Tootfinder

Worst-Case Convergence Time of ML Algorithms via Extreme Value Theory
Saeid Tizpaz-Niari, Sriram Sankaranarayanan
https://arxiv.org/abs/2404.07170 https://…

Worst-Case Convergence Time of ML Algorithms via Extreme Value Theory
This paper leverages the statistics of extreme values to predict the worst-case convergence times of machine learning algorithms. Timing is a critical non-functional property of ML systems, and providing the worst-case converge times is essential to guarantee the availability of ML and its services. However, timing properties such as worst-case convergence times (WCCT) are difficult to verify since (1) they are not encoded in the syntax or semantics of underlying programming languages of AI, (2…

Specifying and Verifying the Convergence Stairs of the Collatz Program
Ali Ebnenasir
https://arxiv.org/abs/2403.04777 https://arxiv.o…

Specifying and Verifying the Convergence Stairs of the Collatz Program
This paper presents an algorithmic method that, given a positive integer $j$, generates the $j$-th convergence stair containing all natural numbers from where the Collatz conjecture holds by exactly $j$ applications of the Collatz function. To this end, we present a novel formulation of the Collatz conjecture as a concurrent program, and provide the general case specification of the $j$-th convergence stair for any $j > 0$. The proposed specifications provide a layered and linearized orientatio…

Prelimit Coupling and Steady-State Convergence of Constant-stepsize Nonsmooth Contractive SA
Yixuan Zhang, Dongyan Huo, Yudong Chen, Qiaomin Xie
https://arxiv.org/abs/2404.06023 <…

Prelimit Coupling and Steady-State Convergence of Constant-stepsize Nonsmooth Contractive SA
Motivated by Q-learning, we study nonsmooth contractive stochastic approximation (SA) with constant stepsize. We focus on two important classes of dynamics: 1) nonsmooth contractive SA with additive noise, and 2) synchronous and asynchronous Q-learning, which features both additive and multiplicative noise. For both dynamics, we establish weak convergence of the iterates to a stationary limit distribution in Wasserstein distance. Furthermore, we propose a prelimit coupling technique for establi…

This https://arxiv.org/abs/2312.16372 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model
We study the convergence of the Ginzburg-Landau (GL) expansion in the context of the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity and the Nambu-Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature $T$ and chemical potential $μ$. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap $Δ$ and dynamical quark mass $M$ ar…

The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
Guangming Hu, Ziping Lei, Yu Sun, Puchun Zhou
https://arxiv.org/abs/2404.05982

The Convergence of Prescribed Combinatorial Ricci Flows for Total Geodesic Curvatures in Spherical Background Geometry
In this paper, we study the existence and rigidity of (degenerated) circle pattern metric with prescribed total geodesic curvatures in spherical background geometry. To find the (degenerated) circle pattern metric with prescribed total geodesic curvatures, we define some prescribed combinatorial Ricci flows and study the convergence of flows for (degenerated) circle pattern metrics. We solve the prescribed total geodesic curvature problem and provide two methods to find the degenerated circle p…

Formal principle with convergence for rational curves of Goursat type
Jun-Muk Hwang
https://arxiv.org/abs/2404.05941 https://arxiv.or…

Formal principle with convergence for rational curves of Goursat type
We propose a conjecture that a general member of a bracket-generating family of rational curves in a complex manifold satisfies the formal principle with convergence, namely, any formal equivalence between such curves is convergent. If the normal bundles of the rational curves are positive, the conjecture follows from the results of Commichau-Grauert and Hirschowitz. We prove the conjecture for the opposite case when the normal bundles are furthest from positive vector bundles among bracket-gen…

Convergence to Nash Equilibrium and No-regret Guarantee in (Markov) Potential Games
Jing Dong, Baoxiang Wang, Yaoliang Yu
https://arxiv.org/abs/2404.06516 …

Convergence to Nash Equilibrium and No-regret Guarantee in (Markov) Potential Games
In this work, we study potential games and Markov potential games under stochastic cost and bandit feedback. We propose a variant of the Frank-Wolfe algorithm with sufficient exploration and recursive gradient estimation, which provably converges to the Nash equilibrium while attaining sublinear regret for each individual player. Our algorithm simultaneously achieves a Nash regret and a regret bound of $O(T^{4/5})$ for potential games, which matches the best available result, without using addi…

Convergence, and lack of convergence, of phase space distributions to microcanonical equilibrium
Casey O. Barkan
https://arxiv.org/abs/2404.05123 https://<…

Convergence, and lack of convergence, of phase space distributions to microcanonical equilibrium
It is well known that phase space distribution functions obeying Liouville's theorem can converge weakly, but not strongly, to the microcanonical distribution. Similarly, coarse-grained distributions can converge pointwise, although unlike weak convergence, coarse-graining involves an arbitrary partition of phase space. We prove a theorem that strengthens the result that strong convergence cannot occur. Specifically, we show that time evolution is an isometry for a broad class of metrics of sta…

Investigating the shortcomings of the Flow Convergence Method for quantification of mitral regurgitation in a pulsatile in-vitro environment and with Computational Fluid Dynamics
Roger Karl, Robin Leister, Lubov Stroh, Derliz Mereles, Matthias Eden, Luis Neff, Raffaele de Simone, Gabriele Romano, Jochen Kriegseis, Matthias Karck, Christoph Lichtenstern, Norbert Frey, Bettina Frohnapfel, Alexander Stroh, Sandy Engelhardt

Investigating the shortcomings of the Flow Convergence Method for quantification of mitral regurgitation in a pulsatile in-vitro environment and with Computational Fluid Dynamics
The flow convergence method includes calculation of the proximal isovelocity surface area (PISA) and is widely used to classify mitral regurgitation (MR) with echocardiography. It constitutes a primary decision factor for determination of treatment and should therefore be a robust quantification method. However, it is known for its tendency to underestimate MR and its dependence on user expertise. The present work systematically compares different pulsatile flow profiles arising from different …

Self-Similar Mass Accretion History in Scale-Free Simulations
John Soltis, Lehman Garrison
https://arxiv.org/abs/2405.05360 https://a…

Self-Similar Mass Accretion History in Scale-Free Simulations
Using a scale-free $N$-body simulation generated with the ABACUS $N$-body code, we test the robustness of halo mass accretion histories via their convergence to self-similarity. We compare two halo finders, ROCKSTAR and COMPASO. We find superior self-similarity in halo mass accretion histories determined using ROCKSTAR, with convergence to 5% or better between $\sim10^2$ to $10^5$ particles. For COMPASO we find weaker convergence over a similar region, with at least 10% between $\sim10^2$ to $1…

Convergence Rates of Online Critic Value Function Approximation in Native Spaces
Shengyuan Niu, Ali Bouland, Haoran Wang, Filippos Fotiadis, Andrew Kurdila, Andrea L'Afflitto, Sai Tej Paruchuri, Kyriakos G. Vamvoudakis
https://arxiv.org/abs/2405.05887

