Tootfinder

Exponential convergence of multiagent systems with lack of connection
Fabio Ancona, Mohamed Bentaibi, Francesco Rossi
https://arxiv.org/abs/2510.11334 https://

Exponential convergence of multiagent systems with lack of connection
Finding conditions ensuring consensus, i.e. convergence to a common value, for a networked system is of crucial interest, both for theoretical reasons and applications. This goal is harder to achieve when connections between agents are temporarily lost. Here, we prove that known conditions (introduced by Moreau) ensure an exponential convergence to consensus, with explicit rate of convergence. The key result is related to the length of the graph (i.e. the number of connections to reach a comm…

Convergence Analysis of Galerkin Approximations for the Lindblad Master Equation
R\'emi Robin, Pierre Rouchon
https://arxiv.org/abs/2510.11416 https://…

Convergence Analysis of Galerkin Approximations for the Lindblad Master Equation
This paper analyzes the numerical approximation of the Lindblad master equation on infinite-dimensional Hilbert spaces. We employ a classical Galerkin approach for spatial discretization and investigate the convergence of the discretized solution to the exact solution. Using \textit{a priori} estimates, we derive explicit convergence rates and demonstrate the effectiveness of our method through examples motivated by autonomous quantum error correction.

Analysis of the Geometric Heat Flow Equation: Computing Geodesics in Real-Time with Convergence Guarantees
Samuel G. Gessow, Brett T. Lopez
https://arxiv.org/abs/2510.11692 http…

Analysis of the Geometric Heat Flow Equation: Computing Geodesics in Real-Time with Convergence Guarantees
We present an analysis on the convergence properties of the so-called geometric heat flow equation for computing geodesics (shortest-path~curves) on Riemannian manifolds. Computing geodesics numerically in real-time has become an important capability in several fields, including control and motion planning. The geometric heat flow equation involves solving a parabolic partial differential equation whose solution is a geodesic. In practice, solving this PDE numerically can be done efficiently, a…

Closing the HPC-Cloud Convergence Gap: Multi-Tenant Slingshot RDMA for Kubernetes
Philipp A. Friese, Ahmed Eleliemy, Utz-Uwe Haus, Martin Schulz
https://arxiv.org/abs/2508.09663

Closing the HPC-Cloud Convergence Gap: Multi-Tenant Slingshot RDMA for Kubernetes
Converged HPC-Cloud computing is an emerging computing paradigm that aims to support increasingly complex and multi-tenant scientific workflows. These systems require reconciliation of the isolation requirements of native cloud workloads and the performance demands of HPC applications. In this context, networking hardware is a critical boundary component: it is the conduit for high-throughput, low-latency communication and enables isolation across tenants. HPE Slingshot is a high-speed network …

Optimal higher-order convergence rates for parabolic multiscale problems
Balaje Kalyanaraman, Felix Krumbiegel, Roland Maier, Siyang Wang
https://arxiv.org/abs/2510.09514 https:…

Optimal higher-order convergence rates for parabolic multiscale problems
In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to enrich the multiscale spaces, ensuring higher-order convergence without requiring assumptions on the coefficient beyond boundedness. This approach addresses the challenge of a reduction of convergence rates when applying higher-order LOD methods to time-depe…

Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
Nicholas Pischke
https://arxiv.org/abs/2510.10697 https://

Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence under a suitable strong monotonicity assumption, together with a probabilistic independence assumption and a separability assumption on the tangent spaces. As a particular case, our results transfer previous work by P. Bianchi on that method in Hilbert space…

Value bounds and Convergence Analysis for Averages of LRP attributions
Alexander Binder, Nastaran Takmil-Homayouni, Urun Dogan
https://arxiv.org/abs/2509.08963 https://

Value bounds and Convergence Analysis for Averages of LRP attributions
We analyze numerical properties of Layer-wise relevance propagation (LRP)-type attribution methods by representing them as a product of modified gradient matrices. This representation creates an analogy to matrix multiplications of Jacobi-matrices which arise from the chain rule of differentiation. In order to shed light on the distribution of attribution values, we derive upper bounds for singular values. Furthermore we derive component-wise bounds for attribution map values. As a main result,…

A probabilistic approach to strong natural boundaries
Stamatis Dostoglou, Petros Valettas
https://arxiv.org/abs/2510.08717 https://arxiv.org/pdf/2510.08717…

A probabilistic approach to strong natural boundaries
We study the local non-extendability of random power series beyond their disk of convergence. We show that random power series formed by independent coefficients which are asymptotically anti-concentrated admit the circle of radius of convergence as strong natural boundary, even in a Nevanlinna sense. Our results complement and extend previous works of Ryll-Nardzewski (1953), and Breuer and Simon (2011).

