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.
Local classification of 4D Ricci solitons with specific algebra properties.
A lemma of Tits establishes a connection between the simple connectivity of an incidence geometry and the universal completion of an amalgam induced by a sufficiently transitive group of automorphisms of that geometry. In the present paper, we generalize this lemma to intransitive geometries, thus opening the door for …
We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the…
There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of intransitive comparisons have been proposed, but in all cases the maximum likeliho…
Investigates CR structures in 7D, showing 8 is max symmetry dimension.
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and prolongation. We show how to construct certain normal forms (Cartan algebroids) …
We consider the problem of estimating a ranking on a set of items from noisy pairwise comparisons given item features. We address the fact that pairwise comparison data often reflects irrational choice, e.g. intransitivity. Our key observation is that two items compared in isolation from other items may be compared bas…
For surfaces, we brush a reasonably sharp picture of the influence of the fundamental group upon the complexity of foliated-dynamics. A metaphor emerges with phase-changes through the solid-liquid-gaseous states. Groups of ranks are frozen with intransitivity reigning ubiquitously. When , th…
This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the equivalence, local and global, of transitive structures. Cartan's Flag Systems illustrate the theory as a major example and, finally, some a…
Lie algebroids are by no means natural as an infinitesimal counterpart of groupoids. In this paper we propose a functorial construction called Nishimura algebroids for an infinitesimal counterpart of groupoids. Nishimura algebroids, intended for differential geometry, are of the same vein as Lawvere's functorial notion…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie algebroid structure. The curvature of this connection vanishes precisely when the struc…
In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to projective geometry formalism and gene…
A multiplicatively closed, horizontal -plane field on a Lie groupoid over generalizes to intransitive geometry the classical notion of a Cartan connection. The infinitesimalization of the connection is a Cartan connection on the Lie algebroid of , a notion already studied elsewhere by th…
The study extends Jacobi-orthogonality to indefinite scalar product spaces.
New characterization of Osserman tensors using Jacobi-orthogonality.
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
New findings on Kähler manifolds restrict orthogonal coordinates existence.
Constructs orthogonal coordinates in curved spaces.
OPT framework improves neural network generalization by learning an orthogonal transformation.
The paper studies surfaces in a bounded domain with orthogonal boundaries and proves curvature estimates.
Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
Novel prior for orthogonal functions improves functional component estimation.
Method constructs orthogonal curvilinear coordinates in constant curvature spaces.
We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mariño-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal Chern-Simons partition function. We prove the degree conjecture and some interesting cases o…
A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is disc…
DONUT improves treatment effect estimation by enforcing orthogonality constraints.
New convergence guarantees for learning with unknown nuisance parameters.
MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.
Orthogonal initialization does not speed up training in ultra-wide neural networks.
A new algorithm POGO optimizes thousands of orthogonal matrices efficiently.
Batch normalization makes deep neural networks' representations increasingly orthogonal.
The paper finds at least N orthogonal Finsler geodesic chords in a disk-like manifold.
Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we…
LOFT separates subspace rotation and transformation for orthogonal fine-tuning.
New method enforces orthogonality in convolutional layers for improved robustness.
We propose orthogonality as a necessary condition for disentangling aleatoric and epistemic uncertainty.
VRSGT algorithm reduces orthogonality constraints in decentralized optimization.
We orthogonalize the NSS model to condition and diagnose its ill-conditioned parameters.
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to be orthogonal across summands, by relating this orthogonal decomposition to the…
New metrics improve landing algorithms for orthogonality constraints.
A notion of orthogonality in multisymplectic geometry has been developed by Cantrijn, Ibort and de León and used by many authors. In this paper, we review this concept and propose a new type of orthogonality in multisymplectic geometry; we prove a number of results regarding this orthogonality and its associated subspa…
New algorithms reduce orthogonality constraint enforcement time in machine learning.
Ranking data arises in a wide variety of application areas but remains difficult to model, learn from, and predict. Datasets often exhibit multimodality, intransitivity, or incomplete rankings---particularly when generated by humans---yet popular probabilistic models are often too rigid to capture such complexities. In…
Study removes bias from chest X-ray embeddings using orthogonalization.
We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error. We call this technique Orthogonal Random Features (ORF), and provide theoretical…
AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
Paper links set derivatives to its orthogonal projections.