Route-Induced Density and Stability (RIDE): Controlled Intervention and Mechanism Analysis of Routing-Style Meta Prompts on LLM Internal States

Abstract

Routing is widely used to scale large language models, from Mixture-of-Experts gating to multi-model/tool selection. A common belief is that routing to a task ``expert'' activates sparser internal computation and thus yields more certain and stable outputs (the Sparsity--Certainty Hypothesis). We test this belief by injecting routing-style meta prompts as a textual proxy for routing signals in front of frozen instruction-tuned LLMs. We quantify (C1) internal density via activation sparsity, (C2) domain-keyword attention, and (C3) output stability via predictive entropy and semantic variation. On a RouterEval subset with three instruction-tuned models (Qwen3-8B, Llama-3.1-8B-Instruct, and Mistral-7B-Instruct-v0.2), meta prompts consistently densify early/middle-layer representations rather than increasing sparsity; natural-language expert instructions are often stronger than structured tags. Attention responses are heterogeneous: Qwen/Llama reduce keyword attention, while Mistral reinforces it. Finally, the densification--stability link is weak and appears only in Qwen, with near-zero correlations in Llama and Mistral. We present RIDE as a diagnostic probe for calibrating routing design and uncertainty estimation.

Figures (3)

• Figure 1: Multi-model overview of $\Delta \mathrm{Hoyer}$ across Early/Middle/Late segments.
• Figure 2: Multi-model overview of $\Delta \mathrm{Attn}$ (mean $\pm$ SEM). Negative values indicate reduced attention share to domain keywords.
• Figure 3: Instance-level correlations between $\Delta \mathrm{C1}$ (prompt Hoyer) and $\Delta \mathrm{C3}$ across models and contrasts. Positive values indicate that instances with larger decreases in Hoyer tend to also exhibit larger decreases in the corresponding instability measure (entropy or semantic variation).