COACH:ASYMMETRIC ANCHOR–HELPER ROUTING IN MIXTURES OF LORA EXPERTS

Combining Low-Rank Adaptation (LoRA) with Mixture-of-Experts (MoE) has been widely studied for parameter-efficient multi-task adaptation of large language models (LLMs). However, the existing routing methods have not fully explored dimension-wise discriminative information across expert regions or candidate utility conditioned on selected experts, potentially limiting multi-task adaptation performance. To address this limitation, this paper proposes **COACH**, an asymmetric Anchor–Helper routing approach for mixtures of LoRA experts based on **C**onditioning **o**n **A**nchors for **C**alibrating **H**elpers. Specifically, COACH comprises two complementary modules: Prototype-Guided Dimension Reweighting (PDR) exploits dimension-wise expert discriminability to stabilize base matching, while Cluster Residual Collaboration (CRC) uses an Anchor-conditioned residual-response prior to recalibrate Helper selection, addressing the lack of selected-expert conditioning in one-shot routing. Together, these two modules calibrate routing without introducing additional trainable parameters or auxiliary training objectives, while preserving the prescribed sparse activation budget. From a feature-weighted clustering perspective, the theoretical analysis derives the optimal dimension weights for PDR, proves that more discriminative dimensions receive higher weights, and applies this result to calibrate base routing. Extensive experiments across seven tasks show that COACH achieves optimal performance in both macro accuracy (equally averaged over tasks) and micro accuracy (computed over all evaluation examples) among the compared methods, exceeding the equally weighted mean performance of six external baselines by **1.87** and **2.11** percentage points, respectively. Further mechanistic experiments demonstrate that PDR improves routing separation and perturbation stability, while CRC selects more useful Helpers through Anchor-conditioned calibration.