Frequency-Domain Feature Learning

Dementia disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD) exhibit overlapping electrophysiological signatures in EEG that challenge accurate diagnosis. Existing EEG-based methods are limited by full-band frequency analysis, which hinders the precise differentiation of dementia subtypes and severity stages. To address this limitation, we propose a Variational Mixture of Graph Neural Experts (VMoGE) framework that integrates multi-band EEG analysis with variational graph neural networks and a mixture-of-experts architecture. Each expert specializes in a specific EEG frequency band and models brain connectivity using a Gaussian Markov random field prior, while a variational gating mechanism adaptively integrates the expert outputs. This design enables the model to learn frequency-specific brain network representations while modeling latent uncertainty through variational inference. Experimental results on two EEG dementia datasets show that VMoGE achieves strong performance, with an AUC of 0.89 for HC vs. AD classification in the main comparison and competitive results across dementia subtyping and CDR staging tasks. Clinically, VMoGE offers three key translational values: the expert gating weights correlate with MMSE scores and CDR severity; slow-wave $δ$- and $θ$-band contributions are associated with AD-related EEG slowing and disease progression; and spatially localized activation maps reveal posterior $θ$- and $α$-band alterations and region-specific $β$-band changes, providing neurophysiologically interpretable markers aligned with known AD neuropathology.

Deep learning-based methods have achieved significant success in remote sensing Earth observation data analysis. Numerous feature fusion techniques address multimodal remote sensing image classification by integrating global and local features. However, these techniques often struggle to extract structural and detail features from heterogeneous and redundant multimodal images. With the goal of introducing frequency domain learning to model key and sparse detail features, this paper introduces the spatial-spectral-frequency interaction network (S$^2$Fin), which integrates pairwise fusion modules across the spatial, spectral, and frequency domains. Specifically, we propose a high-frequency sparse enhancement transformer that employs sparse spatial-spectral attention to optimize the parameters of the high-frequency filter. Subsequently, a two-level spatial-frequency fusion strategy is introduced, comprising an adaptive frequency channel module that fuses low-frequency structures with enhanced high-frequency details, and a high-frequency resonance mask that emphasizes sharp edges via phase similarity. In addition, a spatial-spectral attention fusion module further enhances feature extraction at intermediate layers of the network. Experiments on four benchmark multimodal datasets with limited labeled data demonstrate that S$^2$Fin performs superior classification, outperforming state-of-the-art methods. The code is available at https://github.com/HaoLiu-XDU/SSFin.

Face forgery detection faces critical challenges in generalizing to unseen manipulation techniques and remaining robust under image compression, which often obscures subtle artifacts. Existing methods typically rely on fixed filters or coarse band separation, lacking the adaptability to learn task-specific spectral cues. To address this, we propose the Band-Attention Modulation Network (BAM-Net), a novel framework that pioneers learnable, fine-grained modulation of frequency components for forgery detection. At its core is the Band-Attention Modulation (BAM) mechanism, which transforms an image into its Discrete Cosine Transform (DCT) spectrogram and learns to dynamically reweight frequency bands along anti-diagonals. This process effectively enhances forgery-related spectral signatures while suppressing less informative ones, simulating an adaptive "inverse compression" that counters information loss. The modulated frequency information is then fused with the spatial domain to guide a lightweight yet effective spatial backbone equipped with distance-decayed attention for comprehensive feature extraction. Extensive experiments on FaceForensics++, Celeb-DF, and DFDC datasets demonstrate that BAM-Net achieves state-of-the-art performance. More importantly, it exhibits exceptional generalization in cross-dataset, cross-compression, and cross-manipulation scenarios, underscoring the vital role of adaptive frequency band modulation in building robust forgery detectors.

Time series modeling presents unique challenges due to autocorrelation in both historical data and future sequences. While current research predominantly addresses autocorrelation within historical data, the correlations among future labels are often overlooked. Specifically, modern forecasting models primarily adhere to the Direct Forecast (DF) paradigm, generating multi-step forecasts independently and disregarding label autocorrelation over time. In this work, we demonstrate that the learning objective of DF is biased in the presence of label autocorrelation. To address this issue, we propose the Frequency-enhanced Direct Forecast (FreDF), which mitigates label autocorrelation by learning to forecast in the frequency domain, thereby reducing estimation bias. Our experiments show that FreDF significantly outperforms existing state-of-the-art methods and is compatible with a variety of forecast models. Code is available at https://github.com/Master-PLC/FreDF.

Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very useful in providing both qualitative and quantitative understandings of DNNs. In this paper, we rigorously investigate the F-Principle for the training dynamics of a general DNN at three stages: initial stage, intermediate stage, and final stage. For each stage, a theorem is provided in terms of proper quantities characterizing the F-Principle. Our results are general in the sense that they work for multilayer networks with general activation functions, population densities of data, and a large class of loss functions. Our work lays a theoretical foundation of the F-Principle for a better understanding of the training process of DNNs.

Few-shot fine-grained image classification (FSFGIC) aims to classify similar images with limited labeled examples. This work highlights the critical yet underutilized role of phase information in capturing structural relationships within an image. This study introduces a novel plug-and-play amplitude-phase integration (API) module that effectively combines local and global frequency amplitude and phase information for obtaining more comprehensive feature descriptors. Additionally, a dedicated network, named PSF-Net, is proposed that adaptively fuses phase-based spatial and frequency information for FSFGIS. The designed PSF-Net can be easily integrated into standard episodic training architectures for end-to-end training from scratch. Extensive experiments on five public datasets demonstrate that the method outperforms existing state-of-the-art benchmarks.