The paper shows how reducible complexes affect local indicability.
problem The local indicability of subcomplexes in reducible complexes.
method Characterization of diagrammatic reducibility and application to local indicability.
result Injective labeled oriented trees are locally indicable if reducible of degree 2.
Vaisman's theorem extended to locally reducible Kähler spaces.
problem Existence of locally conformally Kähler metrics on compact Kähler spaces.
method Extended Vaisman's theorem to locally reducible Kähler spaces.
result Vaisman's theorem holds for compact Kähler spaces that are locally reducible.
Optimal lower bounds for eigenvalues of Dirac-Witten operator on certain submanifolds.
problem Estimating eigenvalues of the Dirac-Witten operator on specific submanifolds.
method Optimal lower bounds derived using intrinsic and extrinsic expressions.
result Limiting-cases of eigenvalues studied and optimal bounds obtained.
In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in the sense that, for the first eigenvalue, they reduce to the result of Alexandro…
The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.
problem Creating an arbitrage-free interpolation for option pricing models.
method Generalizing the local variance gamma model to a piecewise quadratic local variance function.
result The quadratic model results in an arbitrage-free interpolation of class C3, reducing knots and computational cost.
Killing tensors on reducible spaces are reducible, except for special cases.
problem Characterizing Killing tensors on reducible spaces.
method Analyzing Killing tensors on product manifolds and their lifts.
result Killing tensors on product manifolds are reducible, except for specific cases.
We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest possible eigenvalue is attained.
Local AdaAlter reduces communication in SGD with adaptive learning rates.
problem Communication overhead in distributed training.
method Novel SGD variant with adaptive learning rates and reduced communication.
result Empirically reduces communication overhead by up to 30%.
Continues work on derived manifolds and symplectic schemes, constructing virtual classes.
problem Constructing virtual fundamental classes for derived manifolds and schemes.
method Cosection localization, reduced virtual fundamental classes, and applications to Donaldson-Thomas theory.
result Virtual fundamental classes for (−2)-shifted symplectic derived schemes are consistent with algebraic and differential geometric constructions. A reliable, accurate, and affordable positioning service is highly required in wireless networks. In this paper, the novel Message Passing Hybrid Localization (MPHL) algorithm is proposed to solve the problem of cooperative distributed localization using distance and direction estimates. This hybrid approach combines t…
Federated learning algorithm reduces global model size by combining local and global representations.
problem Scalability issues in training large models on private data distributed over multiple devices.
method Proposes a federated learning algorithm that jointly learns compact local representations and a global model.
result The global model can be smaller since it only operates on local representations, reducing the number of communicated parameters.
Integrable symmetries of diffieties are studied, leading to local morphisms.
problem Understanding local integrable symmetries of diffieties.
method Integrable infinitesimal symmetries defined as a one-parameter pseudogroup of local diffiety morphisms. Reduction of computation to solving PDEs.
result Preliminary results and examples show integrable symmetries can be reduced to solving linear systems.
Reduced sh-Lie structures have been studied for the case when a Lie group acts on the fibers of a vector bundle while preserving the base space of the bundle. In this paper we investigate how one obtains a reduced sh-Lie structure using the ideas of symmetry reduction where the action of the Lie group is transversal to…
New method solves SLV models faster using Lie algebra.
problem Local stochastic volatility models.
method Wei-Norman factorization method and Lie algebraic techniques.
result Reduces time-dependent SLV models to autonomous PDEs.
VRL-SGD reduces communication complexity in non-identical data settings.
problem Training machine learning models with non-identical data distribution.
method VRL-SGD, which eliminates gradient variance dependency and achieves linear speedup with lower communication complexity.
result VRL-SGD reduces communication complexity from $O(T^{ rac{3}{4}} N^{ rac{3}{4}})$ to $O(T^{ rac{1}{2}} N^{ rac{3}{2}})$.
The aim of the present paper is to provide a global presentation of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and most commonly used special Finsler manifolds: locally Minkowskian, Berwald, Landesberg, genera…
LSB is a new MCMC method for discrete spaces that reduces target evaluations.
problem Sampling in discrete domains with high efficiency and adaptability.
method Local self-balancing proposals, mutual information objective, self-balancing learning.
result LSB converges with fewer target evaluations compared to existing methods.
We prove a holomorphic residue localization formula for odd holomorphic vector fields on compact complex supermanifolds whose fermionic and bosonic dimensions coincide. Under isolated non-degeneracy hypotheses on the reduced zero set, we give an explicit local residue formula.
We reduce the question of local nonsolvability of the Darboux equation, and hence of the isometric embedding problem for surfaces, to the local nonsolvability of a simple linear equation whose type is explicitly determined by the Gaussian curvature.
New method controls error in low-dimensional marginals of spatial models.
problem Inaccurate approximation of low-dimensional marginals in spatial models.
method Stein's method with δ-locality condition for spatial models.
result Uniform error bound for marginals of approximate distributions.
Localized diffusion models reduce training complexity by exploiting low-dimensional structure.
problem Training diffusion models is computationally expensive due to the curse of dimensionality.
method Localized neural networks and localized score matching loss to estimate low-dimensional score functions.
result Localized diffusion models can circumvent the curse of dimensionality with reduced sample complexity.
FedElasticNet reduces communication costs and handles client drift in FL.
problem Expensive communication costs and client drift issues in federated learning.
method Leverages elastic net regularizers to sparsify local updates and limit client drift.
result FedElasticNet effectively resolves communication cost and client drift problems.
Adaptive batch sizes improve local gradient methods in distributed training.
problem Communication bottlenecks in distributed deep learning.
method Adaptive batch size strategies for local gradient methods.
result Adaptive batch sizes reduce minibatch gradient variance and improve training efficiency.
