Diminishing Returns of Data in Sparse Autoencoders: Functional Behavior does not Guarantee Feature Reproducibility

Sparse autoencoders (SAEs) are typically trained on hundreds of millions to billions of activation tokens, yet little work has tested whether this scale is necessary. We study how much activation data SAEs need by training four SAE architectures on three language models with budgets ranging from 5M tokens to a 500M-token reference.

稀疏自动编码器（SAE）通常在数亿到数十亿个激活标记上进行训练，但很少有研究测试这种规模是否必要。我们通过在三个语言模型上训练四种 SAE 架构，并设置从 500 万个标记到 5 亿个标记参考值的预算，来研究 SAE 到底需要多少激活数据。

We measure two notions of convergence: functional behavior on standard evaluations and one-to-one reproducibility of learned features. Functional data requirements are strongly metric-dependent: reconstruction often approaches the full-data reference at substantially smaller budgets, whereas feature reproducibility continues to improve with data.

我们衡量了两种收敛概念：标准评估下的功能行为，以及学习特征的一对一可复现性。功能性数据需求在很大程度上取决于指标：重构通常在预算少得多的情况下就能接近全数据参考值，而特征的可复现性则会随着数据的增加而持续改善。

For Gemma-2-2B BatchTopK, the fraction of strictly matched features rises from 2% at 5M tokens to 29% at 50M. Data selection also matters: random sampling better preserves the original activation distribution and generally favors reconstruction, whereas diversity-based sampling frequently improves AutoInterp.

对于 Gemma-2-2B BatchTopK 模型，严格匹配特征的比例从 500 万标记时的 2% 上升到 5000 万标记时的 29%。数据选择也很重要：随机采样能更好地保留原始激活分布，通常有利于重构，而基于多样性的采样则经常能改善自动解释（AutoInterp）的效果。

A theoretical analysis separates statistical consistency of subsampled training from the stronger identifiability and optimization conditions required for one-to-one feature recovery. Our results show that SAE training can often be made far more data-efficient when budgets are matched to the goal, and feature-level claims are backed by explicit reproducibility checks, paving the way toward cheaper and more reliable SAE research.

一项理论分析将子采样训练的统计一致性与实现一对一特征恢复所需的更强的可识别性和优化条件区分开来。我们的结果表明，当预算与目标相匹配时，SAE 训练通常可以实现更高的数据效率，且特征层面的结论得到了明确的可复现性检查的支持，这为更廉价、更可靠的 SAE 研究铺平了道路。