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.
By James Hartley, Zeropy Surio, Daniel Whitmore, Hannah Clarke, Thomas Reed
arXiv:2605.15240v2 Announce Type: replace-cross
Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
By Yang Liu, Ernest Fokoue, Richard Lange, Daniel Krutz
arXiv:2607. 07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation.
By Adam M. Oberman
arXiv:2606. 06494v1 Announce Type: new Abstract: Parameter-efficient finetuning methods based on spectral decomposition have enabled progress in Continual Learning.
By Marius Dragoi, Ioana Pintilie, Alexandra Dragomir, Antonio Barbalau, Florin Brad
arXiv:2608.19021v2 Announce Type: replace
Abstract: Global Covariance Pooling (GCP) improves deep networks by capturing second-order feature statistics, and is especially effective for fine-grained r...
By Md Rifat Ur Rahman, Md Raihan Khan, Md Sakib Hossain Shovon, Pietro Li\`o, Mohammad Ali Moni
arXiv:2509. 11285v2 Announce Type: replace-cross Abstract: Class-Incremental Learning (CIL) in deep neural networks is conventionally framed as an iterative gradient-based optimization problem, incurring high computational cost, hyperparameter sensitivity, and risk of catastrophic forgetting.
By Alejandro Dopico-Castro, Oscar Fontenla-Romero, Bertha Guijarro-Berdi\~nas, Amparo Alonso-Betanzos
arXiv:2607. 09371v1 Announce Type: cross Abstract: Flexible machine-learning methods can be sensitive to hidden confounding: they may learn associations induced by unobserved confounders rather than stable signals.
By Andrea Nava, Peter B\"uhlmann, Fabio Sigrist
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.
By Zihang Liu, Oleg Balabanov, Yaoqing Yang, Michael W. Mahoney
arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.
By Zhuan Liang, Zheng Zhai
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.
By Hang-Cheng Dong, Pengcheng Cheng
arXiv:2501. 10870v2 Announce Type: replace-cross Abstract: The principal objective of this work is twofold within nonparametric regression settings: (1) to establish the minimax optimal convergence rates for fixed-bandwidth Gaussian kernel spectral algorithms when the true regression function resides in a Sobolev space, and (2) to apply Gaussian spectral algorithms for achieving robust and adaptive transfer learning under concept shift.
By Haotian Lin, Matthew Reimherr
arXiv:2606. 01292v1 Announce Type: cross Abstract: Teacher-Student Knowledge Transfer (KT) is ubiquitous in modern machine learning, ranging from classical model compression via Knowledge Distillation (KD) to the emergent phenomenon of Weak-to-Strong (W2S) generalization.
By Wendao Wu, Fangqing Zhang, Haihan Zhang, Cong Fang