arXiv:2606. 00703v1 Announce Type: cross Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible.
By Munsik Kim
arXiv:2609.37994v1 Announce Type: cross
Abstract: The classical information bottleneck (IB) measures the relevance of a representation $U$ of $X$ to a target $Y$ by $I(U;Y)$, which does not directly...
By Dier Tang, Guangyue Han
arXiv:2609. 29696v1 Announce Type: new Abstract: We construct, for every function class $\mathcal{F}\subseteq[0,1]^{\mathcal{X}}$ and every accuracy $0<\alpha\le 1$, an agnostic sample compression scheme for the empirical squared loss: for every finite sample $S\in(\mathcal{X}\times[0,1])^m$ with arbitrary (noisy) labels, the scheme stores at most $O(\mathrm{fat}(\mathcal{F},c'\alpha)\cdot\log^3(2/\alpha))$ original labeled examples and auxiliary bits, independent of the sample size $m$, and reconstructs a function $\hat f$ with $L_2(\hat f,S)\le\inf_{f\in\mathcal{F}}L_2(f,S)+\alpha$.
By Guangjian Zhang
arXiv:2606. 07931v1 Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes.
By Yunbei Xu
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.
By Aleksandr Storozhenko
arXiv:2609. 08564v1 Announce Type: cross Abstract: We study distributed one-dimensional mean estimation under a 1-bit communication constraint.
By Ivan Lau, Jonathan Scarlett