Study shows convergence speed for Fekete points on specific sets.
problem Understanding convergence speed for Fekete points on certain sets.
method Demonstrates ( C α , C α ′ ) (\mathscr{C}^α, \mathscr{C}^{α'}) ( C α , C α ′ ) -regularity for uniformly polynomially cuspidal sets. result Established convergence speed for Fekete points on these sets.
We establish the equidistribution of zeros of random holomorphic sections of powers of a semipositive singular Hermitian line bundle, with an estimate of the convergence speed.
Improved convergence speed of principal component analysis through modified learning rules.
problem Slow convergence for covariance matrices with close eigenvalues.
method Introduced an additional term to the objective function to mitigate convergence issues.
result Significantly improved convergence speed confirmed through simulations.
FedSARSA converges with heterogeneous agents, achieving linear speed-up.
problem Convergence analysis of Federated SARSA with heterogeneous agents.
method Linear function approximation, local training, multi-step error expansion.
result FedSARSA achieves linear speed-up with respect to the number of agents.
Paper proposes a pre-conditioning method to speed up gradient descent in multi-agent optimization.
problem Speed up convergence of gradient descent in multi-agent optimization problems.
method Iterative pre-conditioning approach to mitigate the effect of problem conditioning.
result Significant improvement in convergence speed of gradient descent method.
Improves distributed SGD convergence speed with reduced computation load.
problem Mitigating stragglers in distributed SGD to speed up convergence.
method Modeling communication and computation times, adapting number of workers and computation load dynamically.
result Significantly reduces computation load while improving convergence speed.
Improved kernel herding algorithm for faster quadrature rule convergence.
problem Slow convergence speed of standard kernel herding algorithm.
method Improved gradient approximation to obtain sparser solutions.
result The cosine of the angle between negative gradient and approximate gradient determines convergence speed.
MTFL improves UA and speeds convergence in personalised DNNs on edge devices.
problem Non-IID user data harms FL convergence and global UA is not always the goal.
method Introduces non-federated BN layers into federated DNNs for personalised training.
result MTFL reduces UA rounds by up to 5x and convergence time by up to 3x.
Federated Learning speeds up speech recognition training by 7x and reduces error rate by 6%.
problem Training acoustic models for speech recognition tasks in a federated manner.
method Hierarchical optimization and dynamic gradient aggregation methods.
result Significant improvement in training convergence speed and model performance.
This paper is concerned with improving the empirical convergence speed of block-coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in-between block updates, referred to as heuristic extrapolation with restarts (HER). HER significantly accelerates t…
Paper refutes EM convergence theory and introduces a new EM algorithm.
problem The convergence theory of the EM algorithm is incorrect and affects its performance.
method Proposes a new EM algorithm called the Channel Matching (CM) EM algorithm and provides an initialization map.
result The locally maximal Q can affect the convergent speed but not the global convergence.
The paper studies how convex hypersurfaces in hyperbolic space evolve under a specific curvature flow.
problem Volume preserving Gauss curvature flow in hyperbolic space.
method Analyzes a flow of smooth, closed, and convex hypersurfaces in hyperbolic space with a nonhomogeneous speed function.
result The flow remains convex, exists for all time, and converges to a geodesic sphere exponentially.
The paper proves convergence of certain curvature flows to the origin.
problem Analyzing the convergence of specific curvature flows in Euclidean space.
method Examining fully nonlinear contracting curvature flows with given normal speeds.
result The flows converge exponentially to a sphere centered at the origin after rescaling.
Paper accelerates diffusion models, improving sampling speed.
problem Low sampling speed in score-based diffusion models.
method Design of novel training-free algorithms for deterministic and stochastic samplers.
result Accelerated samplers converge faster with improved rates.
The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.
problem Estimating the probability of default (PD) using limited historical data.
method Adopted the Merton model and analyzed phase transitions in default correlation.
result PD estimation converges slowly when temporal correlation decays by power law less than one.
Federated learning technique improves convergence speed with communication delays.
problem Communication delays between edge nodes and aggregator in federated learning.
method Developed FedDelAvg, a technique that generalizes federated averaging to incorporate a weighting between current local model and delayed global model.
result FedDelAvg achieves a significant improvement in convergence speed, especially when optimizing the weighting scheme to account for delays.
