Equifinality in Mixture of Experts: Routing Topology Does Not Determine Language Modeling Quality

arXiv:2509.14255v2 Announce Type: replace Abstract: Mixture-of-Experts (MoE) models improve efficiency through sparse activation, but their learned gating functions provide limited insight into routing decisions. This work introduces the Semantic Resonance Architecture (SRA), which routes tokens to experts via cosine similarity between token representations and learnable semantic anchors, making every routing decision directly traceable to anchor-token similarity scores. We evaluate SRA on WikiText-103 across 17 configurations. In a controlled multi-seed comparison (3 seeds x 4 configurations, 256 experts, $D_{ff}=256$), cosine routing achieves competitive perplexity with standard linear routing ($12.57 \pm 0.03$ vs $12.45 \pm 0.03$ for $K=1 \to 4$; $12.52 \pm 0.02$ vs $12.57 \pm 0.02$ for $K=2 \to 4$). The training recipe -- not the routing function -- drives specialization quality, while cosine routing provides inherent inspectability. We introduce a bandpass routing loss -- a floor-and-ceiling corridor on expert utilization -- that reduces dead experts from 30-45% to 0-6% and…