Fan et al. [2021] incorporates high-frequency views into contrastive learning, leading to the transfer However, there are also several works that challenge the validity of this assumption. Yin et al. [2019] proposes a robustness analysis strategy based on Fourier Heatmaps, which utilizes a model's sensitivity to frequency-bases. Maiya et al. [2021] believes that model robustness does not have an intrinsic connection In addition to the perspective on frequency components, Chen et al. [2021] has shown that the CNN model should be consistent with the Human Visual System, with To show the power law distribution of natural images, we select CIFAR-10 Krizhevsky et al. [2009], Tiny-ImageNet Le and Y ang [2015] and ImageNet Deng et al. [2009] to conduct experiments. We show an example of division on ImageNet, as shown in Fig.2, in which the high-and low-frequency components of the image obtained according to the division radius are also in line with our We conduct experiments on naturally trained models. We conduct experiments on test set of CIFAR10, Tiny-ImageNet, ImageNet-1k datasets.

A widely discussed hypothesis regarding the cause of visual models' lack of robustness is that they can exploit human-imperceptible high-frequency components

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The low-resource label analysis and representation visualization further illustrate the effectiveness of our pre-training strategy.

We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of extreme events (e.g., seizures) that can help to identify their occurrence. Numerous studies have established that connectivity-based features are effective for discriminating brain states. Here, we demonstrate the advantage of the proposed approach: that tail connectivity provides additional discriminatory power, enabling more accurate identification of extreme-related events and improved seizure risk management. Common approaches in tail dependence modeling use pairwise summary measures or parametric models. However, these approaches do not identify channels that drive the maximal tail dependence between two groups of signals -- an information that is useful when analyzing electroencephalography of epileptic patients where specific channels are responsible for seizure occurrences. A familiar approach in traditional signal processing is canonical correlation, which we extend to the tails to develop a visualization of extremal channel-contributions. Through the tail pairwise dependence matrix (TPDM), we develop a computationally-efficient estimator for our canonical tail dependence measure. Our method is then used for accurate frequency-based soft clustering of neonates, distinguishing those with seizures from those without.

Multivariate time series forecasts are widely used, such as industrial, transportation and financial forecasts. However, the dominant frequencies in time series may shift with the evolving spectral distribution of the data. Traditional Mixture of Experts (MoE) models, which employ a fixed number of experts, struggle to adapt to these changes, resulting in frequency coverage imbalance issue. Specifically, too few experts can lead to the overlooking of critical information, while too many can introduce noise. To this end, we propose Ada-MoGE, an adaptive Gaussian Mixture of Experts model. Ada-MoGE integrates spectral intensity and frequency response to adaptively determine the number of experts, ensuring alignment with the input data's frequency distribution. This approach prevents both information loss due to an insufficient number of experts and noise contamination from an excess of experts. Additionally, to prevent noise introduction from direct band truncation, we employ Gaussian band-pass filtering to smoothly decompose the frequency domain features, further optimizing the feature representation. The experimental results show that our model achieves state-of-the-art performance on six public benchmarks with only 0.2 million parameters.

Robust decoding and classification of brain patterns measured with electroencephalography (EEG) remains a major challenge for real-world (i.e. outside scientific lab and medical facilities) brain-computer interface (BCI) applications due to well documented inter- and intra-participant variability. Here, we present a large-scale benchmark evaluating over 340,000+ unique combinations of spatial and nonlinear EEG classification. Our methodological pipeline consists in combinations of Common Spatial Patterns (CSP), Riemannian geometry, functional connectivity, and fractal- or entropy-based features across three open-access EEG datasets. Unlike prior studies, our analysis operates at the per-participant level and across multiple frequency bands (8-15 Hz and 8-30 Hz), enabling direct assessment of both group-level performance and individual variability. Covariance tangent space projection (cov-tgsp) and CSP consistently achieved the highest average classification accuracies. However, their effectiveness was strongly dataset-dependent, and marked participant-level differences persisted, particularly in the most heterogeneous of the datasets. Importantly, nonlinear methods outperformed spatial approaches for specific individuals, underscoring the need for personalized pipeline selection. Our findings highlight that no universal 'one-size-fits-all' method can optimally decode EEG motor imagery patterns across all users or datasets. Future work will require adaptive, multimodal, and possibly novel approaches to fully address neurophysiological variability in practical BCI applications where the system can automatically adapt to what makes each user unique.

Electroencephalography (EEG) captures neural activity across multiple temporal and spectral scales, yielding signals that are rich but complex for representation learning. Recently, EEG foundation models trained to predict masked signal-tokens have shown promise for learning generalizable representations. However, their performance is hindered by their signal tokenization modules. Existing neural tokenizers fail to preserve high-frequency dynamics, limiting their ability to reconstruct EEG signals with high fidelity. We introduce NeuroRVQ, a scalable Large Brainwave Model (LBM) centered on a codebook-based tokenizer. Our tokenizer integrates: (i) multi-scale feature extraction modules that capture the full frequency neural spectrum; (ii) hierarchical residual vector quantization (RVQ) codebooks for high-resolution encoding; and, (iii) an EEG signal phase- and amplitude-aware loss function for efficient training. This design enables efficient EEG compression while supporting accurate reconstruction across all frequency bands, leading to robust generative masked modeling. Our empirical results demonstrate that NeuroRVQ achieves lower reconstruction error and outperforms existing LBMs on a variety of downstream tasks. More broadly, NeuroRVQ tokenizer establishes a strong prior for codebook-based general-purpose brainwave models, enabling advances in neural decoding, generative modeling and multimodal biosignal integration.

We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate classification as interpretable geometric optimization on fiber bundles, where categories form the base space and wavelet-transformed features lie in the fibers above each category. We introduce two innovations: (1) learnable Riemannian metrics identifying important frequency feature components, (2) variational prototype optimization through energy function minimization. Classification is performed via Voronoi tessellation under the learned Riemannian metric, where each prototype defines a decision region and test samples are assigned to the nearest prototype, providing clear geometric interpretability. This work demonstrates that the integration of fiber bundle with machine learning provides interpretability and efficiency, which are difficult to obtain simultaneously in conventional deep learning.