TL;DR
The Spectral-Domain Anchor Learning (SDAL) framework is proposed, which transitions from localized spatial gradient descent to explicit spectral-domain parameterization, providing a scalable foundation for large-scale computer vision and continuous spatial learning.
The Graph Spectral Neural Operator is introduced, a neural operator that combines spatial graph spectral decompositions with temporal Fourier transforms through a unified space--time spectral kernel that enables globally coherent operator learning on non-Cartesian discretizations without domain warping or autoregressiv...
Flow-matching diffusion models have recently emerged as a strong paradigm for high-fidelity visual generation. However, their prohibitively high fine-tuning cost limits scalability to downstream tasks. While Low-Rank Adaptation (LoRA) combined with spectral initialization has demonstrated accelerated convergence and im...
Many forms of data, including physical fields, geometric shapes, and visual signals, are naturally described by functions over continuous domains but are observed through discrete samples. Representing these functions on fixed uniform grids imposes a trade-off between resolving localized variation and increasing comput...
FreKoo++ is proposed, a novel continuous spectral-dynamical framework that pioneers the unification of continuous Koopman modal dynamics with adaptive spectral disentanglement and derives modal approximation and generalization bounds that characterize how amplitude and eigenvalue estimation errors propagate with the pr...
This work defines an explicit surrogate posterior path and derives the Posterior-Dynamics Implicit--Explicit sampler (PD-IMEX), a stable method using one score evaluation per diffusion scale and an implicit data-consistency update, and derives continuous posterior dynamics.
Dynamic and spectrally varying degradation severely limits the quality of hyperspectral images and poses great challenges for super-resolution, as conventional methods rely on static models that cannot adapt to real-world complexity. To address this, we propose a Spectral-Spatial Embedded Physical Degradation Perceptio...
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