Abstract:The Linear Representation Hypothesis (LRH) identifies features of a trained deep network (DN) as linear directions in the activation spaces, i.e., output spaces of intermediate layers. This characterization decouples the input-output maps learned by a DN from the organization of feature directions in its activation spaces. We introduce the Linear Centroids Hypothesis (LCH), which instead identifies features with linear directions among a DN's centroid spaces -- where any vector denotes a centroid or summary of a local affine expert characterizing the learned input-output maps of the DN exactly (e.g., for piecewise-affine DNs) or approximately (e.g., for smooth DNs like transformers). We show that replacing intermediate activations with centroids yields a functional drop-in alternative for standard interpretability tools. Empirically, this change yields sparser, more downstream-useful feature dictionaries on DINO ViTs, suppresses spurious directions on a controlled task, recovers interpretable circuits in GPT2-Large, and produces faithful gradient-based saliency maps. LCH unifies dictionaries, probing, circuits, and saliency maps into a single geometric object grounded in the network's input-output map -- making interpretability mechanistic by construction rather than post hoc. Code to study the LCH this https URL .
| Comments: | 23 pages, 17 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2604.11962 [cs.LG] |
| (or arXiv:2604.11962v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.11962 arXiv-issued DOI via DataCite |
From: Thomas Walker [view email]
[v1]
Mon, 13 Apr 2026 18:54:38 UTC (11,427 KB)
[v2]
Thu, 7 May 2026 18:19:16 UTC (25,723 KB)
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