arXiv research

We introduce topological parallelisms of oriented lines (briefly called oriented parallelisms). Every topological parallelism (of lines) on PG(3,R) gives rise to a parallelism of oriented lines, but we show that even the most homogeneous parallelisms of oriented lines other than the Clifford parallelism do not necessar…

Parallelizes MCTS for continuous domains using leaf and root parallelization.

The paper parallelizes HMM inference for efficient long-term computations.

Introduces a natural parallel translation for navigation data.

We prove a conjecture formulated by Pablo M. Chacon and Guillermo A. Lobos in [Pseudo-parallel Lagrangian submanifolds in complex space forms, Differential Geom. Appl.] stating that every Lagrangian pseudo-parallel submanifold of a complex space form of dimension at least 3 is semi-parallel.

This study compares parallel SMC and MCMC for Bayesian deep learning, showing SMC parallel is faster.

The paper explores parallel 1-forms on special Finsler manifolds and their properties.

We propose a new integrated method of exploiting model, batch and domain parallelism for the training of deep neural networks (DNNs) on large distributed-memory computers using minibatch stochastic gradient descent (SGD). Our goal is to find an efficient parallelization strategy for a fixed batch size using $P$ process…

Characterizes regular parallelisms in 3D space with 2-torus action.

Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.

A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden-Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifold…

Classifies simply-connected pluriclosed manifolds with parallel Bismut torsion.

Study on generalized ξ-parallel maps in Riemannian geometry.

Cyclic Data Parallelism reduces memory usage and balances gradient communications.

Betten and Riesinger constructed Parallelisms of $\mathop{\rm PG}(3,\mathbb R)$ with automorphism group $\mathop{\rm SO}(3,\mathbb R)$ by applying the reducible $\mathop{\rm SO}(3,\mathbb R)$-action to a rotational Betten spread. This was generalized by the present author so as to include oriented parallelisms (i.e., p…

The paper examines parallel one forms on Riemannian and Finslerian manifolds.

The paper studies parallel spinor flows on 3D Cauchy hypersurfaces and provides initial data characterizations.

A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important since they are critical points of some natural functionals. In this paper, we su…

A new algorithm for parallel transport on shape spaces is presented and compared to existing methods.

Investigates parallel spinors on Lorentzian four-manifolds using differential geometry.

We characterize compact locally conformal parallel $G_2$ (respectively, $Spin(7)$) manifolds as fiber bundles over $S^1$ with compact nearly Kähler (respectively, compact nearly parallel $G_2$) fiber. A more specific characterization is provided when the local parallel structures are flat.

Compact 3D Cotton-parallel manifolds are always conformally flat.

Linear algebra approach for parallel deep learning models.

Study on balanced Hermitian threefolds with parallel Bismut torsion.

Study on pseudo-Riemannian metrics on Lie groups, finding new non-Einstein examples.

In [dLMu05], DeLellis and Müller proved a quantitative version of Codazzi's theorem, namely for a smooth embedded surface $\ Σ\subseteq \mathbb{R}^3\$ with area normalized to $\ {\cal H}^2(Σ) = 4 π$, it was shown that $\ \parallel A_Σ- id \parallel_{L^2(Σ)} \leq C \parallel A^0_Σ\parallel_{L^2(Σ)}\$, and building on…

A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing parallel skew-symmetric torsion arise naturally in several geometric contexts, e.g. on natural…

The study classifies parallel mean curvature spheres in a sphere-hyperbolic product space.

Method predicts how probability distributions evolve over time.

Classifies Calabi hypersurfaces with parallel Fubini-Pick form.

NeLLoC improves image compression with parallel decoding.

New connections found with specific torsion properties.

Study pp-waves with lightlike parallel spinors in vacuum spacetimes.

Stochastic gradient descent~(SGD) and its variants have become more and more popular in machine learning due to their efficiency and effectiveness. To handle large-scale problems, researchers have recently proposed several parallel SGD methods for multicore systems. However, existing parallel SGD methods cannot achieve…

Paper proves non-existence of certain hypersurfaces in complex quadric.

Betten and Riesinger have shown that Clifford parallelism on real projective space is the only topological parallelism that is left invariant by a group of dimension at least 5. We improve the bound to 4. Examples of different parallelisms admitting a group of dimension 3 are known, so 3 is the "critical dimension".

New method uses higher-order Langevin dynamics for efficient parallel sampling.

Parallelizes autoregressive generation using VSSM.

Parallelization technique for welded links preserves equivalence and yields specific decompositions.

The study finds necessary and sufficient conditions for $C^1$-hypersurfaces to have nowhere $C^1$-regular parallel sets.

This paper focuses on the study of three dimensional real hypersurfaces in non-flat complex space forms whose $^{*}$-Ricci tensor satisfies conditions of parallelism. More precisely, extension of existing results concerning real hypersurfaces with vanishing, semi-parallel and pseudo-parallel $^{*}$-Ricci tensor in case…

MixML unifies analysis of weakly consistent parallel learning.

Defines horocyclic evolutes, parallels, and involutes of spacelike frontals in hyperbolic 2-space.

The ability to leverage large-scale hardware parallelism has been one of the key enablers of the accelerated recent progress in machine learning. Consequently, there has been considerable effort invested into developing efficient parallel variants of classic machine learning algorithms. However, despite the wealth of k…

A scalable parallel BO method for asynchronous settings.

Steinhaus conjectured that every closed oriented $C^1$-curve has a pair of anti-parallel tangents. Porter disproved the conjecture by showing that there exist curves with no anti-parallel tangents. Colin Adams rised the question of whether there exists a nontrivial knot in $\R^3$ which has no parallel or antiparallel t…

Improves parallel deep model performance by restructuring and pruning.

Proposes a method to reduce parallel complexity of MLMC in SGD.