Tootfinder

Algorithmic Randomness, Effective Disintegrations, and Rates of Convergence to the Truth
Simon M. Huttegger, Sean Walsh, Francesca Zaffora Blando
https://arxiv.org/abs/2403.19978 …

Algorithmic Randomness, Effective Disintegrations, and Rates of Convergence to the Truth
Lévy's Upward Theorem says that the conditional expectation of an integrable random variable converges with probability one to its true value with increasing information. In this paper, we use methods from effective probability theory to characterise the probability one set along which convergence to the truth occurs, and the rate at which the convergence occurs. We work within the setting of computable probability measures defined on computable Polish spaces and introduce a new general theory…

Training Dynamics of Multi-Head Softmax Attention for In-Context Learning: Emergence, Convergence, and Optimality
Siyu Chen, Heejune Sheen, Tianhao Wang, Zhuoran Yang
https://arxiv.org/abs/2402.19442

Training Dynamics of Multi-Head Softmax Attention for In-Context Learning: Emergence, Convergence, and Optimality
We study the dynamics of gradient flow for training a multi-head softmax attention model for in-context learning of multi-task linear regression. We establish the global convergence of gradient flow under suitable choices of initialization. In addition, we prove that an interesting "task allocation" phenomenon emerges during the gradient flow dynamics, where each attention head focuses on solving a single task of the multi-task model. Specifically, we prove that the gradient flow dynamics can b…

A closure theorem for $\Gamma$-convergence and H-convergence with applications to non-periodic homogenization
Andrea Braides, Gianni Dal Maso, Claude Le Bris
https://arxiv.org/abs/2402.19031

A closure theorem for $Γ$-convergence and H-convergence with applications to non-periodic homogenization
In this work we examine the stability of some classes of integrals, and in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing at infinity, which has been recently examined in the framework of elliptic PDE. We use localization techniques and higher-integrability Meyers-type results to provide a closure theorem by $Γ$-convergence within a large class of integral functionals. From su…

The Convergence of AI and Synthetic Biology: The Looming Deluge
Cindy Vindman, Benjamin Trump, Christopher Cummings, Madison Smith, Alexander J. Titus, Ken Oye, Valentina Prado, Eyup Turmus, Igor Linkov
https://arxiv.org/abs/2404.18973 https://arxiv.org/pdf/2404.18973
arXiv:2404.18973v1 Announce Type: new
Abstract: The convergence of artificial intelligence (AI) and synthetic biology is rapidly accelerating the pace of biological discovery and engineering. AI techniques, such as large language models and biological design tools, are enabling the automated design, build, test, and learning cycles for engineered biological systems. This convergence promises to democratize synthetic biology and unlock novel applications across domains from medicine to environmental sustainability. However, it also poses significant risks around reliability, dual use, and governance. The opacity of AI models, the deskilling of workforces, and the outdated nature of current regulatory frameworks present challenges in ensuring responsible development. Urgent attention is needed to update governance structures, integrate human oversight into increasingly automated workflows, and foster a culture of responsibility among the growing community of bioengineers. Only by proactively addressing these issues can we realize the transformative potential of AI-driven synthetic biology while mitigating its risks.

Club convergence in green innovation efficiency https://www.sciencedirect.com/science/article/pii/S0140988324001324 @…

Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification
Christian Offen
https://arxiv.org/abs/2404.19626

Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero is provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of…

Algorithmic Randomness, Effective Disintegrations, and Rates of Convergence to the Truth
Simon M. Huttegger, Sean Walsh, Francesca Zaffora Blando
https://arxiv.org/abs/2403.19978 …

Algorithmic Randomness, Effective Disintegrations, and Rates of Convergence to the Truth
Lévy's Upward Theorem says that the conditional expectation of an integrable random variable converges with probability one to its true value with increasing information. In this paper, we use methods from effective probability theory to characterise the probability one set along which convergence to the truth occurs, and the rate at which the convergence occurs. We work within the setting of computable probability measures defined on computable Polish spaces and introduce a new general theory…

This https://arxiv.org/abs/2308.04510 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gromov-Hausdorff convergence of metric pairs and metric tuples
We study the Gromov-Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting. Finally, we get a relative version of Fukaya's theorem about quotient spaces under Gromov--Hausdorff equivariant convergence and a version of Grove-Petersen--Wu's finiteness theorem for stratified spaces.

This https://arxiv.org/abs/2402.07524 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Semialgebraicity of the convergence domain of an algebraic power series
Given a power series in finitely many variables that is algebraic over the corresponding polynomial ring over a subfield of the reals, we show that its convergence domain is semialgebraic over the real closure of the subfield. This gives in particular that the convergence radius of a univariate Puiseux series that is algebraic in the above sense belongs to the real closure or is infinity.

Convergence analysis of the transformed gradient projection algorithms on compact matrix manifolds
Wentao Ding, Jianze Li, Shuzhong Zhang
https://arxiv.org/abs/2404.19392

Convergence analysis of the transformed gradient projection algorithms on compact matrix manifolds
In this paper, to address the optimization problem on a compact matrix manifold, we introduce a novel algorithmic framework called the Transformed Gradient Projection (TGP) algorithm, using the projection onto this compact matrix manifold. Compared with the existing algorithms, the key innovation in our approach lies in the utilization of a new class of search directions and various stepsizes, including the Armijo, nonmonotone Armijo, and fixed stepsizes, to guide the selection of the next iter…

MaxCUCL: Max-Consensus with Deterministic Convergence in Networks with Unreliable Communication
Apostolos I. Rikos, Themistoklis Charalambous, Karl H. Johansson
https://arxiv.org/abs/2402.18719

MaxCUCL: Max-Consensus with Deterministic Convergence in Networks with Unreliable Communication
In this paper, we present a novel distributed algorithm (herein called MaxCUCL) designed to guarantee that max-consensus is reached in networks characterized by unreliable communication links (i.e., links suffering from packet drops). Our proposed algorithm is the first algorithm that achieves max-consensus in a deterministic manner (i.e., nodes always calculate the maximum of their states regardless of the nature of the probability distribution of the packet drops). Furthermore, it allows node…

Quasi-contractivity, Stability and convergence of WCT operators
Y. Estaremi, Z. Huang, S. Muhammad
https://arxiv.org/abs/2404.19466 https://

Quasi-contractivity, Stability and convergence of WCT operators
In this paper we characterize quasi-contraction, stable and convergent weighted conditional type (WCT) operators on $L^p(μ)$. Indeed we provide equivalent conditions for quasi-contraction WCT operators. Also, we prove that convergence, uniformly stability, strongly stability and weakly stability of WCT operators are equivalent. Finally we provided some concrete examples to illustrate our main results.

