The PFAD Not Taken: Measuring Polysemanticity via Feature Affine Decomposition
Kirill Bykov, María A. Bravo, Laura Kopf, Zeynep Akata
Neural Information Processing Systems, NeurIPS
2026

Abstract

Polysemanticity is central to mechanistic interpretability, yet existing evaluations rely primarily on top-activating examples and qualitative inspection. These approaches are sensitive to dataset coverage and miss distribution-wide functional behavior. We model polysemanticity as functional heterogeneity: a feature is polysemantic when it behaves like different semantically meaningful functions on different subsets of the data. We introduce PFAD (Polysemanticity via Feature Affine Decomposition), a method that decomposes a scalar feature into a hard-routed mixture of affine experts in a vision-language embedding space, interpreting each component through aligned text-image retrieval. We further propose the Effective Decomposition Rank (EDR), a redundancy-aware measure of how many active, non-redundant semantic components explain a feature. We evaluate PFAD on controlled benchmarks with known mixtures and apply it to real vision features. PFAD recovers known component structure and reveals polysemantic behavior invisible to top-activation inspection. Our results suggest that polysemanticity is better understood as distribution-wide functional heterogeneity rather than exemplar diversity.

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