Convergence Rates of Online Critic Value Function Approximation in Native Spaces
In this paper, the evolution equation that defines the online critic for the approximation of the optimal value function is cast in a general class of reproducing kernel Hilbert spaces (RKHSs). Exploiting some core tools of RKHS theory, this formulation allows deriving explicit bounds on the performance of the critic in terms of the kernel and definition of the RKHS, the number of basis functions, and the location of centers used to define scattered bases. The performance of the critic is preci…

Further Understanding of a Local Gaussian Process Approximation: Characterising Convergence in the Finite Regime
Anthony Stephenson, Robert Allison, Edward Pyzer-Knapp
https://arxiv.org/abs/2404.06200

Further Understanding of a Local Gaussian Process Approximation: Characterising Convergence in the Finite Regime
We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases. For isotropic kernels such as Matérn and squared-exponential, an upper bound on the predictive MSE can be obtained as $O(n^{-\frac{p}{d}})$ for input dimension $d$, $p$ dictated by the kernel (and $d>p$) and fixed number of nearest-neighbours $m$ with minima…

Elliptic and parabolic problems in thin domains with doubly weak oscillatory boundary
Jos\'e M. Arrieta, Manuel Villanueva-Pesqueira
https://arxiv.org/abs/2405.05607

Elliptic and parabolic problems in thin domains with doubly weak oscillatory boundary
In this work we consider higher dimensional thin domains with the property that both boundaries, bottom and top, present oscillations of weak type. We consider the Laplace operator with Neumann boundary conditions and analyze the behavior of the solutions as the thin domains shrinks to a fixed domain $ω\subset \R^n$. We obtain the convergence of the resolvent of the elliptic operators in the sense of compact convergence of operators, which in particular implies the convergence of the spectra. …

Large Language Model-Aided Evolutionary Search for Constrained Multiobjective Optimization
Zeyi Wang, Songbai Liu, Jianyong Chen, Kay Chen Tan
https://arxiv.org/abs/2405.05767

Large Language Model-Aided Evolutionary Search for Constrained Multiobjective Optimization
Evolutionary algorithms excel in solving complex optimization problems, especially those with multiple objectives. However, their stochastic nature can sometimes hinder rapid convergence to the global optima, particularly in scenarios involving constraints. In this study, we employ a large language model (LLM) to enhance evolutionary search for solving constrained multi-objective optimization problems. Our aim is to speed up the convergence of the evolutionary population. To achieve this, we fi…

A refined convergence estimate for a fourth order finite difference numerical scheme to the Cahn-Hilliard equation
Jing Guo, Cheng Wang, Yue Yan, Xingye Yue
https://arxiv.org/abs/2404.04628

A refined convergence estimate for a fourth order finite difference numerical scheme to the Cahn-Hilliard equation
In this article we present a refined convergence analysis for a second order accurate in time, fourth order finite difference numerical scheme for the 3-D Cahn-Hilliard equation, with an improved convergence constant. A modified backward differentiation formula temporal discretization is applied, and a Douglas-Dupont artificial regularization is included to ensure the energy stability. In fact, a standard application of discrete Gronwall inequality leads to a convergence constant dependent on t…

@… Just one note: it’s been years since 3D converted movies are way better that movies shot in native 3D. It has to do with the limitations of the stereo rigs and the impossibility to fix bad convergence settings on some shots among other things. If Avatar looks better to you in 3D is more because James Cameron is a beast, and because HFR partially solves the problem …

This https://arxiv.org/abs/2405.05079 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

Power Variable Projection for Initialization-Free Large-Scale Bundle Adjustment
Initialization-free bundle adjustment (BA) remains largely uncharted. While Levenberg-Marquardt algorithm is the golden method to solve the BA problem, it generally relies on a good initialization. In contrast, the under-explored Variable Projection algorithm (VarPro) exhibits a wide convergence basin even without initialization. Coupled with object space error formulation, recent works have shown its ability to solve (small-scale) initialization-free bundle adjustment problem. We introduce Pow…

On the convergence of zeta functions of prehomogeneous vector spaces
Tobias Finis, Erez Lapid
https://arxiv.org/abs/2405.04153 https://

On the convergence of zeta functions of prehomogeneous vector spaces
We prove a general convergence result for zeta functions of prehomogeneous vector spaces extending results of H. Saito, F. Sato and Yukie. Our analysis points to certain subspaces which yield boundary terms. We study it further in the setup arising from nilpotent orbits. In certain cases we determine the residue at the rightmost pole of the zeta function.

Unifying Low Dimensional Observations in Deep Learning Through the Deep Linear Unconstrained Feature Model
Connall Garrod, Jonathan P. Keating
https://arxiv.org/abs/2404.06106

Unifying Low Dimensional Observations in Deep Learning Through the Deep Linear Unconstrained Feature Model
Modern deep neural networks have achieved high performance across various tasks. Recently, researchers have noted occurrences of low-dimensional structure in the weights, Hessian's, gradients, and feature vectors of these networks, spanning different datasets and architectures when trained to convergence. In this analysis, we theoretically demonstrate these observations arising, and show how they can be unified within a generalized unconstrained feature model that can be considered analytically…

This https://arxiv.org/abs/2403.01684 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dendrogram of mixing measures: Hierarchical clustering and model selection for finite mixture models
We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and mixture modeling. The dendrogram's construction is derived from the theory of convergence of the mixing measures, and as a result, we can both consistently select the true number of mixing components and obtain the pointwise optimal convergence rate for parameter e…

This https://arxiv.org/abs/2404.19027 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Better Optimization of Variational Quantum Eigensolvers by combining the Unitary Block Optimization Scheme with Classical Post-Processing
Variational Quantum Eigensolvers (VQE) are a promising approach for finding the classically intractable ground state of a Hamiltonian. The Unitary Block Optimization Scheme (UBOS) is a state-of-the-art VQE method which works by sweeping over gates and finding optimal parameters for each gate in the environment of other gates. UBOS improves the convergence time to the ground state by an order of magnitude over Stochastic Gradient Descent (SGD). It nonetheless suffers in both rate of convergence …

This https://arxiv.org/abs/2311.18680 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mourre theory and asymptotic observables in local relativistic quantum field theory
We prove the convergence of Araki-Haag detectors in any Haag-Kastler quantum field theory with an upper and lower mass gap. We cover the case of a single Araki-Haag detector on states of bounded energy, which are selected from the absolutely continuous part of the energy-momentum spectrum sufficiently close to the lower boundary of the multi-particle spectrum. These states essentially encompass those states in the multi-particle spectrum lying below the three-particle threshold. In our proof, w…

This https://arxiv.org/abs/2311.15049 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Atomicity of Boolean algebras and vector lattices in terms of order convergence
We prove that order convergence on a Boolean algebra turns it into a compact convergence space if and only if this Boolean algebra is complete and atomic. We also show that on an Archimedean vector lattice, order intervals are compact with respect to order convergence if and only the vector lattice is complete and atomic. Additionally we provide a direct proof of the fact that uo convergence on an Archimedean vector lattice is induced by a topology if and only if the vector lattice is atomic.