Multi-Source Encapsulation With Guaranteed Convergence Using Minimalist Robots
Himani Sinhmar, Hadas Kress-Gazit
https://arxiv.org/abs/2404.19138 https://<…

This https://arxiv.org/abs/2404.02538 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Convergence Analysis of Flow Matching in Latent Space with Transformers
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a transformer network is trained to predict the velocity field of the transformation from a standard normal distribution to the target latent distribution. Our error analysis demonstrates the effectiveness of this approach, showing that the distribution of samples gener…

This https://arxiv.org/abs/2109.13676 has been replaced.
link: https://scholar.google.com/scholar?q=a

Semi-stable representations as limits of crystalline representations
We construct an explicit sequence $V_{k_n,a_n}$ of crystalline representations of exceptional weights converging to a given irreducible two-dimensional semi-stable representation $V_{k,{\mathcal{L}}}$ of $\mathrm{Gal}({\overline{\mathbb{Q}}}_p/{\mathbb{Q}}_p)$. The convergence takes place in the blow-up space of two-dimensional trianguline representations studied by Colmez and Chenevier. The process of blow-up is described in detail in the rigid analytic setting and may be of independent intere…

This https://arxiv.org/abs/2312.13344 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Improving the five-point bootstrap
We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the $\langleσσεσσ\rangle$ correlator in the 3d critical Is…

This https://arxiv.org/abs/2310.14085 has been replaced.
link: https://scholar.google.com/scholar?q=a

Adaptive, Doubly Optimal No-Regret Learning in Strongly Monotone and Exp-Concave Games with Gradient Feedback
Online gradient descent (OGD) is well known to be doubly optimal under strong convexity or monotonicity assumptions: (1) in the single-agent setting, it achieves an optimal regret of $Θ(\log T)$ for strongly convex cost functions; and (2) in the multi-agent setting of strongly monotone games, with each agent employing OGD, we obtain last-iterate convergence of the joint action to a unique Nash equilibrium at an optimal rate of $Θ(\frac{1}{T})$. While these finite-time guarantees highlight its…

Calabi-Yau metrics of Calabi type with polynomial rate of convergence
Yifan Chen
https://arxiv.org/abs/2404.18070 https://arxiv.org/p…

Calabi-Yau metrics of Calabi type with polynomial rate of convergence
We present new complete Calabi-Yau metrics defined on the complement of a smooth anticanonical divisor with ample normal bundle, approaching the Calabi model space at a polynomial rate. Moreover, we establish the uniqueness of this type of Calabi-Yau metric within a fixed cohomology class.

This https://arxiv.org/abs/2402.17951 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by inherently ill-posed inverse problems. Previous research advanced image quality via post-processing and deep unrolling algorithms but faces challenges, such as extended convergence times with ultra-sparse data. Despite enhancements, resulting images often show significant artifacts, limi…

A Harris theorem for enhanced dissipation, and an example of Pierrehumbert
William Cooperman, Gautam Iyer, Seungjae Son
https://arxiv.org/abs/2403.19858 ht…

A Harris theorem for enhanced dissipation, and an example of Pierrehumbert
In many situations, the combined effect of advection and diffusion greatly increases the rate of convergence to equilibrium -- a phenomenon known as enhanced dissipation. Here we study the situation where the advecting velocity field generates a random dynamical system satisfying certain Harris conditions. If $κ$ denotes the strength of the diffusion, then we show that with probability at least $1 - o(κ^N)$ enhanced dissipation occurs on time scales of order $|\ln κ|$, a bound whic…

Convergence of martingales via enriched dagger categories
Paolo Perrone, Ruben Van Belle
https://arxiv.org/abs/2404.15191 https://arx…

Convergence of martingales via enriched dagger categories
We provide a categorical proof of convergence for martingales and backward martingales in mean, using enriched category theory. The enrichment we use is in topological spaces, with their canonical closed monoidal structure, which encodes a version of pointwise convergence. We work in a topologically enriched dagger category of probability spaces and Markov kernels up to almost sure equality. In this category we can describe conditional expectations exactly as dagger-split idempotent morphisms…

Improved Forecasting Using a PSO-RDV Framework to Enhance Artificial Neural Network
Sales Aribe Jr
https://arxiv.org/abs/2402.18576 https://

Improved Forecasting Using a PSO-RDV Framework to Enhance Artificial Neural Network
Decision making and planning have long relied heavily on AI-driven forecasts. The government and the general public are working to minimize the risks while maximizing benefits in the face of potential future public health uncertainties. This study used an improved method of forecasting utilizing the Random Descending Velocity Inertia Weight (RDV IW) technique to improve the convergence of Particle Swarm Optimization (PSO) and the accuracy of Artificial Neural Network (ANN). The IW technique, in…

This https://arxiv.org/abs/2403.03473 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Inverse-Free Fast Natural Gradient Descent Method for Deep Learning
Second-order optimization techniques have the potential to achieve faster convergence rates compared to first-order methods through the incorporation of second-order derivatives or statistics. However, their utilization in deep learning is limited due to their computational inefficiency. Various approaches have been proposed to address this issue, primarily centered on minimizing the size of the matrix to be inverted. Nevertheless, the necessity of performing the inverse operation iteratively p…

Optimizing Neural Networks for Bermudan Option Pricing: Convergence Acceleration, Future Exposure Evaluation and Interpolation in Counterparty Credit Risk
Vikranth Lokeshwar Dhandapani, Shashi Jain
https://arxiv.org/abs/2402.15936 https://arxiv.org/pdf/2402.15936
arXiv:2402.15936v1 Announce Type: new
Abstract: This paper presents a Monte-Carlo-based artificial neural network framework for pricing Bermudan options, offering several notable advantages. These advantages encompass the efficient static hedging of the target Bermudan option and the effective generation of exposure profiles for risk management. We also introduce a novel optimisation algorithm designed to expedite the convergence of the neural network framework proposed by Lokeshwar et al. (2022) supported by a comprehensive error convergence analysis. We conduct an extensive comparative analysis of the Present Value (PV) distribution under Markovian and no-arbitrage assumptions. We compare the proposed neural network model in conjunction with the approach initially introduced by Longstaff and Schwartz (2001) and benchmark it against the COS model, the pricing model pioneered by Fang and Oosterlee (2009), across all Bermudan exercise time points. Additionally, we evaluate exposure profiles, including Expected Exposure and Potential Future Exposure, generated by our proposed model and the Longstaff-Schwartz model, comparing them against the COS model. We also derive exposure profiles at finer non-standard grid points or risk horizons using the proposed approach, juxtaposed with the Longstaff Schwartz method with linear interpolation and benchmark against the COS method. In addition, we explore the effectiveness of various interpolation schemes within the context of the Longstaff-Schwartz method for generating exposures at finer grid horizons.

