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.
Study optimizes estimation of orthogonal and rotation matrices from noisy data.
Spectral methods achieve near-optimal performance in orthogonal and permutation group synchronization.
Spectral method for joint community detection and group synchronization.
NS-RGS improves orthogonal group synchronization with faster convergence.
Paper addresses group synchronization with incomplete measurements and proves linear convergence of GPM.
Novel higher-order group synchronization for noisy local measurements on hypergraphs.
New method uses neural networks for accurate angle estimation in noisy conditions.
Efficiently estimates rotations with corrupted data.
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work addresses the problem of synchronizing transformations that are not transitively co…
Novel method solves group synchronization with robust corruption tolerance.
We propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of gr…
Paper proposes GPM for simultaneous community detection and group synchronization.
Extends angular synchronization to heterogeneous groups, improving accuracy in multiple applications.
Adapts pivoting technique to circle homeomorphisms for proofs.
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
DS-Sync improves distributed DNN training efficiency by 94% with minimal accuracy loss.
The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost f…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or SO(3). The goal of such problems is to estimate an unknown vector of group eleme…
In this paper, we show synchronization for a group of output passive agents that communicate with each other according to an underlying communication graph to achieve a common goal. We propose a distributed event-triggered control framework that will guarantee synchronization and considerably decrease the required comm…
Detects synchronized behavior in streaming data.
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis (e.g., ranking teams in sports data), computer vision, and machine …
Formula for Laplace-Beltrami on orthogonal group in Euclidean coords.
A Lie group is called orthogonal if it carries a bi-invariant pseudo Riemannian metric. Oscillator Lie groups constitutes a subclass of the class of orthogonal Lie groups. In this paper, we determine the Lie bialgebra structures and the solutions of the classical Yang-Baxter equation on a generic class of oscillator Li…
Algorithm finds isotropy subgroups of orthogonal similarity on symmetric matrices.
Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
Integrable geodesics found on special orthogonal group.
We introduce a novel approach to perform first-order optimization with orthogonal and unitary constraints. This approach is based on a parametrization stemming from Lie group theory through the exponential map. The parametrization transforms the constrained optimization problem into an unconstrained one over a Euclidea…
We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generali…
We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms …
New optimization algorithms on orthogonal group for machine learning.
Paper derives local Plücker formulas for special orthogonal groups.
An algorithm for efficient computation of equivariant neural network layers.
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…
In every dimension we introduce a class of orthogonal graph-manifolds and prove that the fundamental group of any orthogonal graph-manifold quasi-isometrically embeds into a product of trees. As a consequence, we obtain that asymptotic and linearly-controlled asymptotic dimensions of such group are equal t…
Compact holonomy groups found in symmetric spaces.
The space of leftinvariant orthogonal almost complex structures, keeping the orientation, on 6-dimensional Lie groups is researched. To get explicit view of this space elements the isomorphism of and is used. The explicit formula for arbitrary leftinvariant orthogonal almost …
Curious structure of special orthogonal, unitary, and symplectic groups as products of Grassmannians discovered.
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic syste…
Hybrid approach for large-scale network synchronization using KF and PTP.
New algorithm improves PPS for multi-object matching.
We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult …
New Einstein metrics found on orthogonal groups without natural reductivity.
Characterizes group-equivariant neural networks for three groups.
In this paper we study contact structure on 2-step nilpotent, Heisenberg type Lie groups. We decompose this Lie groups to center and orthogonal complement, then investigate properties of both orthogonal Lie subgroups. Finally, we provide a connection between matchings in groups and field extensions and 2-step nilpotent…
New method explains computational barriers in high-dimensional statistical models.
New measures on orbit spaces for orthogonal groups identified.
New algorithm uses PSO to optimize DNN training parameters in distributed systems.
ShadowSync separates background synchronization for scalable distributed training.