Polysemantic Experts, Monosemantic Paths: Routing as Control in MoEs

TL;DR

This paper introduces a decomposition method for Mixture-of-Experts models that separates control signals from content, revealing how routing decisions lead to monosemantic expert paths and improved interpretability.

Contribution

It presents a parameter-free decomposition that uncovers the causal role of control signals in MoEs, enhancing understanding of their routing and semantic specialization.

Findings

Control signals encode an abstract function that rotates across layers.

Expert paths become monosemantic, clustering tokens by semantic function.

Clusters in control subspace are more monosemantic than in full representations.

Abstract

An LLM's residual stream is both state and instruction: it encodes the current context and determines the next transformation. We introduce a parameter-free decomposition for Mixture-of-Experts models that splits each layer's hidden state into a control signal that causally drives routing and an orthogonal content channel invisible to the router. Across six MoE architectures, we find that models preserve surface-level features (language, token identity, position) in the content channel, while the control signal encodes an abstract function that rotates from layer to layer. Because each routing decision is low-bandwidth, this hand-off forces compositional specialization across layers. While individual experts remain polysemantic, expert paths become monosemantic, clustering tokens by semantic function across languages and surface forms. The same token (e.g., ":") follows distinct trajectories depending on whether it serves as a type annotation, an introductory colon, or a time separator. Our decomposition identifies the source of this structure: clusters in the control subspace are substantially more monosemantic than those in the full representation. As a result, the natural unit of interpretability in MoEs is not the expert but the trajectory.