frequency-domain adaptation

This work proposes FreqAdapter, a novel parameter-efficient fine-tuning method that operates in the frequency domain to overcome the limitations of existing spatial-domain approaches, which often introduce information redundancy and struggle to capture multi-scale features. FreqAdapter introduces, for the first time, a text-guided multi-scale adaptation mechanism in the frequency domain, optimizing receptive fields across different frequency bands to enhance model representational capacity while maintaining an extremely low parameter overhead. By shifting adaptation from the spatial to the spectral domain, the method transcends conventional spatial fine-tuning constraints, achieving significant performance gains on multimodal models such as CLIP and LLaVA, and enabling rapid convergence within a single training epoch.

Cross-domain few-shot learning (CD-FSL) confronts dual challenges: severe distribution shift between source and target domains and extreme scarcity of labeled examples. Existing spatial-domain adaptation methods neglect spectral characteristic discrepancies, limiting generalization. To address this, we propose the first frequency-domain disentangled adaptation framework: features are decomposed into low-, mid-, and high-frequency subbands via DFT/IDFT; radial frequency-band masking and multi-scale convolutional branches enable decoupled, parallel, and lightweight adaptive modulation per band; crucially, it supports spectrum-scale-aware, kernel-level customization—novel in CD-FSL. Evaluated on Meta-Dataset, our method consistently outperforms state-of-the-art approaches across both seen and unseen domains, achieving significant accuracy gains. This demonstrates that explicit frequency-domain modeling delivers critical improvements to CD-FSL generalization.

Parameter-efficient fine-tuning (PEFT) methods, particularly LoRA, underperform for large operator models in scientific machine learning due to theoretical limitations in Fourier layers. Method: This work introduces PEFT to scientific ML for the first time and proposes F-Adapter—a frequency-adaptive adapter architecture grounded in the spectral sparsity of physical systems. It allocates parameters dynamically across the frequency domain: high capacity at low frequencies and low capacity at high frequencies. Coupled with a spectral-complexity-driven module-width optimization strategy, F-Adapter jointly enhances parameter efficiency and approximation accuracy. Contribution/Results: On multiple 3D Navier–Stokes benchmarks, F-Adapter significantly outperforms LoRA and other state-of-the-art PEFT methods, achieving new SOTA performance while improving generalization and spectral fidelity.

This work proposes a novel mixture-of-experts (MoE) adapter that overcomes the limitations of existing parameter-efficient fine-tuning methods, which are confined to fixed spatial or frequency domains and struggle to adapt to task-, layer-, or token-specific optimal representations. By introducing the fractional Fourier transform (FrFT) into the MoE architecture for the first time, each expert is equipped with a learnable FrFT order, enabling continuous interpolation between spatial and frequency domains and dynamic selection of the most compact low-rank update space. This design naturally induces expert decorrelation through learnable domain selection, substantially enhancing multi-task compositionality with minimal computational overhead. Experiments on LLaMA-3.1-8B and Qwen2.5-7B demonstrate consistent superiority over strong baselines such as FlyLoRA and FourierMoE across commonsense, mathematical, coding, and knowledge-intensive tasks, while maintaining low active parameter counts and revealing interpretable patterns of order specialization at both task and layer levels.

This work proposes FITMM, a novel framework that addresses the limitations of existing spatial-domain approaches to multimodal recommendation, which often neglect frequency-domain structures and suffer from modality misalignment and redundancy. FITMM is the first to introduce the information bottleneck principle into frequency-domain multimodal recommendation. It constructs item representations via graph augmentation and performs orthogonal decomposition of each modality in the frequency domain to yield lightweight intra-band components. A task-adaptive gating mechanism fuses band-specific information, while intra-band independent modeling and cross-modal spectral consistency constraints enable adaptive band selection and redundancy suppression. Extensive experiments on three real-world datasets demonstrate that FITMM significantly outperforms state-of-the-art baselines, validating the effectiveness and generalizability of frequency-domain modeling for multimodal recommendation.