Communication-efficient and Differentially-private Distributed Nash Equilibrium Seeking with Linear Convergence
Xiaomeng Chen, Wei Huo, Kemi Ding, Subhrakanti Dey, Ling Shi
https://arxiv.org/abs/2405.04757

Communication-efficient and Differentially-private Distributed Nash Equilibrium Seeking with Linear Convergence
The distributed computation of a Nash equilibrium (NE) for non-cooperative games is gaining increased attention recently. Due to the nature of distributed systems, privacy and communication efficiency are two critical concerns. Traditional approaches often address these critical concerns in isolation. This work introduces a unified framework, named CDP-NES, designed to improve communication efficiency in the privacy-preserving NE seeking algorithm for distributed non-cooperative games over dire…

A Monte Carlo algorithm for spin foam intertwiners
Sebastian Steinhaus
https://arxiv.org/abs/2403.04836 https://arxiv.org/pdf/2403.04…

A Monte Carlo algorithm for spin foam intertwiners
Monte Carlo algorithms are barely considered in spin foam quantum gravity. Due to the quantum nature of spin foam amplitudes one cannot readily apply them, and the present sign problem is a threat to convergence and thus efficiency. Yet, ultimately the severity of the sign problem in spin foams is not known. In this article we propose a new probability distribution for coherent (boundary) intertwiners, which we use to define a Markov Chain Monte Carlo algorithm. We apply this algorithm to the S…

Some properties of Wright Operators
Prashantkumar Patel
https://arxiv.org/abs/2404.04651 https://arxiv.org/pdf/2404.04651

Some properties of Wright Operators
This note aims to present novel positive linear operators involving the Wright function. Furthermore, the present research established the moments of these newly defined operators and estimated the convergence rate using the classical modulus of continuity. Additionally, the convergence rate in the Lipschitz spaces, their A-statistical convergence property, and $(λ, γ)$-statistical convergence properties have been covered.

This https://arxiv.org/abs/2311.06439 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Splitting for some classes of homeomorphic and coalescing stochastic flows
The splitting scheme (the Kato-Trotter formula) is applied to stochastic flows with common noise of the type introduced by Th.E.~Harris. The case of possibly coalescing flows with continuous infinitesimal covariance is considered and the weak convergence of the corresponding finite-dimensional motions is established. As applications, results for the convergence of the associated pushforward measures and dual flows are given. Similarities between splitting and the Euler-Maruyama scheme yield est…

Universal exponential pointwise convergence for weighted multiple ergodic averages over $ \mathbb{T}^\infty $
Zhicheng Tong, Yong Li
https://arxiv.org/abs/2405.02866

Universal exponential pointwise convergence for weighted multiple ergodic averages over $ \mathbb{T}^\infty $
By employing an accelerated weighting method, we establish arbitrary polynomial and exponential pointwise convergence for multiple ergodic averages under general conditions in both discrete and continuous settings, involving quasi-periodic and almost periodic cases, which breaks the well known slow convergence rate observed in classical ergodic theory. We also present joint Diophantine rotations as explicit applications. Especially, in the sense that excluding nearly rational rotations with zer…

This https://arxiv.org/abs/2403.00748 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Primal-Dual iLQR
We introduce a new algorithm for solving unconstrained discrete-time optimal control problems. Our method follows a direct multiple shooting approach, and consists of applying the SQP method together with an $\ell_2$ augmented Lagrangian primal-dual merit function. We use the LQR algorithm to efficiently solve the primal-dual Newton-KKT system. As our algorithm is a specialization of NPSQP, it inherits its generic properties, including global convergence, fast local convergence, and the lack of…

A refined convergence estimate for a fourth order finite difference numerical scheme to the Cahn-Hilliard equation
Jing Guo, Cheng Wang, Yue Yan, Xingye Yue
https://arxiv.org/abs/2404.04628

A refined convergence estimate for a fourth order finite difference numerical scheme to the Cahn-Hilliard equation
In this article we present a refined convergence analysis for a second order accurate in time, fourth order finite difference numerical scheme for the 3-D Cahn-Hilliard equation, with an improved convergence constant. A modified backward differentiation formula temporal discretization is applied, and a Douglas-Dupont artificial regularization is included to ensure the energy stability. In fact, a standard application of discrete Gronwall inequality leads to a convergence constant dependent on t…

A Convergence result for a Stefan problem with phase relaxation
Vincenzo Recupero
https://arxiv.org/abs/2405.05570 https://arxiv.org/…

A Convergence result for a Stefan problem with phase relaxation
In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward an integral formulation of the Stefan problem when the relaxation parameter approaches zero. Assuming the natural physical assumption that the initial condition of the phase is constrained, but taking more general boundary conditions, we prove that the solution of this relaxed model converges in a stronger way to the solution of the classical weak Stefan problem.

Bayesian mass mapping with weak lensing data using KARMMA -- validation with simulations and application to Dark Energy Survey Year 3 data
Supranta S. Boruah, Pier Fiedorowicz, Eduardo Rozo
https://arxiv.org/abs/2403.05484

Bayesian mass mapping with weak lensing data using KARMMA -- validation with simulations and application to Dark Energy Survey Year 3 data
We update the field-level inference code KARMMA to enable tomographic forward-modelling of shear maps. Our code assumes a lognormal prior on the convergence field, and properly accounts for the cross-covariance in the lensing signal across tomographic source bins. We use mock weak lensing data from N-body simulations to validate our mass-mapping forward model by comparing our posterior maps to the input convergence fields. We find that KARMMA produces more accurate reconstructions than traditio…

PoPE: Legendre Orthogonal Polynomials Based Position Encoding for Large Language Models
Arpit Aggarwal
https://arxiv.org/abs/2405.04585 https://

PoPE: Legendre Orthogonal Polynomials Based Position Encoding for Large Language Models
There are several improvements proposed over the baseline Absolute Positional Encoding (APE) method used in original transformer. In this study, we aim to investigate the implications of inadequately representing positional encoding in higher dimensions on crucial aspects of the attention mechanism, the model's capacity to learn relative positional information, and the convergence of models, all stemming from the choice of sinusoidal basis functions. Through a combination of theoretical insight…

Non-asymptotic estimates for accelerated high order Langevin Monte Carlo algorithms
Ariel Neufeld, Ying Zhang
https://arxiv.org/abs/2405.05679 https://

Non-asymptotic estimates for accelerated high order Langevin Monte Carlo algorithms
In this paper, we propose two new algorithms, namely aHOLA and aHOLLA, to sample from high-dimensional target distributions with possibly super-linearly growing potentials. We establish non-asymptotic convergence bounds for aHOLA in Wasserstein-1 and Wasserstein-2 distances with rates of convergence equal to $1+q/2$ and $1/2+q/4$, respectively, under a local Hölder condition with exponent $q\in(0,1]$ and a convexity at infinity condition on the potential of the target distribution. Similar res…