A Davydov Ansatz approach to accurate system-bath dynamics in the presence of multiple baths with distinct temperatures
Chenlin Ma, Fulu Zheng, Kewei Sun, Lu Wang, Yang Zhao
https://arxiv.org/abs/2510.09029

A Davydov Ansatz approach to accurate system-bath dynamics in the presence of multiple baths with distinct temperatures
We perform benchmark simulations using the time-dependent variational approach with the multiple Davydov Ansatz (mDA) to study realtime nonequilibrium dynamics in a single qubit model coupled to two thermal baths with distinct temperatures. A broad region of the parameter space has been investigated, accompanied by a detailed analysis of the convergence behavior of the mDA method. In addition, we have compared our mD2 results to those from two widely adopted, numerically "exact" techniques: the…

Repeated-and-Offset QPSK for DFT-s-OFDM in Satellite Access
Renaud-Alexandre Pitaval
https://arxiv.org/abs/2510.11445 https://arxiv.org/pdf/2510.11445

Repeated-and-Offset QPSK for DFT-s-OFDM in Satellite Access
Motivated by the convergence of terrestrial cellular networks with satellite networks, we consider an adaptation of offset quadrature phase shift keying (OQPSK), used with single-carrier waveform in traditional satellite systems, to discrete Fourier transform spread (DFT-s-) orthogonal frequency-division multiplexed (OFDM) waveform employed in the uplink of terrestrial systems. We introduce a new order-one constellation modulation, termed repeated-and-offset QPSK (RO-QPSK), derive its basic pro…

Timelike convergence condition in regular black-hole spacetimes with (anti-)de Sitter core
Johanna Borissova, Stefano Liberati, Matt Visser
https://arxiv.org/abs/2509.08590 http…

Timelike convergence condition in regular black-hole spacetimes with (anti-)de Sitter core
The Hawking-Penrose (1970) singularity theorem weakens the causality assumption of global hyperbolicity used in the Penrose (1965) singularity theorem, at the expense of invoking the stronger timelike (instead of null) convergence condition (TCC). We analyze the TCC for a large class of dynamical spherically symmetric spacetimes, and show that it decomposes into three independent conditions on the Misner-Sharp mass function. For stationary black holes only two of these are non-trivial. One of t…

Spectrum and local weak convergence of sparse random uniform hypergraphs
Kartick Adhikari, Samiron Parui
https://arxiv.org/abs/2509.05102 https://arxiv.org…

Spectrum and local weak convergence of sparse random uniform hypergraphs
The notion of local weak convergence, also known as Benjamini--Schramm convergence, was introduced by Benjamini and Schramm \cite{Benjamini-Schramm-convergence}. It is known that the local weak limit of sparse Erd\H os--Rényi graphs is the Galton--Watson measure with Poisson offspring almost surely. Recently, Adhikari, Kumar and Saha \cite{adhikari2023spectrumrandomsimplicialcomplexes} showed that the local weak limit of the line graph of sparse Linial--Meshulam complexes is the $d$-block Galt…

From amoebas to pluripotential theory on hybrid analytic spaces
Sebastien Boucksom
https://arxiv.org/abs/2510.10239 https://arxiv.org/pdf/2510.10239…

From amoebas to pluripotential theory on hybrid analytic spaces
These lecture notes are an introduction to the use of non-Archimedean geometry in the study of meromorphic degenerations of complex algebraic varieties. They provide a self-contained discussion of hybrid spaces, which fill in one-parameter degenerations with the associated non-Archimedean Berkovich space as a central fiber. The main focus is on the interplay between complex and non-Archimedean pluripotential theory, and on the relation between convergence of psh metrics and the associated Monge…

Interlaced dynamic XCT reconstruction with spatio-temporal implicit neural representations
Mathias Boulanger, Ericmoore Jossou
https://arxiv.org/abs/2510.08641 https://

Interlaced dynamic XCT reconstruction with spatio-temporal implicit neural representations
In this work, we investigate the use of spatio-temporalImplicit Neural Representations (INRs) for dynamic X-ray computed tomography (XCT) reconstruction under interlaced acquisition schemes. The proposed approach combines ADMM-based optimization with INCODE, a conditioning framework incorporating prior knowledge, to enable efficient convergence. We evaluate our method under diverse acquisition scenarios, varying the severity of global undersampling, spatial complexity (quantified via spatial in…

XML Prompting as Grammar-Constrained Interaction: Fixed-Point Semantics, Convergence Guarantees, and Human-AI Protocols
Faruk Alpay, Taylan Alpay
https://arxiv.org/abs/2509.08182

