Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.
problem Exploring properties of second order symmetric parallel tensors in generalized f.pk-space forms.
method Analyzes the properties of second order symmetric parallel tensors and deduces the existence or non-existence of certain tensors and hypersurfaces.
result There does not exist second order skew-symmetric parallel tensor in f.pk-space form. There is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurface.
Study on generalized ξ-parallel maps in Riemannian geometry.
problem Characterizing and understanding generalized ξ-parallel maps.
method Defined energy functional, derived first variation formula, and Euler-Lagrange equation.
result Established fundamental properties and relationships with harmonic and biharmonic maps.
Parallelizes autoregressive generation using VSSM.
problem Autoregressive models' inability to parallelize generation.
method Variational SSM (VSSM) with parallelizable sampling and decoding.
result Parallel generation possible with VSSM.
NeLLoC improves image compression with parallel decoding.
problem Image compression with OOD generalization.
method Local autoregressive model with parallel decoding.
result Significant gains in compression runtime.
The paper explores parallel 1-forms on special Finsler manifolds and their properties.
problem Investigating parallel 1-forms on specific Finsler manifolds.
method Analyzing Landsberg manifolds, metrizability freedom, and specific Finsler metrics.
result Landsberg surfaces with parallel 1-forms are necessarily Berwaldian, and the metrizability freedom is at least 2.
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel tran…
Introduces a natural parallel translation for navigation data.
problem Navigation data geometric representation and parallelism.
method Introduces a natural parallel translation using Riemannian parallelism.
result The natural parallel translation preserves the Randers norm and has a finite-dimensional holonomy group.
Characterizes regular parallelisms in 3D space with 2-torus action.
problem Characterizing regular parallelisms in 3D space with 2-torus action.
method Characterization using compactness, equivalence relations, and properties of complex vector spaces.
result There is a 1-dimensional subtorus fixing every parallel class, leading to 2- or 3-dimensional regular parallelisms.
The paper studies singularities on parallels of tangent developable surfaces of frontal curves.
problem Understanding singularities on parallels of tangent developable surfaces.
method Generalization of tangent developable surfaces and parallel deformations for frontal curves in arbitrary dimensions.
result Classification of generic singularities on parallels of tangent developable surfaces for frontal curves in 3 or 4 dimensional Euclidean spaces.
We prove that a submanifold with parallel focal structure, which is a generalization of isoparametric and equifocal submanifolds, induces a singular Riemannian foliation of the ambient space by its parallel and focal manifolds.
Parallel transport map over reductive spaces is an affine submersion.
problem Understanding parallel transport in reductive homogeneous spaces with torsion.
method Generalizing previous results on affine symmetric spaces, proving compactness of shape operators, and proposing definitions for regularized mean curvatures.
result Each fiber of the parallel transport map over a reductive homogeneous space is minimal in both senses.
Betten and Riesinger constructed Parallelisms of PG(3,R) with automorphism group SO(3,R) by applying the reducible SO(3,R)-action to a rotational Betten spread. This was generalized by the present author so as to include oriented parallelisms (i.e., p…
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed …
The study finds necessary and sufficient conditions for C1-hypersurfaces to have nowhere C1-regular parallel sets.
problem Conditions for C1-hypersurfaces to have nowhere C1-regular parallel sets. method Proves a necessary and sufficient condition for C1-hypersurfaces to have nowhere C1-regular parallel sets. result A necessary and sufficient condition for C1-hypersurfaces to have nowhere C1-regular parallel sets. Theory of parallel transport on non-collapsed RCD spaces established.
problem Parallel transport on non-collapsed RCD spaces.
method General theory developed for parallel transport on non-collapsed RCD spaces, including geodesics and curves via time-dependent vector fields.
result Existence and uniqueness of parallel transport results obtained.
Characterizes Hermitian manifolds with Bismut parallel torsion.
problem Understanding curvature properties of Hermitian manifolds with specific torsion.
method Analyzes Bismut curvature tensor and parallel torsion conditions.
result Characterizes Bismut torsion parallel manifolds using Bismut curvature alone.
Paper proves non-existence of certain hypersurfaces in complex quadric.
problem Non-existence of Hopf real hypersurfaces with parallel normal Jacobi operator.
method Introducing C-parallel and Reeb parallel normal Jacobi operators, proving non-existence theorems. result Non-existence of Hopf real hypersurfaces with C-parallel normal Jacobi operator. Adaptive batch size schedules improve language model training efficiency and generalization.
problem Dilemma of choosing batch sizes in large-scale model training.
method General-purpose adaptive batch size schedules compatible with data and model parallelism.
result Adaptive batch size schedules outperform constant batch sizes and heuristic warmup schedules.
The study characterizes canal hypersurfaces formed by non-null curves with parallel frame in Minkowski space-time.
problem Characterizing canal hypersurfaces in Minkowski space-time.
method Obtained canal hypersurfaces by pseudo hyperspheres or pseudo hyperbolic hyperspheres with parallel timelike normal vector field.
result Gaussian curvature, mean curvature, and principal curvatures of canal hypersurfaces were derived.
Study the effects of data parallelism and sparsity on neural network training.
problem Understanding the effects of data parallelism and sparsity on neural network training.
method Conducted extensive experiments and developed a theoretical analysis.
result Found a general scaling trend between batch size and number of training steps to convergence for the effect of data parallelism, and difficulty of training under sparsity.
There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians G2(Cm+2). Among them, Suh classified Hopf hypersurfaces M in G2(Cm+2) with Reeb parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce a new notion of gene…
Functional-analytic method for stochastic parallel transport in bundles.
problem Stochastic parallel transport in Hermitian bundles over Riemannian manifolds.
method Purely functional-analytic construction.
result Obtained a general Feynman-Kac formula in vector bundles.