The speed of convergence of the Expectation Maximization (EM) algorithm for Gaussian mixture model fitting is known to be dependent on the amount of overlap among the mixture components. In this paper, we study the impact of mixing coefficients on the convergence of EM. We show that when the mixture components exhibit …
Paper analyzes Scaffold algorithm for federated learning, proving linear speed-up with stochastic gradients.
problem Understanding the impact of stochastic gradients on the Scaffold algorithm's performance.
method Proved linear speed-up in the number of clients using a Markov chain analysis of global parameters and control variates.
result Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size, but retains a higher-order bias.
Improved convergence in deep learning networks via gradient transformation.
problem Reduced convergence speed in deep learning networks.
method Gradient transformation to weight gradients and recursive condition number reduction.
result Improved convergence speed and accuracy in image classification tasks.
LEAD algorithm speeds up decentralized optimization with compression.
problem Slow convergence and stability issues in decentralized optimization with compression.
method Proposes the first linearly convergent decentralized algorithm with compression.
result First consensus error bound for coupled dynamics of primal and dual updates.
It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high p p p -tensor powers of the prequantum line bundle. We show that the Fubini-Study forms induced by these embeddin…
Deep neural networks have gained tremendous popularity in last few years. They have been applied for the task of classification in almost every domain. Despite the success, deep networks can be incredibly slow to train for even moderate sized models on sufficiently large datasets. Additionally, these networks require l…
RVI accelerates encoderless VI for faster convergence.
problem Slow convergence in encoderless VI methods.
method Introduces Relay Variational Inference (RVI) for faster learning.
result RVI outperforms existing methods in convergence speed and performance.
The paper analyzes why Gaussianization slows down with higher dimensions and proposes a solution.
problem The convergence rate of Gaussianization slows down as the dimension increases.
method Analytical and empirical analysis of Gaussianization with random rotations.
result The number of required layers scales linearly with the dimension for Gaussian input.
Predictive models can be used on high-dimensional brain images for diagnosis of a clinical condition. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to …
This paper analyzes and improves convergence in federated learning with biased client selection.
problem Analyzing convergence in federated learning with biased client selection.
method First convergence analysis of federated optimization for biased client selection strategies, proposing Power-of-Choice framework.
result Power-of-Choice strategies converge up to 3 times faster and give 10% higher test accuracy than random selection.
Classifies self-similar solutions for heat equations with positive speed.
problem Classifying self-similar solutions for semilinear heat equations.
method Analyzes the semilinear heat equation u t = Δ u + ∣ u ∣ p − 1 u u_t=Δu+|u|^{p-1}u u t = Δ u + ∣ u ∣ p − 1 u for p > 1 p>1 p > 1 . result Finite time blowing up solutions converge to a positive constant after rescaling.
We study the contraction of a convex immersed plane curve with speed (1/α)k^{α}, where αin(0,1] is a constant and show that, if the blow-up rate of the curvature is of type one, it will converge to a homothetic self-similar solution. We also discuss a special symmetric case of type two blow-up and show that it converge…
The paper studies curvature flows of star-shaped hypersurfaces and proves convergence to spheres.
problem Analyzing the convergence of a class of anisotropic curvature flows.
method Using new auxiliary functions, the paper studies a class of flows with specific speed and proves convergence under certain conditions.
result The k k k -convex solution to the flow converges smoothly to a sphere after normalization for specific values of k k k , α α α , and β β β . Sparse perturbations improve convergence in SZO methods for faster training.
problem Dependency of SZO methods on function dimensionality limits their convergence speed.
method Sparse perturbations reduce the effective dimensionality of the optimization problem.
result Sparse SZO optimization leads to faster convergence in training loss and test accuracy.
Improves convergence speed in compressive sensing with a new probabilistic approach.
problem Efficiently solving the best subset selection problem in compressive sensing.
method Smooth probabilistic reformulation of ℓ 0 \ell_0 ℓ 0 regularized regression. result Empirically outperforms existing compressive sensing algorithms across various settings.
