arXiv:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.
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.
The paper introduces a Geometric-to-Semantic Spherical Transfer Learning framework for labeling cortical sulci on brain surfaces. It first pre‑trains a spherical encoder on ~30,000 unlabeled UK Biobank subjects using only curvature and depth, then injects sulcal fundi lines as a soft‑initialized Topological Prior Injector to bridge the geometric‑semantic gap. Experiments show the method surpasses fully supervised baselines, achieving a mean Dice score of 0.77 and delivering the largest gains on variable and tertiary sulci.
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
arXiv:2605. 13834v2 Announce Type: replace-cross Abstract: In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective.
arXiv:2607. 17962v1 Announce Type: cross Abstract: TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs.
arXiv:2607. 06348v1 Announce Type: new Abstract: We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations.
arXiv:2609.24379v1 Announce Type: cross Abstract: Mechanistic interpretability of vision transformers seeks to decompose model computation into human-readable units, but learned representations entan...
arXiv:2608. 06894v1 Announce Type: new Abstract: Neural operators have become a central tool for solving partial differential equations (PDEs), with spectral operators offering efficient global mixing across spatial locations.
Mechanistic interpretability of vision transformers seeks to decompose model computation into human-readable units, but learned representations entangle many concepts in each neuron. Feature superposi...
arXiv:2605. 08318v2 Announce Type: replace Abstract: We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators.
arXiv:2606. 05581v1 Announce Type: cross Abstract: Intrinsic methods fill the default toolbox for geometry processing on meshes.