XML Prompting as Grammar-Constrained Interaction: Fixed-Point Semantics, Convergence Guarantees, and Human-AI Protocols
Structured prompting with XML tags has emerged as an effective way to steer large language models (LLMs) toward parseable, schema-adherent outputs in real-world systems. We develop a logic-first treatment of XML prompting that unifies (i) grammar-constrained decoding, (ii) fixed-point semantics over lattices of hierarchical prompts, and (iii) convergent human-AI interaction loops. We formalize a complete lattice of XML trees under a refinement order and prove that monotone prompt-to-prompt oper…

On the Convergence of Solutions for the Ginzburg-Landau Equation and System
Rejeb Hadiji, Jongmin Han
https://arxiv.org/abs/2509.09231 https://arxiv.org/pd…

On the Convergence of Solutions for the Ginzburg-Landau Equation and System
Let $(u_\varepsilon)$ be a family of solutions of the Ginzburg--Landau equation with boundary condition $u_\varepsilon = g$ on $\partial Ω$ and of degree $0$. Let $u_0$ denote the harmonic map satisfying $u_0 = g$ on $\partial Ω$. We show that, if there exists a constant $C_1 > 0$ such that for $\varepsilon$ sufficiently small we have $\frac{1}{2} \int_Ω|\nabla u_\ve|^2 dx \leq C_1 \leq \frac{1}{2} \int_Ω|\nabla u_0|^2 dx,$ then $C_1 = \frac{1}{2} \int_Ω|\nabla u_0…

FLAMINGO: Baryonic effects on the weak lensing scattering transform
Mariia Marinichenko, Marcel P. van Daalen, Elena Sellentin, Jeger C. Broxterman, Matthieu Schaller, Joop Schaye
https://arxiv.org/abs/2510.09761

FLAMINGO: Baryonic effects on the weak lensing scattering transform
The scattering transform is a wavelet-based statistic capable of capturing non-Gaussian features in weak lensing (WL) convergence maps and has been proven to tighten cosmological parameter constraints by accessing information beyond two-point functions. However, its application in cosmological inference requires a clear understanding of its sensitivity to astrophysical systematics, the most significant of which are baryonic effects. These processes substantially modify the matter distribution o…

Fast and robust parametric and functional learning with Hybrid Genetic Optimisation (HyGO)
Isaac Robledo, Yiqing Li, Guy Y. Cornejo Maceda, Rodrigo Castellanos
https://arxiv.org/abs/2510.09391

Fast and robust parametric and functional learning with Hybrid Genetic Optimisation (HyGO)
The Hybrid Genetic Optimisation framework (HyGO) is introduced to meet the pressing need for efficient and unified optimisation frameworks that support both parametric and functional learning in complex engineering problems. Evolutionary algorithms are widely employed as derivative-free global optimisation methods but often suffer from slow convergence rates, especially during late-stage learning. HyGO integrates the global exploration capabilities of evolutionary algorithms with accelerated lo…

AI-Assisted Geometric Analysis of Cultured Neuronal Networks: Parallels with the Cosmic Web
Wolfgang Kurz, Danny Baranes
https://arxiv.org/abs/2510.10286 https://

AI-Assisted Geometric Analysis of Cultured Neuronal Networks: Parallels with the Cosmic Web
Building on evidence of structural parallels between brain networks and the cosmic web [1], we apply AI-based geometric analysis to cultured neuronal networks. Isolated neurons self-organize into dendritic lattices shaped by reproducible wiring rules. These lattices show non-random features-frequent dendritic convergence, hub nodes, small-world connectivity, and large voids. Synaptic contacts cluster and strengthen at hubs. Strikingly, these properties mirror the cosmic web: dendritic branches …

Convergence and Optimality of the EM Algorithm Under Multi-Component Gaussian Mixture Models
Xin Bing, Dehan Kong, Bingqing Li
https://arxiv.org/abs/2509.08237 https://

Convergence and Optimality of the EM Algorithm Under Multi-Component Gaussian Mixture Models
Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of each Gaussian component. Existing analyses of the EM algorithm's convergence to the true parameter focus primarily on either the two-component case or multi-component settings with both known mixing probabilities and known, isotropic covariance matrices. In this…

Sparse graphs and their Benjamini-Schramm limits: a spectral tour
Charles Bordenave
https://arxiv.org/abs/2510.10299 https://arxiv.org/pdf/2510.10299

Sparse graphs and their Benjamini-Schramm limits: a spectral tour
Sparse graphs with bounded average degree form a rich class of discrete structures where local geometry strongly influences global behavior. The Benjamini-Schramm (BS) convergence offers a natural framework to describe their asymptotic local structure. In this note, we survey spectral aspects of BS convergence and their applications, with a focus on random Schreier graphs and covering graphs. We review some recent progress on the spectral decomposition of the local operators on graphs. We discu…

