Topographic Training Concentrates Causal Circuits Without Improving Neuron Monosemanticity

arXiv:2609.24379v1 Announce Type: cross Abstract: Mechanistic interpretability of vision transformers seeks to decompose model computation into human-readable units, but learned representations entangle many concepts in each neuron. Feature superposition is widely treated as the central obstacle to this decomposition, yet most mitigations (sparse autoencoders, dictionary learning) are post-hoc and leave the underlying network unchanged. We ask whether a spatial-locality training loss (TopoLoss) can act as a lightweight, training-time prior that improves interpretability of standard mech-interp tools. Training ViT on ImageNet-100 across multiple TopoLoss weights $\alpha$, we measure causal sufficiency of topographic clusters via activation patching and feature geometry via sparse autoencoders fit to the same residual stream. At $\alpha=1.0$, topographic clusters are 2.79$\times$ more causally sufficient than random unit sets of the same size, with the effect increasing monotonically in $\alpha$. SAE L0 sparsity decreases by 11% and dead-feature fraction rises 19-fold, yet standard neuron-level monosemanticity scores are unchanged, indicating that topographic pressure acts at circuit level, concentrating causal mass into spatially local structures without disentangling individual neurons. This dissociation suggests current neuron-level monosemanticity metrics are insensitive to a class of real interpretability gains, and positions cheap architectural priors as a viable training-time complement to post-hoc tooling.

Abstract:Mechanistic interpretability of vision transformers seeks to decompose model computation into human-readable units, but learned representations entangle many concepts in each neuron. Feature superposition is widely treated as the central obstacle to this decomposition, yet most mitigations (sparse autoencoders, dictionary learning) are post-hoc and leave the underlying network unchanged. We ask whether a spatial-locality training loss (TopoLoss) can act as a lightweight, training-time prior that improves interpretability of standard mech-interp tools. Training ViT on ImageNet-100 across multiple TopoLoss weights $\alpha$, we measure causal sufficiency of topographic clusters via activation patching and feature geometry via sparse autoencoders fit to the same residual stream. At $\alpha=1.0$, topographic clusters are 2.79$\times$ more causally sufficient than random unit sets of the same size, with the effect increasing monotonically in $\alpha$. SAE L0 sparsity decreases by 11% and dead-feature fraction rises 19-fold, yet standard neuron-level monosemanticity scores are unchanged, indicating that topographic pressure acts at circuit level, concentrating causal mass into spatially local structures without disentangling individual neurons. This dissociation suggests current neuron-level monosemanticity metrics are insensitive to a class of real interpretability gains, and positions cheap architectural priors as a viable training-time complement to post-hoc tooling.

Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)

arXiv:2609.24379 [cs.CV]

(or arXiv:2609.24379v1 [cs.CV] for this version)

https://doi.org/10.48550/arXiv.2609.24379 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Topographic Training Concentrates Causal Circuits Without Improving Neuron Monosemanticity

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