Expert Pyramid Tuning: Efficient Parameter Fine-Tuning for Expertise-Driven Task Allocation

Parameter-efficient fine-tuning (PEFT) has emerged as a crucial paradigm for adapting large language models (LLMs) under constrained computational budgets. However, standard PEFT methods often struggle in multi-task fine-tuning settings, where diverse optimization objectives induce task interference and limited parameter budgets lead to representational deficiency. While recent approaches incorporate mixture-of-experts (MoE) to alleviate these issues, they predominantly operate in the spatial domain, which may introduce structural redundancy and parameter overhead. To overcome these limitations, we reformulate adaptation in the spectral domain. Our spectral analysis reveals that different tasks exhibit distinct frequency energy distributions, and that LLM layers display heterogeneous frequency sensitivities. Motivated by these insights, we propose FourierMoE, which integrates the MoE architecture with the inverse discrete Fourier transform (IDFT) for frequency-aware adaptation. Specifically, FourierMoE employs a frequency-adaptive router to dispatch tokens to experts specialized in distinct frequency bands. Each expert learns a set of conjugate-symmetric complex coefficients, preserving complete phase and amplitude information while theoretically guaranteeing lossless IDFT reconstruction into real-valued spatial weights. Extensive evaluations across 28 benchmarks, multiple model architectures, and scales demonstrate that FourierMoE consistently outperforms competitive baselines in both single-task and multi-task settings while using significantly fewer trainable parameters. These results highlight the promise of spectral-domain expert adaptation as an effective and parameter-efficient paradigm for LLM fine-tuning.

Mixture-of-Experts (MoE) has become a prominent paradigm for scaling Large Language Models (LLMs). Parameter-efficient fine-tuning methods, such as LoRA, are widely adopted to adapt pretrained MoE LLMs to downstream tasks. However, existing approaches typically assign identical LoRA ranks to all expert modules, ignoring the heterogeneous specialization of pretrained experts. This uniform allocation leads to a resource mismatch: task-relevant experts are under-provisioned, while less relevant ones receive redundant parameters. To address this, we propose DR-LoRA, a Dynamic Rank LoRA framework for fine-tuning pretrained MoE models. Specifically, DR-LoRA initializes all expert LoRA modules with a small active rank and uses an expert saliency score, which combines routing frequency and gradient-based rank importance, to identify which experts would benefit most from additional capacity. It then periodically expands the active ranks of the task-critical expert LoRA, progressively constructing a heterogeneous rank distribution tailored to the target task. Experiments on three MoE models across six tasks show that DR-LoRA consistently outperforms LoRA and other strong baselines, demonstrating that task-adaptive heterogeneous rank allocation is an effective strategy to improve active capacity utilization in MoE fine-tuning.

Parameter-Efficient Fine-Tuning (PEFT) is essential for adapting Large Language Models (LLMs) to multi-task scenarios. A prevailing trend in this field involves complex LoRA variants with multiple adapters or heads, which rely on the premise that architectural isolation of task-specific knowledge is necessary. However, this design often introduces dynamic routing, preventing weight merging and causing significant inference latency. In this work, we present a direct challenge to this paradigm. We first reveal a paradox where a simplified, router-free multi-head model with high inter-head redundancy outperforms complex, diversity-driven baselines. Furthermore, we demonstrate that a unified, single-adapter LoRA with increased rank achieves highly competitive performance, questioning the necessity of multi-component structures. Based on these findings, we propose Align-LoRA, a unified and efficient framework that shifts the focus from architectural isolation to representation alignment. Align-LoRA incorporates an explicit alignment loss to encourage the learning of task-shared representations within a shared latent space. Crucially, our method maintains the standard LoRA architecture, ensuring zero inference latency via weight merging. Theoretical analysis and extensive experiments confirm that Align-LoRA significantly surpasses prevailing approaches, establishing a simpler, more effective, and production-friendly paradigm for multi-task PEFT. The code is available at https://github.com/jinda-liu/Align-LoRA.