用样条理论解析稀疏自编码器，提升可解释性与训练效率
SplInterp: Improving our Understanding and Training of Sparse Autoencoders
- 基于样条理论揭示SAE为分段仿射模型，类比k-means但牺牲精度换可解释性
- 提出PAM-SGD算法，在MNIST和LLM上实现更高效训练与更高稀疏性编码
- 通过幂图刻画拓扑结构，为理解SAE提供几何视角，适合可解释性研究者
稀疏自编码器（SAEs）近年来在机制可解释性研究中备受关注，能在大型语言模型中提取可解释特征。然而该领域仍以经验为主，近期对其实际效用存疑。本文借助深度学习的样条理论，将SAE置于该框架下：发现SAE是k-means自编码器的分段仿射推广，但为换取可解释性而牺牲了精度，不如最优的‘类k-means加局部PCA’分段仿射模型。我们通过幂图刻画（TopK）SAE的底层几何结构，并提出一种新型近端交替梯度下降法（PAM-SGD），兼具理论基础与良好实证表现，尤其在样本效率和大模型中的编码稀疏性方面优势显著。所有代码公开于https://github.com/splInterp2025/splInterp。
原文摘要 · Abstract (English)
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
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