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Zijian Zhou

Zijian Zhou contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence Computer Vision Computation and Language math.AG math.OC

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preprint2026arXiv

CGFformer: Cluster-Guidance Frequency Transformer for Pansharpening

Pansharpening aims to generate high-resolution multispectral (HRMS) images by fusing low-resolution multispectral (LRMS) images with high-resolution panchromatic (PAN) images. However, the current mainstream frequency-based pansharpening methods employ fixed frequency filters, which cannot precisely adapt to complex and spatially diversified frequency distributions in PAN and MS images. Furthermore, existing denoising strategies insufficiently exploit frequency components for denoising and struggle to suppress various noise types accurately. To address these challenges, we propose CGFformer, a cluster-guidance frequency Transformer that focuses on varying frequency distribution and interactions between frequency and spatial components. Specifically, we design an adaptive separation module that integrates local features and non-local information through K-means clustering, enabling more precise separation of high- and low-frequency components. Subsequently, we introduce a dual-stream refinement module combined with Transformer-based cross-attention to remove various noise, allowing the network to jointly suppress frequency-relevant and irrelevant disturbances. In addition, we develop a frequency-spatial fusion module designed to enhance detail and facilitate spatial-frequency interaction, ensuring more effective reconstruction of spatial structures in the fused results. Extensive experiments on multiple benchmark datasets demonstrate that the proposed CGFformer achieves notable improvements over existing pansharpening approaches.

preprint2026arXiv

Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes

Deep neural networks exhibit periodic loss spikes during unregularized long-term training, a phenomenon known as the "Slingshot Mechanism." Existing work usually attributes this to intrinsic optimization dynamics, but its triggering mechanism remains unclear. This paper proves that this phenomenon is a result of floating-point arithmetic precision limits. As training enters a high-confidence stage, the difference between the correct-class logit and the other logits may exceed the absorption-error threshold. Then during backpropagation, the gradient of the correct class is rounded exactly to zero, while the gradients of the incorrect classes remain nonzero. This breaks the zero-sum constraint of gradients across classes and introduces a systematic drift in the parameter update of the classifier layer. We prove that this drift forms a positive feedback loop with the feature, causing the global classifier mean and the global feature mean to grow exponentially. We call this mechanism Numerical Feature Inflation (NFI). This mechanism explains the rapid norm growth before a Slingshot spike, the subsequent reappearance of gradients, and the resulting loss spike. We further show that NFI is not equivalent to an observed loss spike: in more practical tasks, partial absorption may not produce visible spikes, but it can still break the zero-sum constraint and drive rapid growth of parameter norms. Our results reinterpret Slingshot as a numerical dynamic of finite-precision training, and provide a testable explanation for abnormal parameter growth and logit divergence in late-stage training.

preprint2026arXiv

RAFNet: Region-Aware Fusion Network for Pansharpening

Pansharpening aims to generate high-resolution multispectral (HRMS) images by fusing low-resolution multispectral (LRMS) and high-resolution panchromatic (PAN) images. Although deep learning has advanced this field, mainstream frequency-based methods relying on standard scaled dot-product attention suffer from quadratic computational complexity and fail to exploit the inherent regional sparsity of remote sensing imagery. Furthermore, existing spatial enhancement strategies typically employ static convolution kernels, which struggle to adapt to the complex frequency and regional variations of PAN and MS images. To address these bottlenecks, we propose a Region-Aware Fusion (RAFNet) Network that synergistically models spatial and frequency information. Specifically, we design a Spatial Adaptive Refinement (SAR) module that leverages the discrete wavelet transform (DWT) for directional frequency separation and K-means clustering for regional partitioning, which enables the dynamic construction of region-specific adaptive convolution kernels, achieving spatially and frequency-adaptive feature enhancement. Moreover, we introduce a Clustered Frequency Aggregation (CFA) module based on a sparse attention mechanism guided by the semantic clusters, which executes a region-aware sparse attention strategy that drastically reduces computational redundancy while ensuring high-quality frequency feature extraction. In addition we integrated these modules into a progressive, multi-level spatial-frequency network architecture to facilitate robust interaction and accurate image reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that the proposed RAFNet significantly outperforms state-of-the-art pansharpening methods in both reduced- and full-resolution assessments. The code is available at https://github.com/PatrickNod/RAFNet.

preprint2020arXiv

Ekedahl-Oort strata of curves of genus four in characteristic three

We study the induced Ekedahl-Oort stratification on the moduli space $\mathcal{M}_4$ of curves of genus $4$ in characteristic $3$. By constructing families of curves with given Ekedahl-Oort type and by computing the dimension of the intersection of the induced Ekedahl-Oort strata and the boundary divisor classes, we show that for certain induced Ekedahl-Oort strata in $\mathcal{M}_4$, they have the same codimension in $\mathcal{M}_4$ as the corresponding Ekedahl-Oort strata in moduli space $\mathcal{A}_4$ of principally polarized abelian varieties of dimension $4$.

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