Optimal LDP mechanisms reduce data unfairness in classification.
problem Reducing data unfairness in classification models.
method Developed a closed-form optimal mechanism for binary attributes and a tractable framework for multi-valued attributes.
result Optimal LDP mechanisms improve fairness in classification while maintaining accuracy close to non-private models.
A new method reduces the complexity of decentralized optimization.
problem Decentralized stochastic non-convex optimization over a network.
method GT-HSGD, a hybrid variance-reduced method.
result Achieves an oracle complexity of O(n^(-1)ε^(-3)) for small ε.
Novel compression method preserves privacy while reducing communication costs.
problem Reducing communication costs in differential privacy mechanisms.
method Poisson private representation (PPR) for compressing and simulating local randomizers.
result Achieves compression within a logarithmic gap from theoretical lower bound.
A new method reduces communication costs in decentralized optimization.
problem Decentralized optimization with non-convex cost functions.
method LU-GT method with local updates.
result LU-GT achieves the same communication complexity as Federated Learning and maintains solution quality.
New method reduces memory usage in deep HRNNs by replacing gradient backpropagation with local losses.
problem Memory constraints in training deep hierarchical RNNs.
method Replace gradient backpropagation with locally computable losses in deep HRNNs.
result Memory requirements reduced by a factor exponential in hierarchy depth.
The paper describes the structure of injective LOT-complexes and proves they are aspherical.
problem The unresolved asphericity question for labeled oriented trees encoding spines of ribbon discs.
method Complete description of the link of a reduced injective LOT complex, proving asphericity.
result Reduced injective LOT complexes are aspherical, with specific conditions for non-boundary sub-LOTs.
We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to characterizing incomplete, simply-connected, Riemannian manifolds with reducible holonomy group whose quotient by a group of homotheties is clo…
We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…
LocalNewton reduces communication in distributed learning.
problem Communication bottleneck in distributed optimization.
method LocalNewton is a distributed second-order algorithm with local averaging, updating models locally and communicating once every few iterations.
result LocalNewton reduces communication rounds and end-to-end running time compared to state-of-the-art algorithms.
A new method reduces communication costs in distributed learning.
problem Reduces communication bottlenecks in distributed learning.
method Local SGD with communication-computation overlap and delay-corrected sparse model averaging.
result Theoretical convergence guarantees for smooth non-convex objectives.
Solves local minima problems on smooth manifolds.
problem Local minima issues on smooth manifolds.
method Introducing valley functions and applying Morse's lemma.
result Eliminates critical points and reduces to 1D.
Communication on heterogeneous edge networks is a fundamental bottleneck in Federated Learning (FL), restricting both model capacity and user participation. To address this issue, we introduce two novel strategies to reduce communication costs: (1) the use of lossy compression on the global model sent server-to-client;…
We construct the most general reducible connection that satisfies the self-dual Yang-Mills equations on a simply connected, open subset of flat R4. We show how all such connections lie in the orbit of the flat connection on R4 under the action of non-local symmetries of the self-dual Yang-Mills …
We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the first author for mean curvature flow and other nonlinear diffusions. Our results apply in particular to Ricci flow, where they yield a local mo…
Fixed point sets of certain group actions are contractible.
problem Fixed point sets of group actions on specific types of complexes.
method Analyzing group actions on diagrammatically reducible complexes with fine 1-skeleton.
result Fixed point sets are contractible under certain conditions.
One type of switch simplifies operations on lattice knots.
problem Operations on lattice knots are complex.
method Reduced operations to one type of local switch.
result Simplified set of operations on lattice knots.
It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps between reduced smooth orbifolds and a definition of a category in terms of mark…
The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.
problem Characterizing and finding examples of keen weakly reducible bridge spheres.
method Analyzing bridge spheres and their properties in terms of compressing disks and width complex.
result Infinitely many examples of keen weakly reducible bridge spheres for links in b-bridge position.
GradSkip reduces local training steps for better communication efficiency.
problem High communication costs in distributed optimization.
method GradSkip redesigns ProxSkip to allow clients with less important data to take fewer local training steps.
result GradSkip converges linearly with reduced local training steps and same accelerated communication complexity.
Control data constructed for smooth weak deformation retraction of stratified spaces.
problem Construct control data for smooth weak deformation retraction of stratified spaces.
method Show smooth local triviality with conical fibers, construct control data, use fiber-wise scalar multiplications.
result Obtain neighbourhood smooth weak deformation retraction of stratified spaces.
New algorithm reduces privacy loss in SGD without learning rate tuning.
problem Locally differentially private stochastic optimization with high privacy loss.
method BANCO (Betting Algorithm for Noisy COins) for ε-LDP SGD. result Matches convergence rate of tuned SGD without learning rate tuning.
Hill-climbing is a powerful baseline for NAS, even with reduced noise.
problem Noise in evaluating neural architectures.
method Hill-climbing algorithm, denoising training pipeline.
result Hill-climbing outperforms state-of-the-art NAS algorithms with reduced noise.
Let M a 3-manifold with torus boundary which is a rational homology circle. We study deformations of reducible representations of p_1(M) into PSL_2(C) associated to a simple zero of the twisted Alexander polynomial. We also describe the local structure of the representation and character varieties.
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous negatively curved manifolds. A main conjecture provides a general description; an extend…
Novikov conjecture reduced to Lipschitz cohomology of groups.
problem Novikov higher signature conjecture for groups.
method Introducing Lipschitz cohomology classes and reducing the conjecture.
result Reduced Novikov conjecture to Lipschitz cohomology.