code is available at: https://github.com/splInterp2025/splInterp
format Preprint
id arxiv_https___arxiv_org_abs_2505_11836
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle SplInterp: Improving our Understanding and Training of Sparse Autoencoders
Budd, Jeremy
Ideami, Javier
Rynne, Benjamin Macdowall
Duggar, Keith
Balestriero, Randall
Machine Learning
Artificial Intelligence
68T07, 65D07
Sparse autoencoders (SAEs) have received considerable recent attention as tools for mechanistic interpretability, showing success at extracting interpretable features even from very large LLMs. However, this research has been largely empirical, and there have been recent doubts about the true utility of SAEs. In this work, we seek to enhance the theoretical understanding of SAEs, using the spline theory of deep learning. By situating SAEs in this framework: we discover that SAEs generalise ``$k$-means autoencoders'' to be piecewise affine, but sacrifice accuracy for interpretability vs. the optimal ``$k$-means-esque plus local principal component analysis (PCA)'' piecewise affine autoencoder. We characterise the underlying geometry of (TopK) SAEs using power diagrams. And we develop a novel proximal alternating method SGD (PAM-SGD) algorithm for training SAEs, with both solid theoretical foundations and promising empirical results in MNIST and LLM experiments, particularly in sample efficiency and (in the LLM setting) improved sparsity of codes. All code is available at: https://github.com/splInterp2025/splInterp
title SplInterp: Improving our Understanding and Training of Sparse Autoencoders
topic Machine Learning
Artificial Intelligence
68T07, 65D07
url https://arxiv.org/abs/2505.11836