Convergence Analysis of Split Federated Learning on Heterogeneous Data
Pengchao Han, Chao Huang, Geng Tian, Ming Tang, Xin Liu
https://arxiv.org/abs/2402.15166

Convergence Analysis of Split Federated Learning on Heterogeneous Data
Split federated learning (SFL) is a recent distributed approach for collaborative model training among multiple clients. In SFL, a global model is typically split into two parts, where clients train one part in a parallel federated manner, and a main server trains the other. Despite the recent research on SFL algorithm development, the convergence analysis of SFL is missing in the literature, and this paper aims to fill this gap. The analysis of SFL can be more challenging than that of federate…

Notes on the Practical Application of Nested Sampling: MultiNest, (Non)convergence, and Rectification
Alexander J. Dittmann
https://arxiv.org/abs/2404.16928

Notes on the Practical Application of Nested Sampling: MultiNest, (Non)convergence, and Rectification
Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has been applied to a wide variety of problems in the physical sciences. However, MultiNest results are frequently unreliable, and accompanying convergence tests are a necessary component of any analysis. Using simple, analytically tractable test problems, I illust…

This https://arxiv.org/abs/2201.11328 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the weak convergence of conditioned Bessel bridges
The purpose of this paper is to introduce the construction of a stochastic process called ``$δ$-dimensional Bessel house-moving" and its properties. We study the weak convergence of $δ$-dimensional Bessel bridges conditioned from above, and we refer to this limit as $δ$-dimensional Bessel house-moving. Applying this weak convergence result, we give the decomposition formula for its distribution and the Radon-Nikodym density for the distribution of the Bessel house-moving with respect to the …

Solving Time-Continuous Stochastic Optimal Control Problems: Algorithm Design and Convergence Analysis of Actor-Critic Flow
Mo Zhou, Jianfeng Lu
https://arxiv.org/abs/2402.17208 <…

Solving Time-Continuous Stochastic Optimal Control Problems: Algorithm Design and Convergence Analysis of Actor-Critic Flow
We propose an actor-critic framework to solve the time-continuous stochastic optimal control problem. A least square temporal difference method is applied to compute the value function for the critic. The policy gradient method is implemented as policy improvement for the actor. Our key contribution lies in establishing the global convergence property of our proposed actor-critic flow, demonstrating a linear rate of convergence. Theoretical findings are further validated through numerical examp…

This https://arxiv.org/abs/2103.10354 has been replaced.
link: https://scholar.google.com/scholar?q=a

Strong modeling limits of graphs with bounded tree-width
The notion of first order convergence of graphs unifies the notions of convergence for sparse and dense graphs. Nešetřil and Ossona de Mendez [J. Symbolic Logic 84 (2019), 452-472] proved that every first order convergent sequence of graphs from a nowhere-dense class of graphs has a modeling limit and conjectured the existence of such modeling limits with an additional property, the strong finitary mass transport principle. The existence of modeling limits satisfying the strong finitary mass …

Investigating the basis set convergence of diagrammatically decomposed coupled-cluster correlation energy contributions for the uniform electron gas
Nikolaos Masios, Felix Hummel, Andreas Gr\"uneis, Andreas Irmler
https://arxiv.org/abs/2402.15907

Investigating the basis set convergence of diagrammatically decomposed coupled-cluster correlation energy contributions for the uniform electron gas
We investigate the convergence of coupled-cluster correlation energies and related quantities with respect to the employed basis set size for the uniform electron gas to gain a better understanding of the basis set incompleteness error. To this end, coupled-cluster doubles (CCD) theory is applied to the three dimensional uniform electron gas for a range of densities, basis set sizes and electron numbers. We present a detailed analysis of individual, diagrammatically decomposed contributions to …

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
Subenoy Chakraborty, Madhukrishna Chakraborty
https://arxiv.org/abs/2402.17799

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing theorem and Convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.

Well-posedness and convergence of entropic approximation of semi-geostrophic equations
Guillaume Carlier, Hugo Malamut
https://arxiv.org/abs/2404.17387 htt…

Well-posedness and convergence of entropic approximation of semi-geostrophic equations
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is also proved for discretizations that can be computed numerically in practice as shown recently in [6].

Metrization of Gromov-Hausdorff-type topologies on boundedly-compact metric spaces
Ryoichiro Noda
https://arxiv.org/abs/2404.19681 https://arxiv.org/pdf/2404.19681
arXiv:2404.19681v1 Announce Type: new
Abstract: We present a new general framework for metrization of Gromov-Hausdorff-type topologies on non-compact metric spaces. We also give easy-to-check conditions for separability and completeness and hence the measure theoretic requirements are provided to study convergence of random spaces with additional random objects. In particular, our framework enables us to define a metric inducing a suitable Gromov-Hausdorff-type topology on the space of rooted boundedly-compact metric spaces with laws of stochastic processes and/or random fields, which was not clear how to do in previous frameworks. In addition to general theory, this paper includes several examples of Gromov-Hausdorff-type topologies, verifying that classical examples such as the Gromov-Hausdorff topology and the Gromov-Hausdorff-Prohorov topology are contained within our framework.