Memo to the media: Steveston–#Richmond East voters care about the planet
National newspapers are overlooking a hot issue in their coverage of former #Conservative MP Kenny Chiu's loss in the 2021 election.
Charlie Smith
May 03, 2024

The Convergence of Sinophobia and Sinofascism in Canada
‘The Chinese’ are a collective of pro-Beijing agents, according to CSIS, the Canadian media, and Xi Jinping

This https://arxiv.org/abs/2403.18236 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Multi-AGV Path Planning Method via Reinforcement Learning and Particle Filters
The Reinforcement Learning (RL) algorithm, renowned for its robust learning capability and search stability, has garnered significant attention and found extensive application in Automated Guided Vehicle (AGV) path planning. However, RL planning algorithms encounter challenges stemming from the substantial variance of neural networks caused by environmental instability and significant fluctuations in system structure. These challenges manifest in slow convergence speed and low learning efficien…

This https://arxiv.org/abs/2403.06883 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Rates of convergence for holomorphic semigroups of finite shift
We study parabolic semigroups of finite shift in the unit disk with regard to the rate of convergence of their orbits to the Denjoy--Wolff point. We examine this rate in terms of Euclidean distance, hyperbolic distance and harmonic measure. In each case, we provide explicit examples to display the sharpness of the results. We further discuss the corresponding rates of convergence for parabolic semigroups of positive hyperbolic step and infinite shift.

This https://arxiv.org/abs/2401.15541 has been replaced.
link: https://scholar.google.com/scholar?q=a

Stitching Satellites to the Edge: Pervasive and Efficient Federated LEO Satellite Learning
In the ambitious realm of space AI, the integration of federated learning (FL) with low Earth orbit (LEO) satellite constellations holds immense promise. However, many challenges persist in terms of feasibility, learning efficiency, and convergence. These hurdles stem from the bottleneck in communication, characterized by sporadic and irregular connectivity between LEO satellites and ground stations, coupled with the limited computation capability of satellite edge computing (SEC). This paper p…

Systematic review, analysis, and characterisation of malicious industrial network traffic datasets for aiding Machine Learning algorithm performance testing
Martin Dobler, Michael Hellwig, Nuno Lopes, Ken Oakley, Mike Winterburn
https://arxiv.org/abs/2405.04866

Systematic review, analysis, and characterisation of malicious industrial network traffic datasets for aiding Machine Learning algorithm performance testing
The adoption of the Industrial Internet of Things (IIoT) as a complementary technology to Operational Technology (OT) has enabled a new level of standardised data access and process visibility. This convergence of Information Technology (IT), OT, and IIoT has also created new cybersecurity vulnerabilities and risks that must be managed. Artificial Intelligence (AI) is emerging as a powerful tool to monitor OT/IIoT networks for malicious activity and is a highly active area of research. AI resea…

This https://arxiv.org/abs/2309.07169 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Spectral Convergence of Simplicial Complex Signals
Topological signal processing (TSP) utilizes simplicial complexes to model structures with higher order than vertices and edges. In this paper, we study the transferability of TSP via a generalized higher-order version of graphon, known as complexon. We recall the notion of a complexon as the limit of a simplicial complex sequence [1]. Inspired by the graphon shift operator and message-passing neural network, we construct a marginal complexon and complexon shift operator (CSO) according to comp…

User Connection and Resource Allocation Optimization in Blockchain Empowered Metaverse over 6G Wireless Communications
Liangxin Qian, Chang Liu, Jun Zhao
https://arxiv.org/abs/2403.05116

User Connection and Resource Allocation Optimization in Blockchain Empowered Metaverse over 6G Wireless Communications
The convergence of blockchain, Metaverse, and non-fungible tokens (NFTs) brings transformative digital opportunities alongside challenges like privacy and resource management. Addressing these, we focus on optimizing user connectivity and resource allocation in an NFT-centric and blockchain-enabled Metaverse in this paper. Through user work-offloading, we optimize data tasks, user connection parameters, and server computing frequency division. In the resource allocation phase, we optimize commu…

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…

Convergence and collapsing of CAT$(0)$-lattices
Nicola Cavallucci, Andrea Sambusetti
https://arxiv.org/abs/2405.01595 https://arxiv.o…

Convergence and collapsing of CAT$(0)$-lattices
We study the theory of convergence for CAT$(0)$-lattices (that is groups $Γ$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces) and their quotients (CAT$(0)$-orbispaces). We describe some splitting and collapsing phenomena, explaining precisely how these action can degenerate to a possibly non-discrete limit action. Finally, we prove a compactness theorem for the class of compact CAT$(0)$-homology orbifolds, and some applications: an isolation result for flat orbispaces and…

Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem
Satyajith Bommana Boyana, Thomas Lewis, Sijing Liu, Yi Zhang
https://arxiv.org/abs/2404.06490

Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem
In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite element methods for the convection-dominated equation cause spurious oscillations. We choose to follow a novel DG finite element differential calculus framework introduced in Feng et al. (2016) and approximate the infinite-dimensional operators in the equation wit…

Graph Neural Network Meets Multi-Agent Reinforcement Learning: Fundamentals, Applications, and Future Directions
Ziheng Liu (Sherman), Jiayi Zhang (Sherman), Enyu Shi (Sherman), Zhilong Liu (Sherman), Dusit Niyato (Sherman), Bo Ai (Sherman), Xuemin (Sherman), Shen
https://arxiv.org/abs/2404.04898…

Graph Neural Network Meets Multi-Agent Reinforcement Learning: Fundamentals, Applications, and Future Directions
Multi-agent reinforcement learning (MARL) has become a fundamental component of next-generation wireless communication systems. Theoretically, although MARL has the advantages of low computational complexity and fast convergence rate, there exist several challenges including partial observability, non-stationary, and scalability. In this article, we investigate a novel MARL with graph neural network-aided communication (GNNComm-MARL) to address the aforementioned challenges by making use of gra…

An Enhanced Grey Wolf Optimizer with Elite Inheritance and Balance Search Mechanisms
Jianhua Jiang, Ziying Zhao, Weihua Li, Keqin Li
https://arxiv.org/abs/2404.06524

An Enhanced Grey Wolf Optimizer with Elite Inheritance and Balance Search Mechanisms
The Grey Wolf Optimizer (GWO) is recognized as a novel meta-heuristic algorithm inspired by the social leadership hierarchy and hunting mechanism of grey wolves. It is well-known for its simple parameter setting, fast convergence speed, and strong optimization capability. In the original GWO, there are two significant design flaws in its fundamental optimization mechanisms. Problem (1): the algorithm fails to inherit from elite positions from the last iteration when generating the next position…

The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method
Thuan Quang Tran, Tuyen Trung Truong
https://arxiv.org/abs/2405.05834 https:/…

The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method
A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - was recently introduced by the second author. This method has good convergence guarantees, specially concerning finding roots of meromorphic functions. This paper explores using BNQN for the Riemann xi function. We show in particular that the Riemann hypothesis is equivalent to that all attractors of BNQN lie on the critical line. We also explain how an apparent relation between the basins of attraction of BNQN…

On a convergence of positive continuous additive functionals in terms of their smooth measures
Yasuhito Nishimori, Matsuyo Tomisaki, Kaneharu Tsuchida, Toshihiro Uemura
https://arxiv.org/abs/2405.03937

On a convergence of positive continuous additive functionals in terms of their smooth measures
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric on the space of measures of finite energy integrals and show some structures of the metric. Then, we show the compactness and give some examples of positive continuous additive functionals that the convergence holds in terms of the associated smooth measures.

