arXiv:2607. 07032v1 Announce Type: new Abstract: Spectral positional encodings (PEs) for \emph{directed} graphs face two obstacles: magnetic Laplacians require an $O(n^3)$ Hermitian eigendecomposition per potential, and their complex eigenvectors are defined only up to unitary gauge, which prior work handles with basis-invariant architectures.
By Jiaqing Xie, Yuxin Wang
arXiv:2607. 28428v1 Announce Type: new Abstract: We introduce Kohn--Sham Spectral Embedding (KSSE), a physics-inspired energy-based model replacing dense CNN classifiers with a sparse-graph spectral embedding evaluated at the Nishimori temperature of an associated Random-Bond Ising Model.
By V. S. Usatyuk, D. A. Sapozhnikov, S. I. Egorov
arXiv:2607. 06621v1 Announce Type: new Abstract: The pre-softmax score of an attention head is a bilinear form $score(i,j) = x_i^T M x_j$ in a learned operator $M = W_q^T W_k$.
By Li Hengyu (Institute for Solid State Physics, The University of Tokyo)
arXiv:2606. 19411v1 Announce Type: new Abstract: Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning -- data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design.
By Richard Yi Da Xu
arXiv:2606. 01227v1 Announce Type: new Abstract: Many networks not only support but also rely on transient non-normal amplification, an orders-of-magnitude increase in the activity of an otherwise stable system.
By James C. Ferguson
arXiv:2607. 04535v1 Announce Type: new Abstract: Orthogonal and Stiefel layers give neural weights exact spectral control, but they also impose a strong modeling constraint: all represented singular values are fixed at one.
By Haiwen Yi, Xinyuan Song