Deep learning is the state-of-the-art in fields such as visual object recognition and speech recognition. This learning uses a large number of layers and a huge number of units and connections. Therefore, overfitting is a serious problem with it, and the dropout which is a kind of regularization tool is used. However, …
New method improves Robbins-Monro algorithm convergence with prior information.
problem Improving convergence speed of Robbins-Monro algorithm.
method Integrates prior information into Robbins-Monro iteration without regression model.
result Prior-information Robbins-Monro sequence converges faster than standard.
New analysis shows surprising results on adaptation speed of causal models.
problem Investigate the adaptation speed of causal models under interventions.
method Use convergence rates from stochastic optimization to measure adaptation speed.
result Surprising findings: anticausal model can be faster than causal model under certain conditions.
We derive new formulas for the price of the European call and put options in the Black-Scholes model, under the form of uniformly convergent series generalizing previously known approximations. We also provide precise boundaries for the convergence speed and apply the results to the calculation of hedge parameters (Gre…
CodedFedL speeds up federated learning in MEC networks by 15x.
problem Slow convergence in federated learning due to heterogeneity and stochastic fluctuations.
method Injects structured coding redundancy into federated learning to mitigate stragglers and speed up training.
result CodedFedL speeds up the training procedure by up to 15x compared to benchmark schemes.
New methods solve graph sparsity optimization problems faster.
problem Complex graph sparsity optimization problems in disease outbreak monitoring and social network analysis.
method Stochastic variance-reduced gradient-based methods GraphSVRG-IHT and GraphSCSG-IHT.
result Our methods achieve linear convergence speed.
FAVANO improves federated learning for resource-constrained environments.
problem Asynchronous communication in federated learning leads to bias and scalability issues.
method FAVANO is a novel asynchronous federated learning framework for resource-constrained environments.
result FAVANO outperforms existing methods on standard benchmarks.
New method speeds up diffusion models without requiring complex assumptions.
problem Slow sampling in diffusion models due to high computational cost.
method Training-free acceleration scheme under minimal assumptions.
result Provable acceleration within O ~ ( d 5 / 4 / ε ) \widetilde{O}(d^{5/4}/\sqrt{\varepsilon}) O ( d 5/4 / ε ) iterations. A lightweight framework improves convergence and stability of PINNs for complex PDEs.
problem Training instability and reduced accuracy in PINNs for complex PDEs.
method Adaptive curvature correction using secant information to optimize first-order optimizers.
result Consistent improvements in convergence speed, stability, and accuracy over standard optimizers.
A new algorithm speeds up sparse-penalized quantile regression solving non-convex penalties.
problem Sparse-penalized quantile regression with non-convex penalties.
method Single-loop smoothing ADMM (SIAD) algorithm for faster convergence.
result SIAD method outperforms existing approaches in solving sparse-penalized quantile regression.
Multirate training speeds up neural network fine-tuning.
problem Efficiently fine-tuning deep neural networks.
method Partitioning neural network parameters into fast and slow parts, updating slowly over longer intervals.
result Significant computational speed-up for transfer learning tasks.
We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that injected noise speeds up the average convergence of the EM algorithm to a local…
APMSqueeze improves Adam for faster training with less communication.
problem Adam's inefficiency in parallel training due to gradient compression limitations.
method Error-compensated gradient compression for Adam-preconditioned Momentum SGD.
result Significantly reduces communication time per epoch without sacrificing accuracy.
Closed-form formulas for path-independent options in a specific Lévy model.
problem Valuation of path-independent options in the exponential NIG model.
method Closed-form pricing formulas derived using a factorized representation in Mellin space and complex analysis.
result Valid closed-form formulas with quickly convergent series for various options.
Formula for European option pricing under jump diffusion model.
problem Option pricing under complex stochastic processes.
method Infinite series of Black-Scholes terms for Levy-driven processes.
result Series solution converges with a radius of convergence.
Exact solver speeds up Weston-Watkins SVM subproblem significantly.
problem Improving performance of Weston-Watkins multiclass SVM.
method Novel reparametrization for exact subproblem solving.
result Significant speed-up over state-of-the-art solvers for large number of classes.
Paper proves convergence of Kalman filter on Stiefel manifolds with measurement errors.
problem Filtering constant particle with measurement errors on Stiefel manifolds.
method Extended Kalman filter applied to Stiefel manifold-valued observations.
result Convergence of the extended Kalman filter proved for constant system process.