Convergence Rate of the Hypersonic Similarity for Two-Dimensional Steady Potential Flows with Large Data
Gui-Qiang G. Chen, Jie Kuang, Wei Xiang, Yongqian Zhang
https://arxiv.org/abs/2405.04720

Convergence Rate of the Hypersonic Similarity for Two-Dimensional Steady Potential Flows with Large Data
We establish the optimal convergence rate of the hypersonic similarity for two-dimensional steady potential flows with {\it large data} past over a straight wedge in the $BV\cap L^1$ framework, provided that the total variation of the large data multiplied by $γ-1+\frac{a_{\infty}^2}{M_\infty^2}$ is uniformly bounded with respect to the adiabatic exponent $γ>1$, the Mach number $M_\infty$ of the incoming steady flow, and the hypersonic similarity parameter $a_\infty$. Our main approach in thi…

This https://arxiv.org/abs/2308.03686 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization
Denoising diffusions are a powerful method to generate approximate samples from high-dimensional data distributions. Recent results provide polynomial bounds on their convergence rate, assuming $L^2$-accurate scores. Until now, the tightest bounds were either superlinear in the data dimension or required strong smoothness assumptions. We provide the first convergence bounds which are linear in the data dimension (up to logarithmic factors) assuming only finite second moments of the data distrib…

This https://arxiv.org/abs/2405.03073 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence and Complexity Guarantee for Inexact First-order Riemannian Optimization Algorithms
We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general nonconvex and constrained setting. We answer these questions in a general framework of tangential Block Majorization-Minimization (tBMM). We establish that tBMM converges to an $ε$-stationary point within $O(ε^{-2})$ iterations. Under a mild assumption, the result…

PoPE: Legendre Orthogonal Polynomials Based Position Encoding for Large Language Models
Arpit Aggarwal
https://arxiv.org/abs/2405.04585 https://

PoPE: Legendre Orthogonal Polynomials Based Position Encoding for Large Language Models
There are several improvements proposed over the baseline Absolute Positional Encoding (APE) method used in original transformer. In this study, we aim to investigate the implications of inadequately representing positional encoding in higher dimensions on crucial aspects of the attention mechanism, the model's capacity to learn relative positional information, and the convergence of models, all stemming from the choice of sinusoidal basis functions. Through a combination of theoretical insight…

Boosted Imaginary Time Evolution of Matrix Product States
Benjamin C. B. Symons, Dilhan Manawadu, David Galvin, Stefano Mensa
https://arxiv.org/abs/2405.04959

Boosted Imaginary Time Evolution of Matrix Product States
In this work, we consider the imaginary time evolution of matrix product states. We present a novel quantum-inspired classical method that, when combined with time evolving block decimation (TEBD), is able to potentially speed-up the convergence to a ground state compared to TEBD alone. Our method, referred to as boosted imaginary time evolution, relies on the use of reflections to boost to lower energy states. Interleaving TEBD steps with boosts reduces the total number of TEBD steps and poten…

This https://arxiv.org/abs/2309.06477 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Constraining Cosmology With the CMB $\times$ LIM-Nulling Convergence
Lensing reconstruction maps from the cosmic microwave background (CMB) provide direct observations of the matter distribution of the universe without the use of a biased tracer. Such maps, however, constitute projected observables along the line of sight that are dominated by their low-redshift contributions. To cleanly access high-redshift information, Maniyar et al. showed that a linear combination of lensing maps from both CMB and line intensity mapping (LIM) observations can exactly null th…

This https://arxiv.org/abs/2311.02490 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Improved Convergence Rates of Windowed Anderson Acceleration for Symmetric Fixed-Point Iterations
This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, $x^{(k+1)}=q(x^{(k)})$. It provides the first proof that when the operator $q$ is linear and symmetric the windowed AA, which uses a sliding window of prior iterates, improves the root-linear convergence factor over the fixed-point iterations. When $q$ is nonlinear, yet has a symmetric Jacobian at a fixed point, a slightly modified AA algorithm is proved to have an analogous root-line…

Memo to the media: Steveston–#Richmond East voters care about the planet
National newspapers are overlooking a hot issue in their coverage of former #Conservative MP Kenny Chiu's loss in the 2021 election.
Charlie Smith
May 03, 2024

The Convergence of Sinophobia and Sinofascism in Canada
‘The Chinese’ are a collective of pro-Beijing agents, according to CSIS, the Canadian media, and Xi Jinping

Convergence of Random Products of Countably Infinitely Many Projections
Rasoul Eskandari, Mohammad Sal Moslehian
https://arxiv.org/abs/2405.04848 https://<…

Convergence of Random Products of Countably Infinitely Many Projections
Let $r \in \mathbb{N}\cup\{\infty\}$ be a fixed number and let $P_j\,\, (1 \leq j\leq r )$ be the projection onto the closed subspace $\mathcal{M}_j$ of $\mathscr{H}$. We are interested in studying the sequence $P_{i_1}, P_{i_2}, \ldots \in\{P_1, \ldots, P_r\}$. A significant problem is to demonstrate conditions under which the sequence $\{P_{i_n}\cdots P_{i_2}P_{i_1}x\}_{n=1}^\infty$ converges strongly or weakly to $Px$ for any $x\in\mathscr{H}$, where $P$ is the projection onto the intersecti…

This https://arxiv.org/abs/2401.03252 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New Lower Bounds for the Schur-Siegel-Smyth Trace Problem
We derive and implement a new way to find lower bounds on the smallest limiting trace-to-degree ratio of totally positive algebraic integers and improve the previously best-known bound to 1.798249. Our method adds new constraints to Smyth's linear programming method to decrease the variables required in the new problem of interest. This allows for faster convergence recovering Schur's bound in the simplest case and Siegel's bound in the second simplest case of our new family of bounds. We als…

This https://arxiv.org/abs/2401.03752 has been replaced.
link: https://scholar.google.com/scholar?q=a

Is Limited Information Enough? An Approximate Multi-agent Coverage Control in Non-Convex Discrete Environments
Conventional distributed approaches to coverage control may suffer from lack of convergence and poor performance, due to the fact that agents have limited information, especially in non-convex discrete environments. To address this issue, we extend the approach of [Marden 2016] which demonstrates how a limited degree of inter-agent communication can be exploited to overcome such pitfalls in one-dimensional discrete environments. The focus of this paper is on extending such results to general di…

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/2403.17700 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Dynamical Zeta functions for differentiable parabolic maps of the interval
This paper explores the domain of meromorphic extension for the dynamical zeta function associated to a class of one-dimensional differentiable parabolic maps featuring an indifferent fixed point. We establish the connection between this domain and the spectrum of the weighted transfer operators of the induced map. Furthermore, we discuss scenarios where meromorphic extensions occur beyond the confines of the natural disc of convergence of the dynamical zeta function.