This work addresses the challenges of feature shift, temporal drift, and spectral discrepancy in source-free domain adaptation for time series. To tackle these issues without access to source-domain data, the authors propose a time–frequency joint alignment approach that explicitly corrects spectral shifts—a first in the source-free setting. By modeling the source domain’s temporal dependencies and spectral characteristics at multiple scales, they design a trainable frequency-domain adaptation module that modulates both phase and amplitude of target-domain signals to achieve distribution alignment. Extensive experiments demonstrate that the proposed method significantly outperforms existing source-free time series adaptation techniques across multiple benchmark datasets, confirming its effectiveness and robustness.

This work addresses the challenges of spectral mismatch and high fine-tuning costs when adapting pretrained geospatial foundation models (GeoFMs) for Earth observation downstream tasks. To this end, we propose the SPECTRA framework, which introduces a Band-Routing Embedding (BRE) mechanism to effectively integrate all downstream spectral bands into the pretrained model’s input space. Additionally, we design a Stage-wise Transferability-aware Low-Rank Adaptation (ST-LoRA) strategy that dynamically allocates adaptation rank across network stages based on their transferability. Experiments across three GeoFM architectures and four segmentation datasets demonstrate that BRE substantially improves performance, while ST-LoRA outperforms both full fine-tuning and standard LoRA with significantly fewer trainable parameters. To our knowledge, this is the first approach to jointly optimize spectral alignment and parameter-efficient fine-tuning in geospatial foundation models.

This work addresses the limitation of conventional Fourier-encoded implicit neural representations (INRs), which employ globally fixed frequencies and struggle to effectively capture spatially varying local spectra, leading to slow convergence of high-frequency details. To overcome this, the authors propose an adaptive local frequency filtering approach that introduces a spatially varying parameter α(x) to dynamically modulate Fourier components, enabling smooth, position-dependent transitions among low-pass, band-pass, and high-pass responses. This method establishes the first spatially adaptive frequency modulation mechanism within Fourier-encoded INRs and leverages neural tangent kernel (NTK) theory to reveal its spectral reshaping effect on the effective kernel, facilitating interpretable visualization of frequency preferences. Experiments demonstrate that the proposed approach significantly improves reconstruction quality and accelerates optimization across 2D image fitting, 3D shape representation, and sparse data reconstruction tasks, outperforming fixed-frequency baselines.

Existing Fourier transform–based parameter-efficient fine-tuning methods assume that weight updates are spectrally sparse; however, empirical observations reveal that their spectral energy is in fact uniformly distributed, limiting performance. This work proposes S2FT, which first uncovers the inherently non-sparse nature of weight-update spectra and introduces an invertible transformation based on row–column permutation to map weight changes into a latent space exhibiting local smoothness. This structural prior induces sparsity in the transformed spectral domain. By integrating this spectral prior with a nearest-neighbor search strategy, S2FT achieves superior fine-tuning performance while updating only 0.08% of the model parameters—outperforming current state-of-the-art approaches.

This work addresses the challenge of transferring priors from optical to synthetic aperture radar (SAR) images in generalized category discovery, hindered by cross-modal incompatibility. To overcome this, the authors propose a spectrum-guided cross-modal prior transfer framework that models the discrepancy in energy distributions between optical and SAR images in the frequency domain. They introduce a novel Modality Discrepancy Curve (MDC) as a structured frequency-domain descriptor and develop an MDC-guided Cross-modal Prior Transfer (MCPT) pretraining paradigm. By integrating adaptive frequency-domain tokenization (AFT), frequency-domain expert refinement (FER), and cross-modal contrastive learning, the method enables band-aware feature optimization on paired optical–SAR data. Experiments demonstrate state-of-the-art performance across multiple benchmark SAR datasets, confirming that explicitly modeling frequency-domain discrepancies is crucial for effective transfer of optical priors to SAR imagery.