A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New Riemannian optimization improves variance estimation in mixed models.
HLRC offers a new curvature metric for hypergraphs that balances interpretability and efficiency.
We compare two ways of interpreting higher order connections. The geometric approach lies in the decomposition of higher order tangent space into the horizontal and vertical structures while the jet--like approach considers a higher order connection as the section of a jet prolongation of a fibered manifold. Particular…
Higher-order tangent bundles have geometric structures compatible with their iterated bundle structure.
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for this higher order situation and derive in this framework the phase equations fro…
Unified geometric framework for quantum states using dual number algebras.
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
Enhanced spectral clustering for geometric graphs improves clustering accuracy.
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting appli…
New symmetry dimensions for higher order ODEs are identified.
Geometric analysis on diffeomorphism groups for fluid dynamics and information geometry.
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann -invariants, which we call higher-order signatures. The higher-order genera o…
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding map covariant derivatives and a careful application of the DeTurck…
Generalizes Carathéodory form for higher-order field theories.
The paper provides estimates for higher-order Ricci curvature along Kähler-Ricci flows.
The paper studies geometric Airy curve flows on R^n and their properties.
Study compares hypergraph and graph-level models for higher-order relational learning.
The paper refines classical covariance asymptotics using geometric information geometry.
We present a geometric approach to the field theory with higher order anisotropic interactions. The concepts of higher order space, or locally anisotropic, space (in brief, h-space, or la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimen…
Graph Convolution Network (GCN) has been recognized as one of the most effective graph models for semi-supervised learning, but it extracts merely the first-order or few-order neighborhood information through information propagation, which suffers performance drop-off for deeper structure. Existing approaches that deal…
In this paper, we show that feedforward and recurrent neural networks exhibit an outer product derivative structure but that convolutional neural networks do not. This structure makes it possible to use higher-order information without needing approximations or infeasibly large amounts of memory, and it may also provid…
New method uses information theory to uncover causal relationships in complex systems.
Combines neural networks and probabilistic graphical models for efficient higher-order inference.
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothn…
The work proposes a geometric background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagra…
A new method for higher-order co-occurrences in hypergraphs.
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
We present an introduction to the geometry of higher order vector and co--vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by higher order nonlinear con…
New minimal surfaces in 4D space derived from parametric equations.
This paper describes the relationship between the first non-vanishing Milnor invariants of a classical link and the intersection invariant of a twisted Whitney tower. This is a certain 2-complex in the 4-ball, built from immersed disks bounded by the given link in the 3-sphere together with finitely many `layers' of Wh…
The paper introduces a geometric flow for Lagrangian submanifolds that preserves Hamiltonian isotopy.
We introduce nonlinear higher-order label spreading for semi-supervised learning.
Neural network learns from higher-order connections in molecules.
Unified framework for higher-order network analysis.
Generative model designs highly designable proteins using geometric algebra.
Geometric AD framework simplifies derivative computation in JAX.
Geometric GNNs improve graph discrimination through GWL.
Unified approach to discrete and smooth isoperimetric inequalities of arbitrary order.
In this note we review some results regarding higher order elliptic differential operators on manifolds without boundary.
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples are provided.
New method combines hypergraph structure and node attributes for better community detection.
HyperBERT enhances BERT for node classification on text-attributed hypergraphs.
Based on ideas of L. Alías, D. Impera and M. Rigoli developed in "Hypersurfaces of constant higher order mean curvature in warped products", we develope a fairly general weak/Omori-Yau maximum principle for trace operators. We apply this version of maximum principle to generalize several higher order mean curvature est…
We formulate higher order variations of a Lagrangian in the geometric framework of jet prolongations of fibered manifolds. Our formalism applies to Lagrangians which depend on an arbitrary number of independent and dependent variables, together with higher order derivatives. In particular, we show that the second varia…
Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.
We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with higher order Lagrangian and the Plateau problem.
This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from known conditional symmetries, and unnecessary previous assumptions of the theory are…