arXiv:2602. 09530v2 Announce Type: replace-cross Abstract: We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization.
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The paper introduces Spectrally Optimised Neural Discretisations (SpeND), a mesh‑free framework that learns discretisation weights from local stencil geometry on unstructured point clouds. By embedding discrete moment conditions into the network architecture, SpeND guarantees polynomial consistency and allows the weights to be optimised for spectral accuracy over a chosen wavenumber band, using an unsupervised Fourier‑mode loss. The resulting operators are PDE‑agnostic, perform well on Poisson, Burgers, and Navier–Stokes equations, and can reduce wall‑clock time by 3–20× compared to existing mesh‑free methods at the same accuracy.
SPARCL introduces a spectral partitioned analytic continual learning method that addresses forgetting in analytic class‑incremental learning. By decomposing the running autocorrelation into a high‑energy core and a residual complement, SPARCL freezes core components for old classes and updates only the residual block, ensuring closed‑form updates with an invariance guarantee. Experiments on CIFAR‑100, CUB‑200, ImageNet‑R, and ImageNet‑A with a frozen ViT‑B/16 protocol show that SPARCL narrows the performance gap between classical analytic learners and strong representation matchers while complementing sparse feature‑decorrelation approaches.
The paper introduces HermNet, a spectral graph neural network that uses Hermite polynomials for nodewise prediction and normalized propagation, avoiding eigendecomposition or learned bases. It compares HermNet to other complete polynomial bases, examining how coordinate choices affect optimization under limited training. Experiments on synthetic and real data show regimes where HermNet outperforms alternatives, and analyze the impact of calibration, regularization, and training duration on performance.
arXiv:2606. 00401v1 Announce Type: cross Abstract: Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies.
arXiv:2609. 23529v1 Announce Type: new Abstract: Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment.
arXiv:2606. 07289v1 Announce Type: new Abstract: Model merging combines several independently fine-tuned experts into a single multi-task model without any training data, reducing the storage, serving, and decentralized-development costs of large foundation models.