This https://arxiv.org/abs/2308.03686 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization
Denoising diffusions are a powerful method to generate approximate samples from high-dimensional data distributions. Recent results provide polynomial bounds on their convergence rate, assuming $L^2$-accurate scores. Until now, the tightest bounds were either superlinear in the data dimension or required strong smoothness assumptions. We provide the first convergence bounds which are linear in the data dimension (up to logarithmic factors) assuming only finite second moments of the data distrib…

This https://arxiv.org/abs/2202.07593 has been replaced.
link: https://scholar.google.com/scholar?q=a

The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem
In this paper we consider the generalized inverse iteration for computing ground states of the Gross-Pitaevskii eigenvector problem (GPE). For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in magnitude of a weighted linear eigenvalue problem. Furthermore, we show that this eigenvalue can be bounded by the first spectral gap of a linearized Gross-Pitaevskii operator, recovering the same rates as for linear eigenvector problems. With this we establish the f…

Large N limit of fuzzy geometries coupled to fermions
Masoud Khalkhali, Nathan Pagliaroli, Luuk S. Verhoeven
https://arxiv.org/abs/2405.05056 https://

Large N limit of fuzzy geometries coupled to fermions
In this paper we present an analysis of the large N limit of a family of quartic Dirac ensembles based on (0, 1) fuzzy geometries that are coupled to fermions. These Dirac ensembles are examples of single-matrix, multi-trace matrix ensembles. Additionally, they serve as examples of integer-valued $β$-ensembles. Convergence of the spectral density in the large N limit for a large class of such matrix ensembles is proven, improving on existing results. The main results of this paper are the addi…

On Convergence of Discrete Schemes for Computing the Rate-Distortion Function of Continuous Source
Lingyi Chen, Shitong Wu, Wenyi Zhang, Huihui Wu, Hao Wu
https://arxiv.org/abs/2405.00474

On Convergence of Discrete Schemes for Computing the Rate-Distortion Function of Continuous Source
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and subsequently solving the associated discrete problem. However, existing literature has predominantly concentrated on the convergence analysis of solving discrete problems, usually neglecting the convergence relationship between the original continuous optimization …

A global Barzilai and Borwein's gradient normalization descent method for multiobjective optimization
Yingxue Yang
https://arxiv.org/abs/2403.05070 htt…

A global Barzilai and Borwein's gradient normalization descent method for multiobjective optimization
In this paper, we consider the unconstrained multiobjective optimization problem. In recent years, researchers pointed out that the steepest decent method may generate small stepsize which leads to slow convergence rates. To address the issue, we propose a global Barzilai and Borwein's gradient normalization descent method for multiobjective optimization (GBBN). In our method, we propose a new normalization technique to generate new descent direction. We demonstrate that line search can achieve…

This https://arxiv.org/abs/2309.07215 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

A New Probe of the High-z BAO scale: BAO tomography With CMB $\times$ LIM-Nulling Convergence
Standard rulers such as the baryon acoustic oscillation (BAO) scale serve as workhorses for precision tests of cosmology, enabling distance measurements that probe the geometry and expansion history of our Universe. Aside from BAO measurements from the cosmic microwave background (CMB), most standard ruler techniques operate at relatively low redshifts and depend on biased tracers of the matter density field. In a companion paper, we explored the scientific reach of nulling estimators, where CM…

Convergence rate for a regularized scalar conservation law
Billel Guelmame, Haroune Houamed
https://arxiv.org/abs/2403.03794 https://…

Convergence rate for a regularized scalar conservation law
This work revisits a recent finding by the first author concerning the local convergence of a regularized scalar conservation law. We significantly improve the original statement by establishing a global convergence result within the Lebesgue spaces $L^\infty_{\mathrm{loc}}(\mathbb{R}^+;L^p(\mathbb{R}))$, for any $p \in [1,\infty)$, as the regularization parameter $\ell$ approaches zero. Notably, we demonstrate that this stability result is accompanied by a quantifiable rate of convergence. A k…

This https://arxiv.org/abs/2304.12759 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the uniform convergence of continuous semigroups
Let $Ω$ be a region in the complex plane $\mathbb C$ and let $\{Φ_t \}_{t\ge 0}$ be a continuous semigroup of functions on $Ω$; that is, $Φ_t:Ω\toΩ$ is holomorphic for every $t\ge 0$, $Φ_0(z)=z$, for every $z\inΩ$, $Φ_t\circΦ_s=Φ_{s+t}$, for every $s$, $t\ge 0$, and \[ Φ_t(z)\to z\,,\quad t\to0^+, \] uniformly on compact subsets of $Ω$. Despite this definition only requires the uniform convergence on compact subsets, P. Gumenyuk proved in 2014 that, when $Ω$ is the unit disc, the …

This https://arxiv.org/abs/2209.05564 has been replaced.
link: https://scholar.google.com/scholar?q=a

Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the Entropic Gradient Descent in the optimization of deep neural networks, via homogenisation. We embed it in a much larger class of two-scale stochastic control problems and rely on convergence results for Hamilton-Jacobi-Bellman equations with unbounded data proved recently by ourselves (ESAIM Control Optim. Calc. Var. 2023). We show that the limit …

Quantitative Propagation of Chaos for Singular Interacting Particle Systems Driven by Fractional Brownian Motion
Lucio Galeati, Khoa L\^e, Avi Mayorcas
https://arxiv.org/abs/2403.05454

Quantitative Propagation of Chaos for Singular Interacting Particle Systems Driven by Fractional Brownian Motion
We consider interacting systems particle driven by i.i.d. fractional Brownian motions, subject to irregular, possibly distributional, pairwise interactions. We show propagation of chaos and mean field convergence to the law of the associated McKean--Vlasov equation, as the number of particles $N\to\infty$, with quantitative sharp rates of order $N^{-1/2}$. Our results hold for a wide class of possibly time-dependent interactions, which are only assumed to satisfy a Besov-type regularity, relate…

On an optimal AFEM for elastoplasticity
Miriam Sch\"onauer, Andreas Schr\"oder
https://arxiv.org/abs/2404.05395 https://arx…

On an optimal AFEM for elastoplasticity
In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [Comput. Math. Appl., 67(6) (2014), 1195-1253], which provides a specific proceeding to prove the optimal convergence of the scheme. The proceeding is based on verifying four axioms, which ensure the optimal convergence. The verification is done by using results from […

Efficient and Provably Convergent Computation of Information Bottleneck: A Semi-Relaxed Approach
Lingyi Chen, Shitong Wu, Jiachuan Ye, Huihui Wu, Wenyi Zhang, Hao Wu
https://arxiv.org/abs/2404.04862

