The Router Already Knows

Overview & Synopsis

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 sixteen times as many candidates reaches 0.481, a candidate-matched control 0.458, and an architecture-matched control with randomized expert identity 0.387. A transcoder variant also leads all three controls: 0.432, against 0.347, 0.371, and 0.118. Part of this advantage is architectural: each expert writes into a subspace of at most a quarter of the model width, so naming the expert names the subspace. How much it explains, we have not measured. At this layer and budget, the router already knows something a dictionary would otherwise have to learn. Our implementation did not train faster, and semantic interpretability, downstream loss, and causal faithfulness remain untested.