This https://arxiv.org/abs/2402.17951 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by inherently ill-posed inverse problems. Previous research advanced image quality via post-processing and deep unrolling algorithms but faces challenges, such as extended convergence times with ultra-sparse data. Despite enhancements, resulting images often show significant artifacts, limi…

The Problem of Split Equality Fixed-Point and its Applications
Lawan Bulama Mohammed, Adem Kilicman
https://arxiv.org/abs/2403.19707 https://

The Problem of Split Equality Fixed-Point and its Applications
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life, to address this issue, we studied the SEFPP involving the class of quasi-pseudocontractive mappings in Hilbert spaces and constructed novel algorithms in this regards, and we proved the algorithms' convergence both with and without prior knowledge of the operator norm for bounded and linear map…

This https://arxiv.org/abs/2303.00872 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Phase transition in a periodic tubular structure
We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on $\mathbb{R}$ which is fourth order at a discrete set of values of the magnetic potential (\emph{critical points}) and second-order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence…

This https://arxiv.org/abs/2401.08258 has been replaced.
link: https://scholar.google.com/scholar?q=a

Time, Simultaneity, and Causality in Wireless Networks with Sensing and Communications
Wireless systems beyond 5G evolve towards embracing both sensing and communication, resulting in increased convergence of the digital and the physical world. The existence of fused digital-physical realms raises critical questions regarding temporal ordering, causality, and the synchronization of events. This paper addresses the temporal challenges arising from the fact that the wireless infrastructure becomes an entity with multisensory perception. With the growing reliance on real-time intera…

Best Arm Identification with Resource Constraints
Zitian Li, Wang Chi Cheung
https://arxiv.org/abs/2402.19090 https://arxiv.org/pdf/2…

Best Arm Identification with Resource Constraints
Motivated by the cost heterogeneity in experimentation across different alternatives, we study the Best Arm Identification with Resource Constraints (BAIwRC) problem. The agent aims to identify the best arm under resource constraints, where resources are consumed for each arm pull. We make two novel contributions. We design and analyze the Successive Halving with Resource Rationing algorithm (SH-RR). The SH-RR achieves a near-optimal non-asymptotic rate of convergence in terms of the probabilit…

This https://arxiv.org/abs/2306.16674 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Online learning for robust voltage control under uncertain grid topology
Voltage control generally requires accurate information about the grid's topology in order to guarantee network stability. However, accurate topology identification is challenging for existing methods, especially as the grid is subject to increasingly frequent reconfiguration due to the adoption of renewable energy. In this work, we combine a nested convex body chasing algorithm with a robust predictive controller to achieve provably finite-time convergence to safe voltage limits in the online …

Dynamic Vulnerability Criticality Calculator for Industrial Control Systems
Pavlos Cheimonidis, Kontantinos Rantos
https://arxiv.org/abs/2404.16854 https:/…

Dynamic Vulnerability Criticality Calculator for Industrial Control Systems
The convergence of information and communication technologies has introduced new and advanced capabilities to Industrial Control Systems. However, concurrently, it has heightened their vulnerability to cyber attacks. Consequently, the imperative for new security methods has emerged as a critical need for these organizations to effectively identify and mitigate potential threats. This paper introduces an innovative approach by proposing a dynamic vulnerability criticality calculator. Our methodo…

On the discrete analogues of Appell function $F_4$
Ravi Dwivedi, Dwivedi Sahai
https://arxiv.org/abs/2402.18931 https://arxiv.org/pdf…

On the discrete analogues of Appell function $F_4$
In this paper, we study the Appell function $F_4$ from discrete point of view. In particular, we obtain regions of convergence, difference-differential equations, finite and infinite summation formulas and a list of recursion relations satisfied by the discrete analogues of Appell function $F_4$.

This https://arxiv.org/abs/2306.15867 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D
We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}Δ^{2}u-Δu=f $ on the unit square $Ω\subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial Ω$, where $\varepsilon \in (0, 1)$ is a small parameter. The problem is solved numerically by means of a weak Galerkin(WG) finite element method, which is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on finite element pa…

Inference for the panel ARMA-GARCH model when both $N$ and $T$ are large
Bing Su, Ke Zhu
https://arxiv.org/abs/2404.18377 https://arx…

Inference for the panel ARMA-GARCH model when both $N$ and $T$ are large
We propose a panel ARMA-GARCH model to capture the dynamics of large panel data with $N$ individuals over $T$ time periods. For this model, we provide a two-step estimation procedure to estimate the ARMA parameters and GARCH parameters stepwisely. Under some regular conditions, we show that all of the proposed estimators are asymptotically normal with the convergence rate $(NT)^{-1/2}$, and they have the asymptotic biases when both $N$ and $T$ diverge to infinity at the same rate. Particularly,…

Approximations of symbolic substitution systems in one dimension
Lior Tenenbaum
https://arxiv.org/abs/2402.19151 https://arxiv.org/pd…

Approximations of symbolic substitution systems in one dimension
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schrödinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra approximate the spectrum of the limiting operator (of the quasicrystal). This naturally leads to study the convergence of the underlying dynamical systems. We treat dynamical systems which are based on one-dimensional substitutions. We first find natural candidates of…

This https://arxiv.org/abs/2309.07779 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Convergence analysis of online algorithms for vector-valued kernel regression
We consider the problem of approximating the regression function from noisy vector-valued data by an online learning algorithm using an appropriate reproducing kernel Hilbert space (RKHS) as prior. In an online algorithm, i.i.d. samples become available one by one by a random process and are successively processed to build approximations to the regression function. We are interested in the asymptotic performance of such online approximation algorithms and show that the expected squared error in…

On a Family of Relaxed Gradient Descent Methods for Quadratic Minimization
Liam MacDonald, Rua Murray, Rachael Tappenden
https://arxiv.org/abs/2404.19255 h…

On a Family of Relaxed Gradient Descent Methods for Quadratic Minimization
This paper studies the convergence properties of a family of Relaxed $\ell$-Minimal Gradient Descent methods for quadratic optimization; the family includes the omnipresent Steepest Descent method, as well as the Minimal Gradient method. Simple proofs are provided that show, in an appropriately chosen norm, the gradient and the distance of the iterates from optimality converge linearly, for all members of the family. Moreover, the function values decrease linearly, and iteration complexity resu…

This https://arxiv.org/abs/2402.17951 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by inherently ill-posed inverse problems. Previous research advanced image quality via post-processing and deep unrolling algorithms but faces challenges, such as extended convergence times with ultra-sparse data. Despite enhancements, resulting images often show significant artifacts, limi…

On convergence of a sequence of mappings with inverse modulus inequality to a discrete mapping
E. O. Sevost'yanov, V. A. Targonskii
https://arxiv.org/abs/2404.17060

On convergence of a sequence of mappings with inverse modulus inequality to a discrete mapping
We have studied the mappings that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform boundary of the family of such mappings is a discrete mapping. We separately considered domains that are locally connected at their boundary and regular domains in the quasiconformal sense.

