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:2608. 11661v1 Announce Type: cross Abstract: A multiplicative dual-encoder network computes a real-valued output for a pair of inputs as the inner product of their separate encodings.
By Zijian Zhao, Sen Li
The paper addresses the limitations of spectral dimension reduction for dynamical systems composed of weakly interacting components, where standard rank‑based methods either require exponentially many modes or omit entire components (a phenomenon termed linear masking). It proposes scoring the σ‑algebra generated by coordinates instead of individual modes, using a χ²‑divergence criterion that guarantees an embedding with twice the intrinsic dimension captures the full operator spectrum. Experiments on benchmark systems show that this algebraic approach recovers masked components and enables accurate prediction from few labels, outperforming traditional rank‑based and VAMP methods.
arXiv:2406. 13944v2 Announce Type: replace-cross Abstract: This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning, where data from diverse distributions are available.
By Yanke Song, Kenneth Gu, Sohom Bhattacharya, Pragya Sur
arXiv:2604. 08625v3 Announce Type: replace-cross Abstract: Benign overfitting describes the ability of minimum norm interpolating estimators to generalize despite fitting noisy data exactly.
By Gustav Olaf Yunus Laitinen-Fredriksson Lundstr\"om-Imanov
arXiv:2408. 01139v4 Announce Type: replace Abstract: Perturbation robustness evaluates the vulnerabilities of models, arising from a variety of perturbations, such as data corruptions and adversarial attacks.
By R\'ois\'in Luo, James McDermott, Colm O'Riordan
arXiv:2609.15825v1 Announce Type: new
Abstract: A self-supervised encoder is trained once, frozen, and reused through lightweight probes on tasks nobody named at training time; the practitioner's que...
By Dier Tang, Jing Yee Tan, Guangyue Han
The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.
By Lei Shi, Jia-Qi Yang, Ding-Xuan Zhou
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
arXiv:2606. 07627v1 Announce Type: new Abstract: Transfer learning presumes that a representation learned on source tasks carries structure that remains usable on related target tasks.
By Luciano Melodia
The paper proposes a new dimension‑reduction strategy for transfer‑operator models of dynamical systems that focuses on scoring the σ‑algebra generated by coordinates rather than the operator’s spectral span. By using a χ²‑divergence criterion between embedded present and future states, the method guarantees that twice the intrinsic system dimension suffices to capture the full operator spectrum, even for systems with weakly interacting components that would otherwise require exponentially many modes. Experiments on benchmark systems show that this algebraic approach recovers masked components missed by rank‑based methods and enables accurate prediction of those components from few labels.
By Mark Kozdoba, Shie Mannor
arXiv:2604. 08625v2 Announce Type: replace-cross Abstract: We develop a theoretical framework for generalization in the interpolating regime of statistical learning.
By Gustav Olaf Yunus Laitinen-Lundstr\"om Fredriksson-Imanov