arXiv:2607. 03347v1 Announce Type: new Abstract: We consider the Multiscale Single-Index Model (MSIM), first introduced in \cite{oymak2021learning}, as a stylized model for hierarchical learning with \emph{scale separation}.
By Joan Bruna
arXiv:2606. 00500v1 Announce Type: cross Abstract: We present a simple and efficient algorithm for robust approximate message passing (AMP) in the spiked matrix setting.
By Misha Ivkov, Tselil Schramm
arXiv:2505. 10882v2 Announce Type: replace Abstract: Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample.
By Alex Saad-Falcon, Brighton Ancelin, Justin Romberg
The paper presents empirical scaling laws for autoregressive language models, linking prediction loss to model size, data size, and compute, and investigates their theoretical basis using a teacher–student linear RNN framework. In this tractable setting, a stable latent linear RNN generates trajectories while a sketched linear recurrent student is trained via full‑batch WSD gradient descent on next‑token prediction. The study derives explicit approximation, optimization, and statistical scaling laws that depend on the sketch dimension, number of trajectories, and trajectory length, revealing how different power‑law exponents for innovation and initialization covariances affect the rates and crossovers between regimes.
By Ziyan Chen, Zhongzhu Zhou, Peilin Liu, Ding-Xuan Zhou
arXiv:2606. 14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity.
By Dhruv Sarkar, Vaneet Aggarwal
arXiv:2602. 05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion.
By Hengrui Luo, Anna Ma, Ludovic Stephan, Yizhe Zhu