Convergence and Divergence of Language Models under Different Random Seeds
Finlay Fehlauer (ETH Zurich), Kyle Mahowald (University of Texas at Austin), Tiago Pimentel (ETH Zurich)
https://arxiv.org/abs/2509.26643

Convergence and Divergence of Language Models under Different Random Seeds
In this paper, we investigate the convergence of language models (LMs) trained under different random seeds, measuring convergence as the expected per-token Kullback--Leibler (KL) divergence across seeds. By comparing LM convergence as a function of model size and training checkpoint, we identify a four-phase convergence pattern: (i) an initial uniform phase, (ii) a sharp-convergence phase, (iii) a sharp-divergence phase, and (iv) a slow-reconvergence phase. Further, we observe that larger mode…

Generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations and its applications
Xiang Lv
https://arxiv.org/abs/2508.09409 https://

Generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations and its applications
This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we present a standard and rigorous procedure for guaranteeing the existence and uniqueness of random equilibria for nonlinear stochastic functional differential equations, which attracts all pull-back trajectories in different types of convergence. Some examples a…

Approximate Sparsity Class and Minimax Estimation
Lucas Z. Zhang
https://arxiv.org/abs/2508.09278 https://arxiv.org/pdf/2508.09278

Approximate Sparsity Class and Minimax Estimation
Motivated by the orthogonal series density estimation in $L^2([0,1],μ)$, in this project we consider a new class of functions that we call the approximate sparsity class. This new class is characterized by the rate of decay of the individual Fourier coefficients for a given orthonormal basis. We establish the $L^2([0,1],μ)$ metric entropy of such class, with which we show the minimax rate of convergence. For the density subset in this class, we propose an adaptive density estimator based on a…

On the Convergence of Elementary Cellular Automata under Sequential Update Modes
Isabel Donoso-Leiva, Eric Goles, Mart\'in R\'ios-Wilson, Sylvain Sen\'e
https://arxiv.org/abs/2509.07797

On the Convergence of Elementary Cellular Automata under Sequential Update Modes
In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential update modes, regardless of the initial configuration. In this context, we classify these rules according to whether all initial configurations converge under all, some, one or none sequential update modes, depending on if they have fixed points under synchronou…

A note on remotal and uniquely remotal sets in normed linear spaces
Uddalak Mukherjee, Sumit Som
https://arxiv.org/abs/2510.10992 https://arxiv.org/pdf/251…

A note on remotal and uniquely remotal sets in normed linear spaces
Remotal and uniquely remotal sets play an important role in the area of farthest point problem as well as nearest point problem in a Banach space $X.$ In this study, we find some sufficient conditions for remotality and uniquely remotality of a bounded subset of a Banach space $X$ through $αβ$-statistical convergence.

Efficient Bayesian Inference from Noisy Pairwise Comparisons
Till Aczel, Lucas Theis, Wattenhofer Roger
https://arxiv.org/abs/2510.09333 https://arxiv.org/…

Efficient Bayesian Inference from Noisy Pairwise Comparisons
Evaluating generative models is challenging because standard metrics often fail to reflect human preferences. Human evaluations are more reliable but costly and noisy, as participants vary in expertise, attention, and diligence. Pairwise comparisons improve consistency, yet aggregating them into overall quality scores requires careful modeling. Bradley-Terry-based methods update item scores from comparisons, but existing approaches either ignore rater variability or lack convergence guarantees,…

Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift
Ren-Rui Liu, Zheng-Chu Guo
https://arxiv.org/abs/2509.05106 https://arxiv…

Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift
This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between source and target domains, while the conditional distribution of outputs given inputs remains unchanged. To address this distributional mismatch, we incorporate importance weights, defined as the ratio of target to source densities, into the learning framewor…

Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
J. Haydel Collins, Kangan Li, Alexei Lozinski, Guglielmo Scovazzi
https://arxiv.org/abs/2508.09613

Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the $L^2$- and $H^1$-norms of the error. The proposed method is built on three stages. First, the distance map between the SBM surrogate boundary and the true boundary is used to construct an approximation to the geometry of the gap between the two. Then, the representations of the numerical solution and test functions are extended…

Metric Convergence of Sequences of Static Spacetimes with the Null Distance
Brian Allen
https://arxiv.org/abs/2510.02237 https://arxiv.org/pdf/2510.02237…

Metric Convergence of Sequences of Static Spacetimes with the Null Distance
How should one define metric space notions of convergence for sequences of spacetimes? Since a Lorentzian manifold does not define a metric space directly, the uniform convergence, Gromov-Hausdorff (GH) convergence, and Sormani-Wenger Intrinsic Flat (SWIF) convergence does not extend automatically. One approach is to define a metric space structure, which is compatible with the Lorentzian structure, so that the usual notions of convergence apply. This approach was taken by C. Sormani and C. Veg…

KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning
Alice Kate Li, Thales C Silva, Victoria Edwards, Vijay Kumar, M. Ani Hsieh
https://arxiv.org/abs/2509.09074

KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning
In this work, we propose a novel flow field-based motion planning method that drives a robot from any initial state to a desired reference trajectory such that it converges to the trajectory's end point. Despite demonstrated efficacy in using Koopman operator theory for modeling dynamical systems, Koopman does not inherently enforce convergence to desired trajectories nor to specified goals -- a requirement when learning from demonstrations (LfD). We present KoopMotion which represents motion f…

Non-trivial critical behavior at the magnetic transitions: A case study of Sm$_7$Pd$_3$
Ajay Kumar, Anis Biswas, Y. Mudryk
https://arxiv.org/abs/2508.09838 https://

Non-trivial critical behavior at the magnetic transitions: A case study of Sm$_7$Pd$_3$
We present a comprehensive analysis of the critical behavior of Sm$_7$Pd$_3$ in the vicinity of its second-order magnetoelastic transition at $T_ {\rm c} = 173$ K. The critical exponents (CEs) $β$ and $γ$, determined using both the standard convergence procedure and the average normalized slope (ANS) method, diverge at $T_{\rm c}$: a characteristic typically associated with first-order transitions. Notably, none of the established universality classes satisfactorily describe the critical beha…

Optimal convergence rates in multiscale elliptic homogenization
Weisheng Niu, Yao Xu, Jinping Zhuge
https://arxiv.org/abs/2509.09410 https://arxiv.org/pdf/…

Optimal convergence rates in multiscale elliptic homogenization
This paper is devoted to the quantitative homogenization of multiscale elliptic operator $-\nabla\cdot A_\varepsilon \nabla$, where $A_\varepsilon(x) = A(x/\varepsilon_1, x/\varepsilon_2,\cdots, x/\varepsilon_n)$, $\varepsilon = (\varepsilon_1, \varepsilon_2,\cdots, \varepsilon_n) \in (0,1]^n$ and $\varepsilon_i > \varepsilon_{i+1}$. We assume that $A(y_1,y_2,\cdots, y_n)$ is 1-periodic in each $y_i \in \mathbb{R}^d$ and real analytic. Classically, the method of reiterated homogenization has be…

Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees
P Sangeerth, David Smith Sundarsingh, Bhabani Shankar Dey, Pushpak Jagtap
https://arxiv.org/abs/2510.10450

Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees
Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability notion called incremental input-to-state practical stability (δ-ISpS), ensuring safety guarantees. We also present a feedback linearization based control design scheme that renders a partially unknown system incrementally input-to-state practically stable and …

Long time strong convergence analysis of one-step methods for McKean-Vlasov SDEs with superlinear growth coefficients
Taiyuan Liu, Yaozhong Hu, Siqing Gan
https://arxiv.org/abs/2509.09274

Long time strong convergence analysis of one-step methods for McKean-Vlasov SDEs with superlinear growth coefficients
This paper presents a strong convergence rate analysis of general discretization approximations for McKean-Vlasov SDEs with super-linear growth coefficients over infinite time horizon. Under some specified non-globally Lipschitz conditions, we derive the propagation of chaos, and the mean-square convergence rate over infinite time horizon for general one-step time discretization schemes for the underlying Mckean-Vlasov SDEs. As an application of the general result it is obtained the mean-square…

Exponential convergence of the local diabatic representation for nonadiabatic models
Mo Sha, Bing Gu
https://arxiv.org/abs/2509.05694 https://arxiv.org/pdf…

Exponential convergence of the local diabatic representation for nonadiabatic models
The discrete variable local diabatic representation (LDR) provides a divergence-free framework for exact conical intersection dynamics simulation. In this work, we investigate the convergence with respect to the number of "nuclear" grid points and "electronic" states of LDR for the eigenvalue problems using coupled oscillator models. The performance of LDR is compared with traditional approaches based on the Born-Huang ansatz and on the crude adiabatic representation. Our results demonstrate th…

Composite Lyapunov Criteria for Stability and Convergence with Applications to Optimization Dynamics
Hassan Saoud
https://arxiv.org/abs/2510.08259 https://…

Composite Lyapunov Criteria for Stability and Convergence with Applications to Optimization Dynamics
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of dissipation measures, convergence to a critical set, and semistability under mild conditions, without relying on invariance principles or compactness assumptions. The framework unifies convergence to points and sets and is illustrated through applications to inertial …

