EquiReg introduces an equivariance‑regularized diffusion framework that penalises sampling trajectories deviating from the data manifold, thereby improving posterior sampling for inverse problems. By formalising manifold‑preferential equivariant functions—naturally arising from data augmentation or inherent symmetries—EquiReg guides diffusion steps toward symmetry‑preserving regions of the solution space. The method shows consistent gains in both linear and nonlinear image restoration tasks and partial differential equation solving, especially under reduced sampling and measurement consistency steps, and is available as open‑source code.
By Bahareh Tolooshams, Aditi Chandrashekar, Rayhan Zirvi, Abbas Mammadov, Jiachen Yao, Chuwei Wang, Anima Anandkumar
ChebBooster is a training‑free extrapolation framework that accelerates Diffusion Transformers (DiTs) by using Chebyshev polynomial theory. It employs a Barycentric formulation for numerically stable evaluation and separates the process into an offline weight precomputation phase and a lightweight online application stage. Experiments on DiT‑XL/2, PixArt‑Σ, and FLUX.1‑dev show consistent visual quality gains and up to 3.68× latency speedup and 5.12× FLOPs reduction compared to existing training‑free baselines.
By Chengjie Lu, Tianchi Deng, Zhengqi He, Chengwen Luo, Xueliang Li
arXiv:2512. 06143v2 Announce Type: replace Abstract: Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists.
By Marcus M. Noack, Mark D. Risser, Hengrui Luo, Vardaan Tekriwal, Ronald J. Pandolfi
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.
By Lucas Gerken Starepravo, Henry Broadley, Steven Lind, Jack R. C. King
arXiv:2606. 07495v1 Announce Type: new Abstract: Understanding how training data shape neural network predictions is a central problem in modern learning theory.
By Jin Guo, Roy Y. He, Jean-Michel Morel
arXiv:2111. 10722v4 Announce Type: replace-cross Abstract: We propose a novel deterministic sampling method, EVI-MMD, to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD).
By Yindong Chen, Yiwei Wang, Lulu Kang, Chun Liu