arXiv:2608. 17802v1 Announce Type: new Abstract: Let $\varepsilon_1,\ldots,\varepsilon_n$ be independent Rademacher signs and let $a=(a_1,\ldots,a_n)\in\R^n$ satisfy the normalization below.
arXiv:2608. 09870v1 Announce Type: cross Abstract: Uniform stability is a classical tool for controlling the generalization error of a learning algorithm.
arXiv:2609. 30105v1 Announce Type: new Abstract: For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant.
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.
Uniform stability controls how much one training example can change the loss at any test point. A new logarithmic-free upper bound shows that a $γ$-uniformly stable algorithm with loss in $[0,L]$ has...
arXiv:2608.24098v1 Announce Type: new Abstract: Uniform stability controls how much one training example can change the loss at any test point. A new logarithmic-free upper bound shows that a $\gamma...
arXiv:2609.38834v1 Announce Type: cross Abstract: Contrastive learning is a successful paradigm for learning $d$-dimensional geometric representations from a collection of ``anchor--positive--negativ...
arXiv:2607. 25492v2 Announce Type: replace Abstract: We study stochastic optimization with heavy-tailed gradient noise.
arXiv:2607. 22620v1 Announce Type: cross Abstract: Yun, Sra, and Jadbabaie (COLT 2021, open question) conjectured the SS--RS--GD inequalities: for well-conditioned symmetric matrices $A_1,\dots,A_n$, the operators $W_{ss}$, $W_{rs}$, and $W_{gd}$ that encode the expected iterate of single-shuffle SGD, random-reshuffle SGD, and gradient descent on a quadratic finite sum should satisfy \[ \|W_{ss}\|\le \| W_{rs}\|\le \|W_{gd}\|.
arXiv:2606.00661v2 Announce Type: replace-cross Abstract: Median-of-means (MoM) is a powerful technique that theoretically enables near sub-Gaussian finite-sample rate for parameter estimation when t...
arXiv:2608. 15558v1 Announce Type: cross Abstract: For $m\geq 2$, let $c_p(m)$ be the all-dimensional best constant in $$ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p.
Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem. Standard subspace embeddings guarantee that the cost of the regress...
arXiv:2609.09480v1 Announce Type: cross Abstract: We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences genera...