We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Ricci tensor is parallel with respect to the generalized Tanaka-Webster connection.
MixML unifies analysis of weakly consistent parallel learning.
problem Lack of insight into how communication structure affects convergence in parallel learning.
method Proposes MixML framework for analyzing convergence of weakly consistent parallel machine learning.
result Shows dependency of convergence on mixing time tmix.
Study on BAS manifolds with parallel torsion and curvature.
problem Characterizing and classifying BAS manifolds.
method Canonical reduction theorem, classification in homogeneous settings, construction of combined geometries.
result Classification of BAS manifolds in various settings.
A nice differential-geometric framework for (non-abelian) higher gauge theory is provided by principal 2-bundles, i.e. categorified principal bundles. Their total spaces are Lie groupoids, local trivializations are kinds of Morita equivalences, and connections are Lie-2-algebra-valued 1-forms. In this article, we const…
Parallelization technique for welded links preserves equivalence and yields specific decompositions.
problem Defining and proving equivalence of parallel welded link diagrams.
method Introduced a parallelization construction for welded link diagrams and showed its well-definedness.
result Parallel diagrams maintain equivalence under specific orientations and yield decompositions.
Method predicts how probability distributions evolve over time.
problem Predicting how systems described by probability distributions evolve under different conditions.
method Wasserstein Parallel Transport
result Wasserstein Parallel Transport provides counterfactual comparisons of distributional dynamics.
Study left invariant spray geometry on Lie groups using parallel translations.
problem Understanding parallel translations in left invariant spray geometry.
method Using invariant frames and differential equations on Lie algebra, study parallel translations and curvature.
result Alternative interpretations and proofs of homogeneous curvature formulae.
We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal butterfly and 3-dimensional D4± singularities. We give criteria for these singularities type…
We give the parallelism between locally conformal symplectic manifolds and contact manifolds. We also give the generalization of exact contact manifolds.
This work proposes an efficient autoregressive model for text generation.
problem The challenge of generating high-quality text with autoregressive models.
method Introduces a cascaded decoding approach using Markov transformers to achieve sub-linear parallel time generation.
result Shows competitive accuracy/speed tradeoff compared to existing methods on five machine translation datasets.
A deep-learning inference accelerator is synthesized from a C-language software program parallelized with Pthreads. The software implementation uses the well-known producer/consumer model with parallel threads interconnected by FIFO queues. The LegUp high-level synthesis (HLS) tool synthesizes threads into parallel FPG…
Parallel spinors help characterize G2* structures and isotropic forms.
problem Characterizing G2* structures and isotropic forms on pseudo-Riemannian manifolds.
method Using a correspondence between irreducible parallel spinors and solutions of a differential system for three-forms.
result Explicit description of isotropic irreducible spinors in signature (4,3) and characterization of G2* structures.
Improves parallel deep model performance by restructuring and pruning.
problem Latency in parallel deep model execution due to interdependency among sub-models.
method Layer-wise model restructuring and pruning, using ℓ0 optimization and Munkres assignment algorithm. result Significantly improves efficiency of distributed inference in terms of communication and computational complexity.
This paper proposes a method that allows non-parallel many-to-many voice conversion (VC) by using a variant of a generative adversarial network (GAN) called StarGAN. Our method, which we call StarGAN-VC, is noteworthy in that it (1) requires no parallel utterances, transcriptions, or time alignment procedures for speec…
This note addresses the construction of a notion of parallel transport along superpaths arising from the concept of a superconnection on a vector bundle over a manifold M. A superpath in M is, loosely speaking, a path in M together with an odd vector field in M along the path. We also develop a notion of parall…
In this paper, we present Paranom, a parallel anomaly dataset generator. We discuss its design and provide brief experimental results demonstrating its usefulness in improving the classification correctness of LSTM-AD, a state-of-the-art anomaly detection model.
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.
problem Solving challenging tasks in continuous domains using MCTS.
method Extends existing parallelization strategies to continuous domains, focusing on leaf and root parallelization.
result Proposes two final selection strategies for continuous states in root parallelization.
Study SKT and CYT manifolds with parallel Bismut torsion.
problem Characterize and construct compact complex manifolds with specific geometric properties.
method Characterization via universal cover, construction using mapping torus, investigation of generalized Kaehler structures.
result Existence of non-Bismut flat examples and characterization of universal covers.
We propose Stochastic Weight Averaging in Parallel (SWAP), an algorithm to accelerate DNN training. Our algorithm uses large mini-batches to compute an approximate solution quickly and then refines it by averaging the weights of multiple models computed independently and in parallel. The resulting models generalize equ…
We present a generic framework for parallel coordinate descent (CD) algorithms that includes, as special cases, the original sequential algorithms Cyclic CD and Stochastic CD, as well as the recent parallel Shotgun algorithm. We introduce two novel parallel algorithms that are also special cases---Thread-Greedy CD and …
DreamPropeller accelerates text-to-3D generation by 4.7x with minimal loss in quality.
problem Long generation times in text-to-3D generation algorithms degrade user experience.
method DreamPropeller uses Picard iterations generalized for non-ODE paths to accelerate parallel sampling.
result Empirically achieves up to 4.7x speedup with negligible quality loss.
The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor algebra over a differentiable manifold are considered.
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we introduce: local trivializations and smooth descent data. This provides a way to…
Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to…
Decomposes submanifolds with special tensors into simpler parts.
problem Understanding the structure of submanifolds with special tensors.
method Established a decomposition theorem for submanifolds with nonnegative sectional curvature and a Codazzi tensor with parallel mean curvature.
result Submanifolds with these tensors are locally isometric to a direct product of irreducible factors.