Efficient and Provably Convergent Computation of Information Bottleneck: A Semi-Relaxed Approach
Information Bottleneck (IB) is a technique to extract information about one target random variable through another relevant random variable. This technique has garnered significant interest due to its broad applications in information theory and deep learning. Hence, there is a strong motivation to develop efficient numerical methods with high precision and theoretical convergence guarantees. In this paper, we propose a semi-relaxed IB model, where the Markov chain and transition probability co…

Denoising Diffusion Delensing Delight: Reconstructing the Non-Gaussian CMB Lensing Potential with Diffusion Models
Thomas Fl\"oss, William R. Coulton, Adriaan J. Duivenvoorden, Francisco Villaescusa-Navarro, Benjamin D. Wandelt
https://arxiv.org/abs/2405.05598

Denoising Diffusion Delensing Delight: Reconstructing the Non-Gaussian CMB Lensing Potential with Diffusion Models
Optimal extraction of cosmological information from observations of the Cosmic Microwave Back- ground critically relies on our ability to accurately undo the distortions caused by weak gravitational lensing. In this work, we demonstrate the use of denoising diffusion models in performing Bayesian lensing reconstruction. We show that score-based generative models can produce accurate, uncor- related samples from the CMB lensing convergence map posterior, given noisy CMB observations. To validate…

Revisiting Theoretical Guarantees of Direct-Search Methods
K. J. Dzahini, F. Rinaldi, C. W. Royer, D. Zeffiro
https://arxiv.org/abs/2403.05322 https://

Revisiting Theoretical Guarantees of Direct-Search Methods
Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization and may thus seem intractable other than by using heuristics. However, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct search, is particularly popular thanks to its simplicity of implementation, …

On the impact of measure pre-conditionings on general parametric ML models and transfer learning via domain adaptation
Joaqu\'in S\'anchez Garc\'ia
https://arxiv.org/abs/2403.02432

On the impact of measure pre-conditionings on general parametric ML models and transfer learning via domain adaptation
We study a new technique for understanding convergence of learning agents under small modifications of data. We show that such convergence can be understood via an analogue of Fatou's lemma which yields gamma-convergence. We show it's relevance and applications in general machine learning tasks and domain adaptation transfer learning.

This https://arxiv.org/abs/2205.04397 has been replaced.
link: https://scholar.google.com/scholar?q=a

Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs
Norm-resolvent convergence with order-sharp error estimate is established for Neumann Laplacians on thin domains in $\mathbb{R}^d,$ $d\ge2,$ converging to metric graphs in the limit of vanishing thickness parameter in the resonant case. The vertex matching conditions of the limiting quantum graph are revealed as being closely related to $δ'$ type.

On an optimal AFEM for elastoplasticity
Miriam Sch\"onauer, Andreas Schr\"oder
https://arxiv.org/abs/2404.05395 https://arx…

On an optimal AFEM for elastoplasticity
In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [Comput. Math. Appl., 67(6) (2014), 1195-1253], which provides a specific proceeding to prove the optimal convergence of the scheme. The proceeding is based on verifying four axioms, which ensure the optimal convergence. The verification is done by using results from […

Opinion dynamics of two populations with time-delayed coupling
Chiara Cicolani, Cristina Pignotti
https://arxiv.org/abs/2404.07007 https://

Opinion dynamics of two populations with time-delayed coupling
We study a Hegselmann-Krause type opinion formation model for a system of two populations. The two groups interact with each other via subsets of individuals, namely the leaders, and natural time delay effects are considered. By using careful estimates of the system's trajectories, we are able to prove an asymptotic convergence to consensus result. Some numerical tests illustrate the theoretical result and point out some possible applications.

On the impact of measure pre-conditionings on general parametric ML models and transfer learning via domain adaptation
Joaqu\'in S\'anchez Garc\'ia
https://arxiv.org/abs/2403.02432

On the impact of measure pre-conditionings on general parametric ML models and transfer learning via domain adaptation
We study a new technique for understanding convergence of learning agents under small modifications of data. We show that such convergence can be understood via an analogue of Fatou's lemma which yields gamma-convergence. We show it's relevance and applications in general machine learning tasks and domain adaptation transfer learning.

This https://arxiv.org/abs/2402.18108 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Large Deviation Principle for Multi-Scale Fully Local Monotone Stochastic Dynamical Systems with Multiplicative Noise
This paper is devoted to proving the small noise asymptotic behaviour, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main techniques are based on a combination of the weak convergence approach, the time discretization technique and the theory of pseudo-monotone operator. The main results derived in this paper have broad applicability to various multi-scale models, where the slow com…

Learned Finite-Time Consensus for Distributed Optimization
Aaron Fainman, Stefan Vlaski
https://arxiv.org/abs/2404.07018 https://arxi…

Learned Finite-Time Consensus for Distributed Optimization
Most algorithms for decentralized learning employ a consensus or diffusion mechanism to drive agents to a common solution of a global optimization problem. Generally this takes the form of linear averaging, at a rate of contraction determined by the mixing rate of the underlying network topology. For very sparse graphs this can yield a bottleneck, slowing down the convergence of the learning algorithm. We show that a sequence of matrices achieving finite-time consensus can be learned for unknow…

Refined asymptotics for the Cauchy problem for the fast $p$-Laplace evolution equation
Matteo Bonforte, Iwona Chlebicka, Nikita Simonov
https://arxiv.org/abs/2405.05405

Refined asymptotics for the Cauchy problem for the fast $p$-Laplace evolution equation
Our focus is on the fast diffusion equation $\partial_t u=Δ_p u$ with $p<2$ in the whole Euclidean space of dimension $N\geq 2$. The properties of the solutions to the $p$-Laplace Cauchy problem change in several special values of the parameter $p$. In the range of $p$ when mass is conserved, non-negative and integrable solutions behave like the Barenblatt (or fundamental) solutions for large times. By making use of the entropy method, we establish the polynomial rates of the convergence in …

This https://arxiv.org/abs/2106.07243 has been replaced.
link: https://scholar.google.com/scholar?q=a

Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks
In this paper, we propose two communication efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm, termed Compressed Push-Pull (CPP), combines the gradient tracking Push-Pull method with communication compression. We show that CPP is applicable to a general class of unbiased compression operators and achieves linear convergence rate for strongly convex and smooth objective functions. The second algorithm is a broadcast-like version of C…

Convergence Analysis of Flow Matching in Latent Space with Transformers
Yuling Jiao, Yanming Lai, Yang Wang, Bokai Yan
https://arxiv.org/abs/2404.02538 htt…

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…

Global Solutions and Asymptotic Behavior for the Three-dimensional Viscous Non-resistive MHD System with Some Large Perturbations
Youyi Zhao
https://arxiv.org/abs/2403.05203

