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arXiv:2610. 12358v1 Announce Type: cross Abstract: We study Gaussian regression under squared population $L_2$ loss in a known $m$-dimensional subspace of degree-at-most-$k$ functions on the $d$-dimensional Boolean cube.
An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input-dependent sparsity in the one-hidden-layer ReLU model of Awasthi et al.
arXiv:2609.09130v1 Announce Type: new Abstract: An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input...
The paper establishes the optimal incremental first‑order oracle (IFO) complexity for nonconvex finite‑sum optimization under individual smoothness, proving a matching lower bound that closes a previously missing √{n} factor. It also refines the analysis of the PAGE algorithm under the global Polyak‑Lojasiewicz condition, providing tighter guarantees for different ranges of the condition number. The authors introduce a novel dense weak hiding construction that yields these lower bounds and demonstrates the limits of existing methods.
arXiv:2608.28150v2 Announce Type: replace Abstract: How much matrix rank is required to preserve every bounded value output of normalized softmax attention? We study the unrestricted maximum-row-\(\e...
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 $L_2(\hat f,S)\le\inf_{f\in\mathcal{F}}L_2(f,S)+\alpha$.