Convergence of stochastic integrals with applications to transport equations and conservation laws with noise
Kenneth H. Karlsen, Peter H. C. Pang
https://arxiv.org/abs/2404.16157

Convergence of stochastic integrals with applications to transport equations and conservation laws with noise
Convergence of stochastic integrals driven by Wiener processes $W_n$, with $W_n \to W$ almost surely in $C_t$, is crucial in analyzing SPDEs. Our focus is on the convergence of the form $\int_0^T V_n\, \mathrm{d} W_n \to \int_0^T V\, \mathrm{d} W$, where $\{V_n\}$ is bounded in $L^p(Ω\times [0,T];X)$ for a Banach space $X$ and some finite $p > 2$. This is challenging when $V_n$ converges to $V$ weakly in the temporal variable. We supply convergence results to handle stochastic integral limits …

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
Subenoy Chakraborty, Madhukrishna Chakraborty
https://arxiv.org/abs/2402.17799

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing theorem and Convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.

This https://arxiv.org/abs/2312.01047 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A New Random Reshuffling Method for Nonsmooth Nonconvex Finite-sum Optimization
Random reshuffling techniques are prevalent in large-scale applications, such as training neural networks. While the convergence and acceleration effects of random reshuffling-type methods are fairly well understood in the smooth setting, much less studies seem available in the nonsmooth case. In this work, we design a new normal map-based proximal random reshuffling (norm-PRR) method for nonsmooth nonconvex finite-sum problems. We show that norm-PRR achieves the iteration complexity $O(n^{-1/3…

This https://arxiv.org/abs/2209.03077 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Convergence of the ELBO to Entropy Sums
The variational lower bound (a.k.a. ELBO or free energy) is the central objective for many established as well as many novel algorithms for unsupervised learning. During learning such algorithms change model parameters to increase the variational lower bound. Learning usually proceeds until parameters have converged to values close to a stationary point of the learning dynamics. In this purely theoretical contribution, we show that (for a very large class of generative models) the variational l…

This https://arxiv.org/abs/1812.11880 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the zeros of sum from n=1 to 00 of lambda_P(n)/n^s
Our main result is to answer a question of Michel Balazard by giving a Dirichlet series with only one zero in its half-plane of convergence. At the end of the paper we also give several sufficient conditions for the Generalized Riemann Hypothesis and ask if any of them are true.

Energy solutions of the Cauchy-Dirichlet problem for fractional nonlinear diffusion equations
Goro Akagi, Florian Salin
https://arxiv.org/abs/2403.20176 ht…

Energy solutions of the Cauchy-Dirichlet problem for fractional nonlinear diffusion equations
The present paper is concerned with the Cauchy-Dirichlet problem for fractional (and non-fractional) nonlinear diffusion equations posed in bounded domains. Main results consist of well-posedness in an energy class with no sign restriction and convergence of such (possibly sign-changing) energy solutions to asymptotic profiles after a proper rescaling. They will be proved in a variational scheme only, without any use of semigroup theories nor classical quasilinear parabolic theories. Proofs are…

Matrix Domination: Convergence of a Genetic Algorithm Metaheuristic with the Wisdom of Crowds to Solve the NP-Complete Problem
Shane Storm Strachan
https://arxiv.org/abs/2403.17939

Matrix Domination: Convergence of a Genetic Algorithm Metaheuristic with the Wisdom of Crowds to Solve the NP-Complete Problem
This research explores the application of a genetic algorithm metaheuristic enriched by the wisdom of crowds in order to address the NP-Complete matrix domination problem (henceforth: TMDP) which is itself a constraint on related problems applied in graphs. Matrix domination involves accurately placing a subset of cells, referred to as dominators, within a matrix with the goal of their dominating the remainder of the cells. This research integrates the exploratory nature of a genetic algorithm …

This https://arxiv.org/abs/2307.09726 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a post processing procedure of solving a constrained minimization in each time step. Such a constrained optimization can be formulated as a nonsmooth convex minimization, which can be efficiently solved by first order optimization methods, if using the optimal algorithm parameters. By analyzing the asymptotic linear convergence rate of the generalized Douglas-Rachford spl…

Proximal Dogleg Opportunistic Majorization for Nonconvex and Nonsmooth Optimization
Yiming Zhou, Wei Dai
https://arxiv.org/abs/2402.19176 https://

Proximal Dogleg Opportunistic Majorization for Nonconvex and Nonsmooth Optimization
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from slow convergence or high implementation complexity or both. To overcome these limitations, we develop a fast and user-friendly second-order proximal algorithm. Key innovation involves building and solving a series of opportunistically majorized problems along…

This https://arxiv.org/abs/2401.16955 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spherical maximal functions and Hardy spaces for Fourier integral operators
We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact subset of $(0,\infty)$. These bounds extend to general hypersurfaces with non-vanishing Gaussian curvature, to the complex spherical means, and to geodesic spheres on compact manifolds. We also obtain improved maximal function bounds and pointwise convergence statements for wave equations, both on…

Faster Convergence for Transformer Fine-tuning with Line Search Methods
Philip Kenneweg, Leonardo Galli, Tristan Kenneweg, Barbara Hammer
https://arxiv.org/abs/2403.18506

Faster Convergence for Transformer Fine-tuning with Line Search Methods
Recent works have shown that line search methods greatly increase performance of traditional stochastic gradient descent methods on a variety of datasets and architectures [1], [2]. In this work we succeed in extending line search methods to the novel and highly popular Transformer architecture and dataset domains in natural language processing. More specifically, we combine the Armijo line search with the Adam optimizer and extend it by subdividing the networks architecture into sensible units…

This https://arxiv.org/abs/2311.04027 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Harmonic analysis of Gaussian multiplicative chaos on the circle
In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means that its Fourier coefficients converge to $0$ when the frequency goes to infinity. We supplement this result with a convergence in law result for the rescaled Fourier coefficients.

Spectral Kernels and Holomorphic Morse Inequalities for Sequence of Line Bundles
Yueh-Lin Chiang
https://arxiv.org/abs/2404.18079 https://arxiv.org/pdf/2404.18079
arXiv:2404.18079v1 Announce Type: new
Abstract: Given a sequence of Hermitian holomorphic line bundles $(L_k,h_k)$ over a complex manifold $M$ which may not be compact, we generalize the scaling method in arXiv:2310.08048 to study the asymptotic behavior of the Bergman kernels and spectral kernels with respect to the space of global holomorphic sections of $L_k$ with $(0,q)$-forms. We derive the leading term of the Bergman and spectral kernels under the local convergence assumption in the sequence of Chern curvatures $c_1(L_k,h_k)$, inspired by arXiv:2012.12019. The manifold $M$ may be non-K\"ahler and $c_1(L_k,h_k)$ may be negative or degenerate. Moreover, we establish the $L_k$-asymptotic version of Demailly's holomorphic Morse inequalities as an application to compact complex manifolds.

