spectral perturbation filtering

Spectrum prediction in dynamic spectrum access (DSA) faces significant challenges due to strong noise interference and severe time-frequency domain feature entanglement. To address these issues, this paper proposes the Spectrum Forecasting via Fractional Fourier Domain (SFFP) framework—the first to incorporate adaptive fractional Fourier transform (AFrFT) into spectrum modeling. By learning optimal transform orders, SFFP achieves maximal signal-noise separation in the fractional domain. Furthermore, it integrates complex-valued neural networks with adaptive filtering to enable end-to-end feature enhancement and trend prediction directly within the fractional domain. Experimental evaluation on real-world spectrum datasets demonstrates that SFFP consistently outperforms state-of-the-art time-frequency domain methods, achieving 12.6%–23.4% improvements in prediction accuracy while exhibiting superior robustness under noisy and nonstationary conditions. This work establishes a novel paradigm for intelligent spectrum management in highly dynamic wireless environments.

This work addresses the challenges of model drift and degraded generalization in federated learning caused by heterogeneous client data, exacerbated by Sharpness-Aware Minimization (SAM) due to inconsistent local perturbations across clients that lead to optimization divergence. For the first time, the authors analyze SAM perturbations from a frequency-domain perspective and reveal that their inconsistency predominantly resides in low-frequency components. Building on this insight, they propose FedFFT, a lightweight, plug-and-play method that applies low-pass filtering to SAM perturbations without increasing communication overhead, effectively suppressing harmful updates while preserving shared learning signals. Extensive experiments demonstrate that FedFFT consistently outperforms existing federated SAM approaches across various non-IID settings, achieving superior robustness, generalization, and convergence stability.

Large language model (LLM) fine-tuning faces challenges including high computational and memory overhead, and difficulty in adapting to non-square weight matrices. This paper proposes a parameter-efficient fine-tuning (PEFT) method based on circulant-diagonal decomposition (CDD), the first to introduce CDD into the Fourier domain. It replaces computationally expensive 2D FFTs with efficient 1D FFTs for accelerated frequency-domain operations and introduces a block-wise mechanism for non-square weights, eliminating explicit construction of the weight update matrix. Crucially, the method models arbitrary-shaped low-rank updates without introducing additional trainable parameters, substantially reducing both FLOPs and memory footprint. Experiments across multiple downstream tasks demonstrate performance on par with or superior to state-of-the-art PEFT methods—including LoRA and AdaLoRA—while reducing trainable parameters by up to 90% and peak memory usage by up to 67%.

Existing FFT implementations—including real-to-complex FFT (rFFT)—are not truly in-place: rFFT maps a length-$n$ real input to a complex output of size $n/2+1$, causing dimensional mismatch and non-negligible auxiliary memory overhead. This work proposes rdFFT—the first fully in-place real-domain FFT framework—that jointly leverages implicit complex-number encoding, frequency-domain conjugate symmetry modeling, and in-place butterfly computation to enable input and output to share a single $n$-dimensional real memory buffer, eliminating all intermediate storage. rdFFT achieves the first strictly in-place realization of rFFT, reducing peak training memory by 32%–47%. We validate its effectiveness across multiple NLU tasks using BERT and RoBERTa, demonstrating consistent accuracy preservation. By providing an efficient, memory-optimal primitive, rdFFT establishes foundational support for lightweight, frequency-domain deep learning.

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 study critically examines whether spectral graph neural networks (spectral GNNs) genuinely leverage spectral properties of graphs to achieve performance gains in node classification tasks. Through theoretical analysis grounded in graph signal processing, examination of Vandermonde systems, and demonstration of equivalence with message-passing neural networks (MPNNs), the work reveals that existing spectral GNNs—such as MagNet and HoloNet—fail to correctly implement the graph Fourier transform. Their reported performance advantages are instead attributable to implicit MPNN-like architectures or implementation artifacts. Rigorous reimplementation and ablation studies confirm that when spectral GNNs strictly adhere to spectral theory, their performance deteriorates significantly, thereby challenging the theoretical foundation underpinning their use in node classification.

This work addresses the severe client drift caused by non-independent and identically distributed (Non-IID) data in federated learning, which significantly impedes model convergence. It reveals for the first time that such drift manifests as a pronounced bias in the low-frequency components of gradients in the frequency domain, while high-frequency components remain relatively consistent across clients. Building on this insight, the authors propose a general spectral gradient filtering framework that mitigates data heterogeneity by suppressing inconsistent low-frequency signals. The framework accommodates both exact truncation via Fast Fourier Transform (FFT) and spatial-domain approximations such as Gaussian detrending. Extensive experiments demonstrate that the proposed method substantially improves performance under Non-IID settings on standard benchmarks including CIFAR-10, CIFAR-100, and Tiny-ImageNet, with negligible additional communication overhead.

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 severe communication bottleneck in distributed Fourier Neural Operators (FNOs) at high resolutions, where spectral layers require frequent all-to-all communication. To mitigate this, the authors propose Distributed Truncated Spectral Transform (DTST), which computes only a small set of critical frequency modes locally on each GPU and aggregates them with minimal communication, achieving equivalence to truncated FFT while drastically reducing communication overhead during both training and inference. DTST uniquely integrates local discrete Fourier transforms with efficient collective communication, unifying spatial data parallelism and spectral weight model parallelism. Experiments demonstrate that, across 4–32 GPUs (up to 8 nodes), DTST accelerates forward propagation by 38–64× and training by 37×, reducing communication time from 97% to under 6% of total execution time, with scalability improving further as resolution increases.

This work addresses the limitation of conventional Fourier Neural Operators (FNOs), which exhibit a low-frequency bias due to spectral truncation and struggle to accurately approximate solutions of partial differential equations (PDEs) featuring strong high-frequency oscillations. To overcome this, the authors propose SirenFNO, a novel framework that integrates Sinusoidal Representation Networks (SIRENs) into the FNO architecture for the first time. By enabling mode-wise kernel parameterization, SirenFNO achieves full-spectrum learning without frequency truncation while preserving discretization invariance. Coupled with functional tensor decomposition, the method substantially enhances parameter efficiency: across multiple PDE benchmarks, SirenFNO maintains or improves accuracy with 4–15 times fewer parameters, and its decomposed variant reduces parameter count by up to 73-fold while achieving superior accuracy.