Measuring Semantic Abstractness of SAE Features via Nonlocality

• URL: http://arxiv.org/abs/2608.10537v1
• Date: Tue, 11 Aug 2026 06:19:48 GMT
• Title: Measuring Semantic Abstractness of SAE Features via Nonlocality
• Abstract summary: We introduce emphFeature Nonlocality (FNL), defined as the entropy of the normalized per-position influence on an SAE feature's activation.<n>FNL provides an LLM-independent, label-free, correlational witness of the abstraction level of an SAE feature.
• Score: 0.19116784879310025
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sparse autoencoders (SAEs) have helped uncover mechanistic explanations for LLM behaviours such as reasoning, jailbreaking etc., via understanding the corresponding task-relevant and causally effective features. To evaluate such mechanistic explanations, downstream studies must distinguish surface lexical features from genuinely high-level ones. However, neither an autointerp-based semantic description nor causal steering utility fully resolves the abstraction level of a feature. To this end, we introduce \emph{Feature Nonlocality} (FNL), defined as the entropy of the normalized per-position influence on an SAE feature's activation. We report that FNL correlates with existing LLM-based proxy metrics of feature semantic abstractness, and successfully distinguishes context-dependent reasoning features from token-driven ones, correctly assigning the higher FNL to the contextual feature in $73$--$84\%$ of randomly drawn pairs that consist of one contextual and one token-level feature. We demonstrate two downstream applications. We audit SAE-based features used for jailbreak mitigation and find surprisingly that most effective features are positional features with low FNL rather than genuinely recognizing harmful intents. We report that steering high-FNL features in DeepSeek-R1-Distill-Llama-8B improves MATH-500 accuracy by $4.6$ points over the unsteered model and outperforms steering low-FNL features, though the gains are model-specific. We conclude that FNL provides an LLM-independent, label-free, correlational witness of the abstraction level of an SAE feature, with applications in evaluating mechanistic explanations as well as selecting features for downstream interventions.

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