Stochastic Approximation Proximal Subgradient Method for Stochastic Convex-Concave Minimax Optimization
Yu-Hong Dai, Jiani Wang, Liwei Zhang
https://arxiv.org/abs/2403.20205

Stochastic Approximation Proximal Subgradient Method for Stochastic Convex-Concave Minimax Optimization
This paper presents a stochastic approximation proximal subgradient (SAPS) method for stochastic convex-concave minimax optimization. By accessing unbiased and variance bounded approximate subgradients, we show that this algorithm exhibits ${\rm O}(N^{-1/2})$ expected convergence rate of the minimax optimality measure if the parameters in the algorithm are properly chosen, where $N$ denotes the number of iterations. Moreover, we show that the algorithm has ${\rm O}(\log(N)N^{-1/2})$ minimax opt…

This https://arxiv.org/abs/2303.00696 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Trust your source: quantifying source condition elements for variational regularisation methods
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as the solution of convex minimisation problems that can be solved with first-order algorithms. We demonstrate the validity of our approach by testing it on two inverse problem case studies in machine learning and image processing: sparse coefficient estimation…

Interplay between Contractivity and Monotonicity for Reaction Networks
Alon Duvall, M. Ali Al-Radhawi, Dhruv D. Jatkar, Eduardo Sontag
https://arxiv.org/abs/2404.18734

Interplay between Contractivity and Monotonicity for Reaction Networks
This work studies relationships between monotonicity and contractivity, and applies the results to establish that many reaction networks are weakly contractive, and thus, under appropriate compactness conditions, globally convergent to equilibria. Verification of these properties is achieved through a novel algorithm that can be used to generate cones for monotone systems. The results given here allow a unified proof of global convergence for several classes of networks that had been previously…

This https://arxiv.org/abs/2309.10454 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Maximum principle for a Markovian regime switching system with partial information under model uncertainty
In this paper, we study a stochastic optimal control problem for a Markovian regime switching system, where the coefficients of the state equation and the cost functional are uncertain. First, we obtain the variational inequality by showing the continuity of solutions to variational equations with respect to the uncertainty parameter $θ$. Second, using the linearization and weak convergence techniques, we prove the necessary stochastic maximum principle of the stochastic optimal control. Final…

This https://arxiv.org/abs/2402.03091 has been replaced.
link: https://scholar.google.com/scholar?q=a

Optimal rate of convergence in periodic homogenization of viscous Hamilton-Jacobi equations
We study the optimal rate of convergence in periodic homogenization of the viscous Hamilton-Jacobi equation $u^\varepsilon_t + H(\frac{x}{\varepsilon},Du^\varepsilon) = \varepsilon Δu^\varepsilon$ in $\mathbb R^n\times (0,\infty)$ subject to a given initial datum. We prove that $\|u^\varepsilon-u\|_{L^\infty(\mathbb R^n \times [0,T])} \leq C(1+T) \sqrt{\varepsilon}$ for any given $T>0$, where $u$ is the viscosity solution of the effective problem. Moreover, we show that the $O(\sqrt{…

On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients
Aur\'elien Alfonsi, Guillaume Szulda
https://arxiv.org/abs/2402.19203

On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients
We consider one-dimensional stochastic Volterra equations with jumps for which we establish conditions upon the convolution kernel and coefficients for the strong existence and pathwise uniqueness of a non-negative càdlàg solution. By using the approach recently developed in arXiv:2302.07758, we show the strong existence by using a nonnegative approximation of the equation whose convergence is proved via a variant of the Yamada--Watanabe approximation technique. We apply our results to Lévy-…

Global convergence of iterative solvers for problems of nonlinear magnetostatics
Herbert Egger, Felix Engertsberger, Bogdan Radu
https://arxiv.org/abs/2403.18520

Global convergence of iterative solvers for problems of nonlinear magnetostatics
We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the damped Newton-method, fixed-point iteration, and the Kacanov iteration, which can all be interpreted as generalized gradient descent methods. Armijo backtracking isconsidered for an adaptive choice of the stepsize. The general assumptions required for our analy…

QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
Ishak Ayad, Nicolas Larue, Ma\"i K. Nguyen
https://arxiv.org/abs/2402.17951

QN-Mixer: A Quasi-Newton MLP-Mixer Model for Sparse-View CT Reconstruction
Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by inherently ill-posed inverse problems. Previous research advanced image quality via post-processing and deep unrolling algorithms but faces challenges, such as extended convergence times with ultra-sparse data. Despite enhancements, resulting images often show significant artifacts, limi…

Finding Birkhoff Averages via Adaptive Filtering
Maximilian Ruth, David Bindel
https://arxiv.org/abs/2403.19003 https://arxiv.org/pdf…

Finding Birkhoff Averages via Adaptive Filtering
In many applications, one is interested in classifying trajectories of Hamiltonian systems as invariant tori, islands, or chaos. The convergence rate of ergodic Birkhoff averages can be used to categorize these regions, but many iterations of the return map are needed to implement this directly. Recently, it has been shown that a weighted Birkhoff average can be used to accelerate the convergence, resulting in a useful method for categorizing trajectories. In this paper, we show how a modifie…

Monitoring the Convergence Speed of PDHG to Find Better Primal and Dual Step Sizes
Olivier Fercoq (S2A, LTCI)
https://arxiv.org/abs/2403.19202 https://

Monitoring the Convergence Speed of PDHG to Find Better Primal and Dual Step Sizes
Primal-dual algorithms for the resolution of convex-concave saddle point problems usually come with one or several step size parameters. Within the range where convergence is guaranteed, choosing well the step size can make the difference between a slow or a fast algorithm. A usual way to adaptively set step sizes is to ensure that there is a fair balance between primal and dual variable's amount of change. In this work, we show how to find even better step sizes for the primal-dual hybrid grad…

This https://arxiv.org/abs/2308.04075 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Boundary-preserving Lamperti-splitting schemes for some Stochastic Differential Equations
We propose and analyse boundary-preserving schemes for the strong approximations of some scalar SDEs with non-globally Lipschitz drift and diffusion coefficients whose state-space is bounded. The schemes consists of a Lamperti transform followed by a Lie--Trotter splitting. We prove $L^{p}(Ω)$-convergence of order $1$, for every $p \geq 1$, of the schemes and exploit the Lamperti transform to confine the numerical approximations to the state-space of the considered SDE. We provide numerical ex…

This https://arxiv.org/abs/2207.07321 has been replaced.
link: https://scholar.google.com/scholar?q=a

Averaged Deep Denoisers for Image Regularization
Plug-and-Play (PnP) and Regularization-by-Denoising (RED) are recent paradigms for image reconstruction that leverage the power of modern denoisers for image regularization. In particular, they have been shown to deliver state-of-the-art reconstructions with CNN denoisers. Since the regularization is performed in an ad-hoc manner, understanding the convergence of PnP and RED has been an active research area. It was shown in recent works that iterate convergence can be guaranteed if the denoiser…

Weak convergence of probability measures on hyperspaces with the upper Fell-topology
Dietmar Ferger
https://arxiv.org/abs/2403.18798 https://

Weak convergence of probability measures on hyperspaces with the upper Fell-topology
Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak convergence of probability measures on the corresponding hyperspaces with a focus on the upper Fell topology. The results can be transferred to distributional convergence of random closed sets in E with applications to the asymptotic behavior of measurable selection.