Low-redshift constraints on structure growth from CMB lensing tomography
Andrea Rubiola, Matteo Zennaro, Carlos Garc\'ia-Garc\'ia, David Alonso
https://arxiv.org/abs/2510.09563

Low-redshift constraints on structure growth from CMB lensing tomography
We present constraints on the amplitude of matter fluctuations from the clustering of galaxies and their cross-correlation with the gravitational lensing convergence of the cosmic microwave background (CMB), focusing on low redshifts ($z\lesssim0.3$), where potential deviations from a perfect cosmological constant dominating the growth of structure could be more prominent. Specifically, we make use of data from the 2MASS photometric survey (\tmpz) and the \wisc galaxy survey, in combination wit…

On the convergence of the variational quantum eigensolver and quantum optimal control
Marco Wiedmann, Daniel Burgarth, Gunther Dirr, Thomas Schulte-Herbr\"uggen, Emanuel Malvetti, Christian Arenz
https://arxiv.org/abs/2509.05295

On the convergence of the variational quantum eigensolver and quantum optimal control
When does a variational quantum algorithm converge to a globally optimal problem solution? Despite the large literature around variational approaches to quantum computing, the answer is largely unknown. We address this open question by developing a convergence theory for the variational quantum eigensolver (VQE). By leveraging the terminology of quantum control landscapes, we prove a sufficient criterion that characterizes when convergence to a ground state of a Hamiltonian can be guaranteed fo…

Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games
Brian Hu Zhang, Ioannis Anagnostides, Tuomas Sandholm
https://arxiv.org/abs/2510.04407

Scale-Invariant Regret Matching and Online Learning with Optimal Convergence: Bridging Theory and Practice in Zero-Sum Games
A considerable chasm has been looming for decades between theory and practice in zero-sum game solving through first-order methods. Although a convergence rate of $T^{-1}$ has long been established since Nemirovski's mirror-prox algorithm and Nesterov's excessive gap technique in the early 2000s, the most effective paradigm in practice is *counterfactual regret minimization*, which is based on *regret matching* and its modern variants. In particular, the state of the art across most benchmarks …

Capillary Rise in Pipes with Variable Cross Section
Isidora Rapaji\'c (Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia, Department of Mathematics and Informatics, Faculty of Sciences, Novi Sad, Serbia), Srboljub Simi\'c (Department of Mathematics and Informatics, Faculty of Sciences, Novi Sad, Serbia)
https://…

Capillary Rise in Pipes with Variable Cross Section
This work proposes an ODE model for a capillary rise in pipes with variable cross section and compares it to the lubrication theory model. Two key assumptions are made: (1) radius of the pipe varies with axial coordinate, and (2) pipe's convergence angle is small. The model reduction process involves the identification of critical parameters and simplifies the governing equations by neglecting higher-order terms. Under appropriate scaling, it is shown that generalized Washburn's equation for ca…

Convergence Theorems for Entropy-Regularized and Distributional Reinforcement Learning
Yash Jhaveri, Harley Wiltzer, Patrick Shafto, Marc G. Bellemare, David Meger
https://arxiv.org/abs/2510.08526

Convergence Theorems for Entropy-Regularized and Distributional Reinforcement Learning
In the pursuit of finding an optimal policy, reinforcement learning (RL) methods generally ignore the properties of learned policies apart from their expected return. Thus, even when successful, it is difficult to characterize which policies will be learned and what they will do. In this work, we present a theoretical framework for policy optimization that guarantees convergence to a particular optimal policy, via vanishing entropy regularization and a temperature decoupling gambit. Our approac…

Taylor expansions over generalised power series
Vincent Bagayoko, Vincenzo Mantova
https://arxiv.org/abs/2509.08473 https://arxiv.org/pdf/2509.08473…

Taylor expansions over generalised power series
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an exponential function, and apply this to the case of standard fields of transseries, such as $\log$-$\exp$ transseries and $ω$-series.

On convergence structures in infinite graphs
Paulo S\'ergio Farias Magalh\~aes Junior, Renan Maneli Mezabarba, Rodrigo Santos Monteiro
https://arxiv.org/abs/2510.06336 https…

On convergence structures in infinite graphs
It is well known that a graph admits a natural closure operator defined on its vertex set, which also corresponds to a pretopology. In this paper, we describe the classical pretopology on a graph in terms of nets, with the aim of relating combinatorial properties to convergence properties.

Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
Ian Melbourne, Zhe Wang
https://arxiv.org/abs/2509.07657 https://

Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
We obtain $q$-Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows, where $q\ge1$ depends on the degree of nonuniformity. Utilizing a martingale-coboundary decomposition for nonuniformly expanding semiflows, we extend techniques from the discrete-time setting to the continuous-time case. Our results apply to uniformly hyperbolic (Axiom A) flows, nonuniformly hyperbolic flows that can be modelled by suspensions over Young towers with exponential tails (such…

Got the convergence mostly fixed after trying to fix it previously. Learned a heluva lot, but time to enjoy the fruits of my labor.
#retrogaming #snes #crt

CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models
Runpeng Dai, Linfeng Song, Haolin Liu, Zhenwen Liang, Dian Yu, Haitao Mi, Zhaopeng Tu, Rui Liu, Tong Zheng, Hongtu Zhu, Dong Yu
https://arxiv.org/abs/2509.09675

CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models
Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for enhancing the reasoning ability of Large Language Models (LLMs). Yet current RLVR methods often explore poorly, leading to premature convergence and entropy collapse. To address this challenge, we introduce Curiosity-Driven Exploration (CDE), a framework that leverages the model's own intrinsic sense of curiosity to guide exploration. We formalize curiosity with signals from both the actor and the critic: for the a…

CRACI: A Cloud-Native Reference Architecture for the Industrial Compute Continuum
Hai Dinh-Tuan
https://arxiv.org/abs/2509.07498 https://arxiv.org/pdf/2509…

CRACI: A Cloud-Native Reference Architecture for the Industrial Compute Continuum
The convergence of Information Technology (IT) and Operational Technology (OT) in Industry 4.0 exposes the limitations of traditional, hierarchical architectures like ISA-95 and RAMI 4.0. Their inherent rigidity, data silos, and lack of support for cloud-native technologies impair the development of scalable and interoperable industrial systems. This paper addresses this issue by introducing CRACI, a Cloud-native Reference Architecture for the Industrial Compute Continuum. Among other features,…

Compression for Coinductive Infinitary Rewriting: A Generic Approach, with Applications to Cut-Elimination for Non-Wellfounded Proofs
R\'emy Cerda, Alexis Saurin
https://arxiv.org/abs/2510.08420

Compression for Coinductive Infinitary Rewriting: A Generic Approach, with Applications to Cut-Elimination for Non-Wellfounded Proofs
Infinitary rewriting, i.e. rewriting featuring possibly infinite terms and sequences of reduction, is a convenient framework for describing the dynamics of non-terminating but productive rewriting systems. In its original definition based on metric convergence of ordinal-indexed sequences of rewriting steps, a highly desirable property of an infinitary rewriting system is Compression, i.e. the fact that rewriting sequences of arbitrary ordinal length can always be 'compressed' to equivalent seq…

Random Greedy Fast Block Kaczmarz Method for Solving Large-Scale Nonlinear Systems
Renjie Ding, Dongling Wang
https://arxiv.org/abs/2508.09596 https://arxi…

Random Greedy Fast Block Kaczmarz Method for Solving Large-Scale Nonlinear Systems
To efficiently solve large scale nonlinear systems, we propose a novel Random Greedy Fast Block Kaczmarz method. This approach integrates the strengths of random and greedy strategies while avoiding the computationally expensive pseudoinversion of Jacobian submatrices, thus enabling efficient solutions for large scale problems. Our theoretical analysis establishes that the proposed method achieves linear convergence in expectation, with its convergence rates upper bound determined by the stocha…

Energy distance and evolution problems: a promising tool for kinetic equations
Gennaro Auricchio, Giuseppe Toscani
https://arxiv.org/abs/2510.09123 https://

Energy distance and evolution problems: a promising tool for kinetic equations
We study the rate of convergence to equilibrium of the solutions to Fokker-Planck type equations with linear drift by means of Cramér and Energy distances, which have been recently widely used in problems related to AI, in particular for tasks related to machine learning. In all cases in which the Fokker-Planck type equations can be treated through these distances, it is shown that the rate of decay is improved with respect to known results which are based on the decay of relative entropy.

On the convergence rate of the Douglas-Rachford splitting algorithm
Hadi Abbaszadehpeivasti, Moslem Zamani
https://arxiv.org/abs/2509.06676 https://arxiv.o…

On the convergence rate of the Douglas-Rachford splitting algorithm
This work is concerned with the convergence rate analysis of the Douglas-Rachford splitting (DRS) method for finding a zero of the sum of two maximally monotone operators. We obtain an exact rate of convergence for the DRS algorithm and demonstrate its sharpness in the setting of convex feasibility problems. Furthermore, we investigate the linear convergence of the DRS algorithm, providing both necessary and sufficient conditions that characterize this behavior. We further examine the performan…

A generalized Cheeger inequality and the Steklov Problem on finite graphs
Bobo Hua, Supanat Kamtue, Shiping Liu, Florentin M\"unch, Norbert Peyerimhoff
https://arxiv.org/abs/2509.05667

