FourierMoE: Fourier Mixture-of-Experts Adaptation of Large Language Models

TL;DR

FourierMoE introduces a spectral domain mixture-of-experts approach for large language model fine-tuning, improving task performance and parameter efficiency by leveraging frequency-aware adaptation.

Contribution

It reformulates MoE adaptation in the spectral domain using IDFT, enabling frequency-specific expert routing and lossless real-valued weight reconstruction.

Findings

Outperforms baselines across 28 benchmarks in various scales.

Achieves better multi-task and single-task performance with fewer parameters.

Spectral domain adaptation reveals task-specific frequency energy distributions.

Abstract

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.