Paper Detail

FRAME: Learning the Adaptation Domain with a Mixture of Fractional-Fourier Experts

Tom Saliencro, Maya Lindqvist, Rohan Desai, Priya Nair, Daniel Whitmore

arxiv Score 5.8

Published 2026-06-30 · First seen 2026-07-03

General AI

Abstract

Parameter-efficient fine-tuning (PEFT) reparameterizes weight updates in a fixed basis: low-rank adapters operate in the spatial domain, while a recent line of spectral methods operates in a fixed Fourier domain. We argue that the choice of domain is itself a design degree of freedom that should be learned, and that no single basis is optimal across tasks, layers, or tokens. We introduce Fractional-Fourier Mixture of Experts, a mixture-of-experts adapter in which every expert carries a learnable fractional-Fourier order that continuously interpolates between the spatial domain (recovering vanilla LoRA) and the Fourier domain (recovering a spectral adapter). Routing tokens through experts that occupy different points on this spatial-spectral continuum lets the model place each low-rank update in the domain where it is most compact, and -- because fractional-Fourier operators of different orders are mutually incoherent -- makes the experts naturally decorrelated, which reduces interference and improves multi-task composition. The order is a single scalar per expert, trained with a separate optimizer, and the transform is computed with an $\mathcal{O}(d\log d)$ chirp--FFT surrogate, so Fractional-Fourier Mixture of Experts adds negligible cost over standard MoE-LoRA. Across commonsense, mathematical, code, and knowledge benchmarks on LLaMA-3.1-8B and Qwen2.5-7B, Fractional-Fourier Mixture of Experts improves over strong MoE-LoRA and spectral baselines -- including FlyLoRA, FourierMoE, and HMoRA -- while keeping the active-parameter budget small, and analysis shows that the learned orders specialize by task and layer in interpretable ways.

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BibTeX

@article{saliencro2026frame,
  title = {FRAME: Learning the Adaptation Domain with a Mixture of Fractional-Fourier Experts},
  author = {Tom Saliencro and Maya Lindqvist and Rohan Desai and Priya Nair and Daniel Whitmore},
  year = {2026},
  abstract = {Parameter-efficient fine-tuning (PEFT) reparameterizes weight updates in a fixed basis: low-rank adapters operate in the spatial domain, while a recent line of spectral methods operates in a fixed Fourier domain. We argue that the choice of domain is itself a design degree of freedom that should be learned, and that no single basis is optimal across tasks, layers, or tokens. We introduce Fractional-Fourier Mixture of Experts, a mixture-of-experts adapter in which every expert carries a learnable},
  url = {https://arxiv.org/abs/2607.00162},
  keywords = {cs.LG},
  eprint = {2607.00162},
  archiveprefix = {arXiv},
}

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