Signed-Permutation Coordinate Transport for RMSNorm Transformers
Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-$k$ neuron sets, attribution lists, and merge alignments. This is only well posed after fixing the model's residual-stream gauge, which we show is architecture-dependent: LayerNorm residual charts have permutation gauge $S_d$ (up to a global sign flip), while RMSNorm charts with generic per-channel gain have signed-permutation gauge $B_d = S_d \ltimes \{\pm 1\}^d$. Permutation-only alignment is therefore symmetry-incomplete for RMSNorm models. We introduce sign-marginalized Hungarian matching and prove a sharp failure mode: with decorrelated coordinates, raw signed-correlati...
| Authors | John Sweeney |
|---|---|
| Primary category | cs.LG |
| Published | 30 June 2026 |
| Last updated at source | 30 June 2026 |
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