7053 papers
This paper proposes D-APDB, a distributed accelerated primal-dual algorithm with backtracking that achieves optimal convergence for decentralized constrained optimization over undirected networks without requiring prior knowledge of Lipschitz constants, making it the first method of its kind to handle private nonlinear constraints efficiently.
This paper investigates non-semisimple near-group categories in the braided setting, proving that non-degenerate instances are braided simple extensions of with specific Lagrangian properties, while general cases arise canonically as extensions by the Picard group of a symmetric subcategory.
This paper proposes a Bayesian nonparametric framework for finite mixture models with nonparametric components, establishing theoretical guarantees for component identifiability and near-polynomial posterior contraction rates while providing an efficient MCMC algorithm for inference.
This paper establishes homological stability for automorphisms of symmetric bilinear forms over a broad class of principal ideal domains, thereby determining a significant portion of the stable cohomology of odd orthogonal groups over the integers in low degrees.
The paper demonstrates that various categories of trees, including the dendroidal category , the category of trees with a -action, and the category of genuine equivariant trees , can be modeled as Grothendieck constructions on categories of trees with a fixed set of leaves.
This paper establishes the first rigorous Nekhoroshev-type stability results for ultra-differentiable solutions of non-local semilinear Schrödinger equations without external parameters by employing rational normal forms and a novel global vector field norm, achieving optimal stability times under Gevrey regularity assumptions.
This paper establishes a minimax theory for operator learning in Hilbert spaces, proving that even with higher regularity assumptions, learning generic Lipschitz operators from noisy samples inevitably suffers from a curse of sample complexity where the risk cannot decay at any algebraic rate.
This paper provides an elementary proof for Ramanujan-type identities expressing the squares of the Riemann zeta function at integer points through series involving hyperbolic functions, the digamma function, and Bernoulli numbers, while also correcting previous inaccuracies and adding new sections, a figure, and a reference.
This paper constructs a diagrammatic categorification of the spherical module over the Hecke algebra, establishes a basis for its morphism spaces, and proves its equivalence to an existing algebraic spherical category.
This paper establishes that a -generic non-trivial sectional-hyperbolic chain-recurrent class satisfies a trichotomy, being either a homoclinic loop, a union of saddle connections between singularities, or robustly a homoclinic class, thereby providing a partial answer to questions posed in a 2021 publication.
This paper confirms Xin and Zhang's conjecture by deriving a simple product formula for the characteristic polynomial of a specific tridiagonal matrix related to the enumeration of nonnegative integer matrices with fixed row and column sums, while also extending these results to broader families of such matrices.
This paper investigates the total population levels in heterogeneous environments with directed diffusion for any power-law relationship between intrinsic growth rate and carrying capacity, disproving the existence of a critical exponent that determines population prevalence over carrying capacity and analyzing how the total population depends on the diffusion coefficient under a generalized dispersal strategy.
This paper introduces xBound, the first theoretical framework for computing provable join size lower bounds, which addresses the critical issue of cardinality underestimation in production databases by correcting 23.6% of errors and delivering up to 20.1x query speedups on Microsoft's Fabric Data Warehouse.
This paper establishes sharper convergence guarantees for the Muon optimizer by providing a direct, simplified analysis that achieves faster convergence rates under broader problem settings than existing restrictive theoretical frameworks.
This paper introduces a novel numerical method that combines a functional equation for the Laplace-Stieltjes transform with a moment-matching technique to efficiently and stably compute the density of the Kesten-Stigum limit for supercritical Galton-Watson processes with arbitrary offspring laws.
This paper introduces Latent-IMH, an efficient Bayesian sampling method for inverse problems with expensive operators that leverages cost-effective approximations to shift computational costs to an offline phase, achieving significantly faster performance than state-of-the-art methods like NUTS.
This paper extends previous results on the sum-product problem by proving that any set of 10 or 11 natural numbers must generate at least 30 or 34 distinct pairwise sums or products, respectively, while providing a classification of extremal sets and analyzing additive structures in small subsets of generalized geometric progressions.
This paper proposes a variational framework that interprets transformer layers as optimization iterations, enabling the design of a Nesterov-accelerated transformer architecture that outperforms standard baselines on language modeling tasks.
This paper establishes the previously unprinted universal property of the bicategory of modules () constructed from -enriched categories, presenting it as an objective generalization of Joyal's homological functors that characterizes the inclusion of a bicategory into its module bicategory as a completion with respect to freely adjoining lax colimits.
This paper investigates the deformation behavior of pseudo-effective canonical divisors and volumes of adjoint classes in Kähler families, establishing global stability results under specific conditions and confirming Siu's invariance of plurigenera conjecture for smooth Kähler threefolds.