arXiv:2606.14040cs.LG2026-06

发现模型激活中存在高效但难稀疏化的核心计算结构。

Decompose Sparsely Where You Should, Absorb Densely Where You Should No

论文配图:Decompose Sparsely Where You Should, Absorb Densely Where You Should No
图 1 · 摘自论文原文
  • 在稀疏自编码器前加低秩瓶颈,先吸收密集成分再稀疏重构。
  • 减少84%密集隐变量,提升稀疏探针效果与扰动响应能力。
  • 该结构是关键计算支架,稀疏表示效率低下且冗余严重。

稀疏自编码器(SAEs)通常试图通过稀疏字典重建整个残差流,隐含假设所有激活内容都适合稀疏单义分解。本文质疑此假设,提出激活中存在一个低秩、密集但计算重要的成分,难以稀疏化,是训练中持续出现密集隐变量的主要原因。为此,我们在标准SAE(BatchTopK和Matryoshka)并行加入一个小的秩-$r$线性瓶颈,允许密集结构在稀疏重构前被吸收。在Gemma-2-2B第12层,秩24瓶颈使密集隐变量数量最多减少84%,同时在相同稀疏度下提升了稀疏探针性能及目标扰动响应。被吸收成分具有三重特性:(i) 结构上可识别为前主成分与异常维度;(ii) 因果必要,移除后下一词交叉熵上升7.5倍,远超移除几何相近的前24个PCA方向(仅2.8倍);(iii) 被稀疏字典冗余编码,删去787个最大对齐特征仅致交叉熵上升2.9倍,删去2048个主题对齐特征几乎不影响MMLU主题分类,而移除该结构则使准确率从98.7%降至随机水平。结果揭示了一种紧凑、语义丰富且因果关键的残差流组件(称为‘计算支架’),传统稀疏字典对其表示效率低下,提示应重新审视基于稀疏性的可解释性方法适用范围。

原文摘要 · Abstract (English)

Sparse autoencoders (SAEs) are typically trained to reconstruct the \textbf{entire} residual stream through a sparse dictionary, implicitly assuming that all activation content is amenable to sparse, monosemantic decomposition. We question this assumption and hypothesize that activations contain a low-rank, dense component that is computationally important to the model yet inherently unsuitable for sparse representation, which serves as a major source of the persistent dense latents widely observed in trained SAEs. To test this, we add a small rank-$r$ linear bottleneck in parallel with standard SAEs (BatchTopK and Matryoshka), allowing dense structure to be absorbed before sparse reconstruction. On Gemma-2-2B layer 12, a rank-24 bottleneck reduces dense latent count by up to 84\% while improving sparse probing and targeted probe perturbation on both architectures at matched sparsity. The absorbed component is (i) \textbf{structurally identifiable} as the top principal components and outlier dimensions; (ii) \textbf{causally necessary}, with removing it raising next-token cross-entropy by 7.5$\times$, far exceeding the 2.8$\times$ from removing the geometrically near-identical top-24 PCA directions; and (iii) \textbf{redundantly encoded by sparse dictionaries}, with ablating 787 maximally aligned sparse features raising cross-entropy by only 2.9$\times$ and ablating 2,048 topic-aligned features leaving MMLU topic classification virtually unchanged, whereas removing the scaffold drops it from 98.7\% to chance. Together, our findings identify a compact, semantically informative and causally important component of residual stream activations (which we term a \textbf{computational scaffold}) that standard sparse dictionaries represent inefficiently, suggesting that the scope of sparsity-based interpretability methods warrants careful re-examination.

稀疏编码模型可解释性计算支架

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