Global Solutions and Asymptotic Behavior for the Three-dimensional Viscous Non-resistive MHD System with Some Large Perturbations
We revisit the global existence of solutions with some large perturbations to the incompressible, viscous, and non-resistive MHD system in a three-dimensional periodic domain, where the impressed magnetic field satisfies the Diophantine condition, and the intensity of the impressed magnetic field, denoted by $m$, is large compared to the perturbations. It was proved by Jiang--Jiang that the highest-order derivatives of the velocity increase with $m$, and the convergence rate of the nonlinear sy…

This https://arxiv.org/abs/2312.08450 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

The FLAMINGO project: Baryonic impact on weak gravitational lensing convergence peak counts
Weak gravitational lensing convergence peaks, the local maxima in weak lensing convergence maps, have been shown to contain valuable cosmological information complementary to commonly used two-point statistics. To exploit the full power of weak lensing for cosmology, we must model baryonic feedback processes because these reshape the matter distribution on non-linear and mildly non-linear scales. We study the impact of baryonic physics on the number density of weak lensing peaks using the FLAMI…

A preconditioned iteration method for solving saddle point problems
Juan Zhang, Yiyi Luo
https://arxiv.org/abs/2404.06061 https://arx…

A preconditioned iteration method for solving saddle point problems
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the approximate inverse matrix of sparse matrices is presented. The effectiveness of the proposed method is demonstrated through numerical examples, emphasizing its efficacy in approximating the inverse matrix. Furthermore, the preprocessing technology includes a low-ra…

This https://arxiv.org/abs/2305.03605 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence of the Preconditioned Proximal Point Method and Douglas-Rachford Splitting in the Absence of Monotonicity
The proximal point algorithm (PPA) is the most widely recognized method for solving inclusion problems and serves as the foundation for many numerical algorithms. Despite this popularity, its convergence results have been largely limited to the monotone setting. In this work, we study the convergence of (relaxed) preconditioned PPA for a class of nonmonotone problems that satisfy an oblique weak Minty condition. Additionally, we study the (relaxed) Douglas-Rachford splitting (DRS) method in the…

Optimization methods for solving matrix equations
Juan Zhang, Xiao Luo
https://arxiv.org/abs/2404.06030 https://arxiv.org/pdf/2404.06…

Optimization methods for solving matrix equations
In this paper, we focus on using optimization methods to solve matrix equations by transforming the problem of solving the Sylvester matrix equation or continuous algebraic Riccati equation into an optimization problem. Initially, we use a constrained convex optimization method (CCOM) to solve the Sylvester matrix equation with $\ell_{2,1}$-norm, where we provide a convergence analysis and numerical examples of CCOM; however, the results show that the algorithm is not efficient. To address this…

This https://arxiv.org/abs/2211.05463 has been replaced.
link: https://scholar.google.com/scholar?q=a

Stability and Convergence of a Randomized Model Predictive Control Strategy
RBM-MPC is a computationally efficient variant of Model Predictive Control (MPC) in which the Random Batch Method (RBM) is used to speed up the finite-horizon optimal control problems at each iteration. In this paper, stability and convergence estimates are derived for RBMMPC of unconstrained linear systems. The obtained estimates are validated in a numerical example that also shows a clear computational advantage of RBM-MPC.

Preprocessed GMRES for fast solution of linear equations
Juan Zhang, Yiyi Luo
https://arxiv.org/abs/2404.06018 https://arxiv.org/pdf/…

Preprocessed GMRES for fast solution of linear equations
The article mainly introduces preprocessing algorithms for solving linear equation systems. This algorithm uses three algorithms as inner iterations, namely RPCG algorithm, ADI algorithm, and Kaczmarz algorithm. Then, it uses BA-GMRES as an outer iteration to solve the linear equation system. These three algorithms can indirectly generate preprocessing matrices, which are used for solving equation systems. In addition, we provide corresponding convergence analysis and numerical examples. Throug…

Error estimates for a bilinear optimal control problem of Maxwell's equations
Francisco Fuica, Felipe Lepe, Pablo Venegas
https://arxiv.org/abs/2405.05532

Error estimates for a bilinear optimal control problem of Maxwell's equations
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal solutions, and analyze first- and second-order optimality conditions. We devise an approximation scheme based on the lowest order Nédélec finite elements to approximate optimal solutions. We analyze convergence properties of the proposed scheme and prove a …

Nonlinear and degenerate discounted approximation in discrete weak KAM theory
Panrui Ni, Maxime Zavidovique
https://arxiv.org/abs/2403.04563 https://

Nonlinear and degenerate discounted approximation in discrete weak KAM theory
In this paper, we introduce a discrete version of the nonlinear implicit Lax-Oleinik operator. We consider the associated vanishing discount problem with a non-degenerate condition and prove convergence of solutions as the discount factor goes to $0$. We also discuss the uniqueness of the discounted solution. The convergence result is a selection principle for fixed points of a family of nonlinear operators.

This https://arxiv.org/abs/2312.11093 has been replaced.
link: https://scholar.google.com/scholar?q=a

MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the algorithm design process for a class of PDEs through training, which requires only training data of coefficient distributions. The proposed method is anchored by three core principles: (1) a multilevel hierarchy to promote rapid convergence, (2) adherence to li…

Convergence and Complexity Guarantee for Inexact First-order Riemannian Optimization Algorithms
Yuchen Li, Laura Balzano, Deanna Needell, Hanbaek Lyu
https://arxiv.org/abs/2405.03073

Convergence and Complexity Guarantee for Inexact First-order Riemannian Optimization Algorithms
We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general nonconvex and constrained setting. We answer these questions in a general framework of tangential Block Majorization-Minimization (tBMM). We establish that tBMM converges to an $ε$-stationary point within $O(ε^{-2})$ iterations. Under a mild assumption, the result…

Global Convergence of High-Order Regularization Methods with Sums-of-Squares Taylor Models
Wenqi Zhu, Coralia Cartis
https://arxiv.org/abs/2404.03035 https…

Global Convergence of High-Order Regularization Methods with Sums-of-Squares Taylor Models
High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have superior, and even optimal, worst-case global convergence rates and local rates compared to Newton's method. Finding rigorous and efficient techniques for minimizing the Taylor polynomial sub-problems remains a challenging aspect for these algorithms. Ahmadi et …

This https://arxiv.org/abs/2402.07060 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spectral convergence of a semi-discretized numerical system for the spatially homogeneous Boltzmann equation with uncertainties
In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied for approximation in the velocity space whereas the generalized polynomial chaos (gPC)-based stochastic Galerkin (SG) method is employed to discretize the random variable. Our proof is based on a delicate energy estimate for showing the well-posedness of the n…

This https://arxiv.org/abs/2402.07060 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spectral convergence of a semi-discretized numerical system for the spatially homogeneous Boltzmann equation with uncertainties
In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied for approximation in the velocity space whereas the generalized polynomial chaos (gPC)-based stochastic Galerkin (SG) method is employed to discretize the random variable. Our proof is based on a delicate energy estimate for showing the well-posedness of the n…

This https://arxiv.org/abs/2307.12615 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite-sum optimization: Adaptivity to smoothness and loopless variance reduction
For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past …