Higher-Order
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
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...
From Time to Space: The Impact of Linearity in Higher-Order Datalog
Announce Type: new Abstract: We consider a fragment of Higher-Order Datalog with negation and argue that it generalizes the familiar and important fragment of Linear Datalog. We investigate the expressive power of this fragment, establishing a tight connection with the hierarchy of space complexity classes. In particular, we demonstrate that for all $k \ge 1$, the $(k+1)$-order fragment of Stratified Linear Higher-Order Datalog$^\neg$ captures $(k-1)$-EXPSPACE.
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...
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...
HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations
Announce Type: replace Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations--such as simplicial or cellular complexes--to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order...
Coexistence of dipolar and quadrupolar higher-order topology
Announce Type: new Abstract: Two-dimensional higher-order topological insulators are typically classified either as dipolar or quadrupolar depending on the relevant invariant. These two classes were previously considered non-overlapping. Here we put forward an example system exhibiting dipolar and quadrupolar higher-order topology simultaneously, suggest its implementation using the arrays of laser-written evanescently coupled optical waveguides and support our conclusions by the full-wave...
Equilibrium Semantics and Strong Equivalence for Higher-Order Logic Programs
arXiv:2606.02387v1 Announce Type: new Abstract: One of the most significant achievements of equilibrium logic was the characterization of strong equivalence, a property crucial for program transformation and optimization in Answer Set Programming (ASP). While ASP has recently been extended to a higher-order setting to enhance its expressive power, the lack of a comparable purely logical foundation has made verifying strong equivalence for higher-order programs or even proving the correctness...
Defining and classifying models of groups: The social ontology of higher-order networks
arXiv:2507.02758v2 Announce Type: replace Abstract: In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information broadcasting, showing how higher-order networks can capture group effects more directly than pairwise models. However, equating hyperedges-edges involving more than two agents-with groups can be misleading, as it...
Essential Unitarity for Higher-Order Quantum Computation
arXiv:2606.04080v1 Announce Type: cross Abstract: We develop a semantic framework for higher-order quantum computation based on a boundary-centric presentation of compact closed categories, building on Kelly--Laplaza and Abramsky. Morphisms are polarized boundary linkings composed by execution, with a unit-free monoidal sum providing reversible control and branching. We identify a notion of \emph{essential unitarity} generalizing unitarity from first-order processes to higher-order...
HoT-SSM:Higher-order Temporal Knowledge Graph Reasoning with State Space Models for Health Care
Announce Type: new Abstract: Medical knowledge graphs (MKGs) infused with clinical knowledge have been increasingly used to model electronic health records (EHRs) to support interpretable predictions in healthcare domain. However, existing MKG-based approaches are limited in capturing pairwise relations between clinical concepts (e.g., conditions, procedures, and medications), and restricts their ability to model higher-order interactions among co-occurring or semantically related concepts....