This https://arxiv.org/abs/2311.18426 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence Analysis of Fractional Gradient Descent
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence analysis of fractional gradient descent is currently limited both in the methods analyzed and the settings analyzed. This paper aims to fill in these gaps by analyzing variations of fractional gradient descent in smooth and convex, smooth and strongly convex, an…

Finding Birkhoff Averages via Adaptive Filtering
Maximilian Ruth, David Bindel
https://arxiv.org/abs/2403.19003 https://arxiv.org/pdf…

Finding Birkhoff Averages via Adaptive Filtering
In many applications, one is interested in classifying trajectories of Hamiltonian systems as invariant tori, islands, or chaos. The convergence rate of ergodic Birkhoff averages can be used to categorize these regions, but many iterations of the return map are needed to implement this directly. Recently, it has been shown that a weighted Birkhoff average can be used to accelerate the convergence, resulting in a useful method for categorizing trajectories. In this paper, we show how a modifie…

Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations
Luigi C. Berselli, Alex Kaltenbach
https://arxiv.org/abs/2402.16606

Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations
In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations employing an implicit Euler step in time and a discretely inf-sup-stable finite element approximation in space. Moreover, numerical experiments are carried out that supplement the theoretical findings.

Note on the complete moment convergence for moving average process of a class of random variables under sub-linear expectations
Mingzhou Xu
https://arxiv.org/abs/2403.19209

Note on the complete moment convergence for moving average process of a class of random variables under sub-linear expectations
In this paper, the complete moment convergence for the partial sums of moving average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ is proved under some proper conditions, where $\{Y_i,-\infty

This https://arxiv.org/abs/2309.05393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations
We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a semilinear elliptic equation. The objective functional may include a sparsity promoting term and we allow for box control constraints.

Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations
Luigi C. Berselli, Alex Kaltenbach
https://arxiv.org/abs/2402.16606

Convergence analysis for a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations
In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations employing an implicit Euler step in time and a discretely inf-sup-stable finite element approximation in space. Moreover, numerical experiments are carried out that supplement the theoretical findings.

Non-asymptotic Global Convergence Analysis of BFGS with the Armijo-Wolfe Line Search
Qiujiang Jin, Ruichen Jiang, Aryan Mokhtari
https://arxiv.org/abs/2404.16731

Non-asymptotic Global Convergence Analysis of BFGS with the Armijo-Wolfe Line Search
In this paper, we establish the first explicit and non-asymptotic global convergence analysis of the BFGS method when deployed with an inexact line search scheme that satisfies the Armijo-Wolfe conditions. We show that BFGS achieves a global convergence rate of $(1-\frac{1}κ)^k$ for $μ$-strongly convex functions with $L$-Lipschitz gradients, where $κ=\frac{L}μ$ denotes the condition number. Furthermore, if the objective function's Hessian is Lipschitz, BFGS with the Armijo-Wolfe line search…

Fast convergence rates and trajectory convergence of a Tikhonov regularized inertial primal\mbox{-}dual dynamical system with time scaling and vanishing damping
Ting-Ting Zhu, Rong Hu, Ya-Ping Fang
https://arxiv.org/abs/2404.14853

Fast convergence rates and trajectory convergence of a Tikhonov regularized inertial primal\mbox{-}dual dynamical system with time scaling and vanishing damping
A Tikhonov regularized inertial primal\mbox{-}dual dynamical system with time scaling and vanishing damping is proposed for solving a linearly constrained convex optimization problem in Hilbert spaces. The system under consideration consists of two coupled second order differential equations and its convergence properties depend upon the decaying speed of the product of the time scaling parameter and the Tikhonov regularization parameter (named the rescaled regularization parameter) to zero. Wh…

Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergence
Ilyas Fatkhullin, Niao He
https://arxiv.org/abs/2402.17722 https://

Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergence
This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be differentiable with Lipschitz continuous gradients, thereby excluding important setups such as Shannon entropy. In this work, we present a new convergence analysis of nonconvex SMD supporting general DGF, that overcomes the above limitations and relies solely on…

Convergence rates under a range invariance condition with application to electrical impedance tomography
Barbara Kaltenbacher
https://arxiv.org/abs/2403.18704

Convergence rates under a range invariance condition with application to electrical impedance tomography
This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to achieve this, often an appropriate relaxation of the problem needs to be found that is usually based on an augmentation of the set of unknowns and leads to a particularly structured reformulation of the inverse problem. We analyze three approaches that make use …

Complete moment convergence of moving average processes for $m$-widely acceptable sequence under sub-linear expectations
Mingzhou Xu, Xuhang Kong
https://arxiv.org/abs/2403.18304 …

Complete moment convergence of moving average processes for $m$-widely acceptable sequence under sub-linear expectations
In this article, the complete moment convergence for the partial sum of moving average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ is estabished under some proper conditions, where $\{Y_i,-\infty

This https://arxiv.org/abs/2309.04846 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-commutative Optimal Transport for semi-definite positive matrices
We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive matrices (not necessarily with trace one). We prove the existence of a minimizer, compute the weak dual formulation and prove $Γ$-convergence results, demonstrating convergence to both Unbalanced Non-commutative Optimal Transport (as the Entropy-regularization parameter tends to zero) and von Neumann entropy regulariz…

Generalized convergence of the deep BSDE method: a step towards fully-coupled FBSDEs and applications in stochastic control
Balint Negyesi, Zhipeng Huang, Cornelis W. Oosterlee
https://arxiv.org/abs/2403.18552

