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Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization

arXiv:2606.05438v1 Announce Type: new Abstract: We study the deterministic first-order oracle complexity of finding \(\epsilon\)-stationary points in smooth nonconvex optimization when the objective satisfies higher-order smoothness assumptions. While the classical \(\epsilon^{-2}\) rate is optimal under only Lipschitz gradients, higher-order smoothness leads to accelerated first-order upper bounds, most notably the \(\epsilon^{-7/4}\) rate under Lipschitz Hessians and the...

arXiv CS 6d ago

State-Space Neural Network with Ordered Variance for Model Order Determination

arXiv:2406.10359v3 Announce Type: replace Abstract: This paper addresses the problem of identifying a nonlinear state-space model, along with an adequate model order, from a given input-output training dataset. To this end, a novel framework, termed state-space neural network with ordered variance (SSNNO), is proposed. In SSNNO, the state variables are ordered according to their variances computed using the training data.

arXiv CS 9d ago

Competing heterogeneities shape ordering via higher-order interactions

arXiv:2605.30948v1 Announce Type: cross Abstract: Higher-order interactions admit richer structural heterogeneity than pairwise networks. To understand how heterogeneity impacts collective phenomena we develop a framework based on the cavity method and apply it to the simplicial Ising model on heterogeneous hypergraphs. Unlike in homogeneous structures, group size and node degree play fundamentally different roles: size heterogeneity sharpens the transition via large-group unanimity, while...

arXiv Physics 10d ago

High-Order Summation-By-Parts Schemes for First-Order Hyperbolic Systems in Curvilinear Coordinates with Singularities

Announce Type: cross Abstract: Formulating stable numerical methods for hyperbolic systems in curvilinear coordinate with singularities, e.g. spherical coordinates, is complicated by the presence of these singularities. We present a method for constructing high-order accurate, energy-stable finite difference operators satisfying the Summation-by-Parts (SBP) property on spherical domains, extending ideas presented by [C. Gundlach, J. M. Mart\'in-Garc\'ia, and D. Garfinkle, CQG 30, 145003 (2013)].

arXiv CS 7d ago

Meaning in Order, Order in Meaning: Semantic R-precision for Keyphrase Evaluation

Announce Type: new Abstract: Evaluating the quality of automatically generated keyphrases remains a complex challenge. Traditional metrics either rely on exact lexical matching or consider semantic similarity while ignoring prediction ranking, both of which misalign with how humans judge informativeness and relevance. We introduce Semantic R-Precision (SemR-p), a novel evaluation metric that integrates semantic similarity into the rank-aware R-Precision framework.

arXiv CS 3d ago

High-order thermodynamic nonequilibrium in three-dimensional compressible flows: Kinetic moment closure and multigradient coupling

arXiv:2606.05938v1 Announce Type: new Abstract: High-order thermodynamic nonequilibrium (TNE) in three-dimensional compressible flows reflects the breakdown of low-order kinetic moment closure in strong-gradient regions. Using Chapman-Enskog analysis, we identify the kinetic moment constraints required to describe third-order TNE. The analysis yields the third-order constitutive relations and evolution equations for the viscous stress and heat flux, together with second-order expressions for...

arXiv Physics 6d ago

Cathay Pacific plans more aircraft orders across fleet, CEO says

Cathay Pacific plans more aircraft orders across fleet, CEO says RIO DE JANEIRO: Cathay Pacific is considering additional orders for widebody, narrowbody and freighter aircraft as it looks to expand rapidly over the next decade, taking advantage of a third runway at its Hong Kong hub, Chief Executive Officer Ronald Lam said on Sunday (Jun 7). Lam said this could include fresh orders and exercising options to expand previous orders. Cathay already has more than 100 new aircraft on order,...

Channel News Asia 3d ago

Higher-order bialgebraic semantics

Announce Type: replace Abstract: Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which provides off-the-shelf compositionality results for first-order languages, so far does not apply to higher-order languages. In the present work, we develop a theory of abstract GSOS specifications for higher-order languages, in...

arXiv CS 10d ago

Learning a Zeroth-Order Optimizer for Fine-Tuning LLMs

Announce Type: replace Abstract: Zeroth-order optimizers have recently emerged as an attractive approach for fine-tuning large language models (LLMs), as they avoid backpropagation and can substantially reduce memory overhead relative to standard first-order training. However, existing zeroth-order methods rely on hand-crafted, static sampling strategies that are not adaptable to model-specific structures. To address this, we propose ZO-Finetuner, a learning-based zeroth-order optimizer for...

arXiv CS 10d ago

CAREAgent: Clinical Agent with Structured Reasoning and Tool-Integrated for Order Generation

Announce Type: new Abstract: Clinical order generation serves as a critical bridge between clinical decision-making and real-world practice, translating medical decisions into concrete and executable orders. Existing agents mainly focus on coarse-grained decisions and overlook the fine-grained, executable information required for clinical orders. To address this gap, we propose CAREAgent, an agent for clinical order generation.

arXiv CS 9d ago