arXiv AI By Dengdi Sun, Xiaoya Zhou, Xiao Wang, Wanli Lyu, Jin Tang, Bin Luo

SPEAR: A Spectral-Disentangled MoE Neural Operator with Knowledge-Guided Expert Aggregation for Large-Scale PDE Pretraining

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arXiv AI
Oct 15

SLEM: Spectrum-Aware Latent Expert Merging

arXiv:2610.16484v1 Announce Type: cross Abstract: Mixture-of-Experts (MoE) models scale model capacity efficiently by activating only a small subset of experts for each input, while still requiring a...

By Dohyeon Kim, Bedionita Soro, Bruno Andreis, Sung Ju Hwang
arXiv Machine Learning
Sep 4

Towards a Statistical Understanding of Mixture-of-Experts

The paper presents a statistical framework for Mixture-of-Experts (MoE) models, treating them as localized aggregation systems. It derives oracle risk bounds that separate approximation, expert‑learning, and router‑estimation errors for both dense and sparse routing with evolving experts. The authors also analyze how sparse Top‑K routing balances computational cost with performance, interpret gating geometrically, and explain how shared experts can capture common predictive structure while allowing routed experts to focus on local residuals.

By Siyuan He, Bokai Yang, Jie Hu, Ziwen Gao, Yuhong Yang
arXiv Machine Learning
Oct 12

PDE-PFN: Prior-Data Fitted Neural PDE Solver

PDE-PFN is a prior‑data fitted neural solver that uses in‑context learning to approximate the posterior predictive mean of partial differential equation (PDE) solutions. It builds on a Transformer‑based PFN architecture with self‑ and cross‑attention, and is pre‑trained on noisy approximate solutions generated by physics‑informed neural networks. Experiments on various two‑dimensional PDEs show that PDE‑PFN generalizes across heterogeneous equations, remains robust to noisy priors, and can perform zero‑gradient‑update inference while achieving competitive or better predictive accuracy compared to baselines.

By Jaehyeon Park, Mingu Kang, Dongseok Lee, Woojin Cho, Kookjin Lee, Anthony Gruber, Youngjoon Hong, Noseong Park