The Router Already Knows

arXiv:2610.27421v1 Announce Type: cross Abstract: Mixture-of-experts (MoE) models already make a sparse choice for every token: which experts should process it. We ask whether a sparse dictionary should reuse that choice. NR-SAE gives each routed expert a small dictionary and opens only those the frozen router selects. At block 15 of Gemma 4 26B-A4B, after ten million C4 training tokens and across three seeds, the expert-aligned autoencoder explains 0.518 of the variance in router-weighted expert outputs on a fixed evaluation capture. A rank-addressed control with the same parameters but sixte

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