Generalized convergence of the deep BSDE method: a step towards fully-coupled FBSDEs and applications in stochastic control
We are concerned with high-dimensional coupled FBSDE systems approximated by the deep BSDE method of Han et al. (2018). It was shown by Han and Long (2020) that the errors induced by the deep BSDE method admit a posteriori estimate depending on the loss function, whenever the backward equation only couples into the forward diffusion through the Y process. We generalize this result to fully-coupled drift coefficients, and give sufficient conditions for convergence under standard assumptions. The…

This https://arxiv.org/abs/2012.02303 has been replaced.
link: https://scholar.google.com/scholar?q=a

Decentralized State-Dependent Markov Chain Synthesis with an Application to Swarm Guidance
This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical conditions, without relying on any connectivity assumptions regarding the dynamic network topology. Utilizing the proposed consensus protocol, we develop the DSMC algorithm, updating the Markov matrix based on the current state while ensuring the convergence conditi…

This https://arxiv.org/abs/2311.01959 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A First Order Method for Linear Programming Parameterized by Circuit Imbalance
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates have been established for first order LP algorithms, despite the fact that the underlying formulations are not strongly convex. However, the convergence rate typically depends on the Hoffman constant of a large matrix that contains the constraint matrix, as we…

This https://arxiv.org/abs/2303.01101 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

BIG Hype: Best Intervention in Games via Distributed Hypergradient Descent
Hierarchical decision making problems, such as bilevel programs and Stackelberg games, are attracting increasing interest in both the engineering and machine learning communities. Yet, existing solution methods lack either convergence guarantees or computational efficiency, due to the absence of smoothness and convexity. In this work, we bridge this gap by designing a first-order hypergradient-based algorithm for Stackelberg games and mathematically establishing its convergence using tools from…

This https://arxiv.org/abs/2402.17072 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Proximal Algorithms for a class of abstract convex functions
In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of algorithms, namely an abstract proximal point method, an abstract forward-backward method and an abstract projected subgradient method. Global convergence results for all algorithms are discussed and numerical examples are given

This https://arxiv.org/abs/2402.04689 has been replaced.
link: https://scholar.google.com/scholar?q=a

Stein Boltzmann Sampling: A Variational Approach for Global Optimization
In this paper, we introduce a new flow-based method for global optimization of Lipschitz functions, called Stein Boltzmann Sampling (SBS). Our method samples from the Boltzmann distribution that becomes asymptotically uniform over the set of the minimizers of the function to be optimized. Candidate solutions are sampled via the \emph{Stein Variational Gradient Descent} algorithm. We prove the asymptotic convergence of our method, introduce two SBS variants, and provide a detailed comparison wit…

This https://arxiv.org/abs/2305.17224 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fast and Accurate Estimation of Low-Rank Matrices from Noisy Measurements via Preconditioned Non-Convex Gradient Descent
Non-convex gradient descent is a common approach for estimating a low-rank $n\times n$ ground truth matrix from noisy measurements, because it has per-iteration costs as low as $O(n)$ time, and is in theory capable of converging to a minimax optimal estimate. However, the practitioner is often constrained to just tens to hundreds of iterations, and the slow and/or inconsistent convergence of non-convex gradient descent can prevent a high-quality estimate from being obtained. Recently, the techn…

This https://arxiv.org/abs/2305.00424 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Policy Iteration Reinforcement Learning Method for Continuous-time Mean-Field Linear-Quadratic Optimal Problem
This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear quadratic mean-field control problems in the infinite horizon. The drift and diffusion terms in the dynamics involve the state as well as the control. We investigate the stability and convergence of the RL algorithm using a Lyapunov Recursion. Instead of solving a pair of coupled Riccati equations, the RL technique focuses on strengthening an auxiliary function and the cost functional as the…

An interior-point trust-region method for nonsmooth regularized bound-constrained optimization
Geoffroy Leconte, Dominique Orban
https://arxiv.org/abs/2402.18423

An interior-point trust-region method for nonsmooth regularized bound-constrained optimization
We develop an interior-point method for nonsmooth regularized bound-constrained optimization problems. Our method consists of iteratively solving a sequence of unconstrained nonsmooth barrier subproblems. We use a variant of the proximal quasi-Newton trust-region algorithm TR of arXiv:2103.15993v3 to solve the barrier subproblems, with additional assumptions inspired from well-known smooth interior-point trust-region methods. We show global convergence of our algorithm with respect to the criti…

This https://arxiv.org/abs/2305.11469 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

(Rectified Version) The Barzilai-Borwein Method for Distributed Optimization over Unbalanced Directed Networks
This paper studies optimization problems over multi-agent systems, in which all agents cooperatively minimize a global objective function expressed as a sum of local cost functions. Each agent in the systems uses only local computation and communication in the overall process without leaking their private information. Based on the Barzilai-Borwein (BB) method and multi-consensus inner loops, a distributed algorithm with the availability of larger stepsizes and accelerated convergence, namely AD…

Revisiting Convergence of AdaGrad with Relaxed Assumptions
Yusu Hong, Junhong Lin
https://arxiv.org/abs/2402.13794 https://arxiv.org/…

Revisiting Convergence of AdaGrad with Relaxed Assumptions
In this study, we revisit the convergence of AdaGrad with momentum (covering AdaGrad as a special case) on non-convex smooth optimization problems. We consider a general noise model where the noise magnitude is controlled by the function value gap together with the gradient magnitude. This model encompasses a broad range of noises including bounded noise, sub-Gaussian noise, affine variance noise and the expected smoothness, and it has been shown to be more realistic in many practical applicati…

This https://arxiv.org/abs/2305.03938 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees
In this paper, we present a comprehensive study on the convergence properties of Adam-family methods for nonsmooth optimization, especially in the training of nonsmooth neural networks. We introduce a novel two-timescale framework that adopts a two-timescale updating scheme, and prove its convergence properties under mild assumptions. Our proposed framework encompasses various popular Adam-family methods, providing convergence guarantees for these methods in training nonsmooth neural networks. …

This https://arxiv.org/abs/2404.04357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Why does the two-timescale Q-learning converge to different mean field solutions? A unified convergence analysis
We revisit the unified two-timescale Q-learning algorithm as initially introduced by Angiuli et al. \cite{angiuli2022unified}. This algorithm demonstrates efficacy in solving mean field game (MFG) and mean field control (MFC) problems, simply by tuning the ratio of two learning rates for mean field distribution and the Q-functions respectively. In this paper, we provide a comprehensive theoretical explanation of the algorithm's bifurcated numerical outcomes under fixed learning rates. We achiev…