A generalized Cheeger inequality and the Steklov Problem on finite graphs
We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Cheeger inequalities for Steklov eigenvalues. In particular, we get a sharp estimate for the first non-trivial Steklov eigenvalue via Escobar Cheeger constant. At the end, we extend Hassannezhad and Miclo's convergence result to non-reversible Markov chains via a different method based on resolvent convergence, answering…

Strong convergence of a semi tamed scheme for stochastic differential algebraic equation under non-global Lipschitz coefficients
Guy Tsafack, Antoine Tambue
https://arxiv.org/abs/2509.09032

Strong convergence of a semi tamed scheme for stochastic differential algebraic equation under non-global Lipschitz coefficients
We are investigating the first strong convergence analysis of a numerical method for stochastic differential algebraic equations (SDAEs) under a non-global Lipschitz setting. It is well known that the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDEs) when at least one of the coefficients grows superlinearly. The problem becomes more challenging in the case of stochastic differential-algebraic equations (SDAEs) due to the singular…

Improved High-probability Convergence Guarantees of Decentralized SGD
Aleksandar Armacki, Ali H. Sayed
https://arxiv.org/abs/2510.06141 https://arxiv.org/p…

Improved High-probability Convergence Guarantees of Decentralized SGD
Convergence in high-probability (HP) has been receiving increasing interest, due to its attractive properties, such as exponentially decaying tail bounds and strong guarantees for each individual run of an algorithm. While HP guarantees are extensively studied in centralized settings, much less is understood in the decentralized, networked setup. Existing HP studies in decentralized settings impose strong assumptions, like uniformly bounded gradients, or asymptotically vanishing noise, resultin…

Second-order Optimization under Heavy-Tailed Noise: Hessian Clipping and Sample Complexity Limits
Abdurakhmon Sadiev, Peter Richt\'arik, Ilyas Fatkhullin
https://arxiv.org/abs/2510.10690

Second-order Optimization under Heavy-Tailed Noise: Hessian Clipping and Sample Complexity Limits
Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in light-tailed or bounded-noise settings, such algorithms are often brittle and lack guarantees under heavy-tailed noise -- precisely the regimes where robustness is most critical. In this work, we take a first step toward a theoretical understanding of second-order opt…

Parallel, Asymptotically Optimal Algorithms for Moving Target Traveling Salesman Problems
Anoop Bhat, Geordan Gutow, Bhaskar Vundurthy, Zhongqiang Ren, Sivakumar Rathinam, Howie Choset
https://arxiv.org/abs/2509.08743

Parallel, Asymptotically Optimal Algorithms for Moving Target Traveling Salesman Problems
The Moving Target Traveling Salesman Problem (MT-TSP) seeks an agent trajectory that intercepts several moving targets, within a particular time window for each target. In the presence of generic nonlinear target trajectories or kinematic constraints on the agent, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The key idea behind IRG is to alternate between randomly sampling a set of agent con…

Quantitative convergence of trained single layer neural networks to Gaussian processes
Eloy Mosig, Andrea Agazzi, Dario Trevisan
https://arxiv.org/abs/2509.24544 https://…

Quantitative convergence of trained single layer neural networks to Gaussian processes
In this paper, we study the quantitative convergence of shallow neural networks trained via gradient descent to their associated Gaussian processes in the infinite-width limit. While previous work has established qualitative convergence under broad settings, precise, finite-width estimates remain limited, particularly during training. We provide explicit upper bounds on the quadratic Wasserstein distance between the network output and its Gaussian approximation at any training time $t \ge 0…

Convergence of Discrete Percolation Models to the Brownian Web Distance
Craig Belair
https://arxiv.org/abs/2510.06450 https://arxiv.org/pdf/2510.06450

Convergence of Discrete Percolation Models to the Brownian Web Distance
The Brownian web is a collection of coalescing Brownian motions started from every space-time point in R2. The Brownian web can be constructed as a scaling limit of coalescing one-dimensional simple random walks started at every point in a two-dimensional space-time lattice. Veto and Virag (2023) introduced a family of discrete random distance functions defined on these sequences of rescaled lattices. It was shown that, given the appropriate notion of convergence, these discrete distance functi…

On the exponential convergence to equilibrium for ultrafast diffusion equations
Yi C. Huang, Xinhang Tong
https://arxiv.org/abs/2509.07382 https://arxiv.or…

On the exponential convergence to equilibrium for ultrafast diffusion equations
We propose a simple proof of the exponential convergence to equilibrium for ultrafast diffusion equations in $\mathbb{R}^n$. Our approach, based on the direct use of Poincaré inequality, gets rid of the optimal transport arguments used in \cite{fathi2025} which are valid for Gaussian-excluded one-dimensional weights. This simplification allows us to extend their results to Gaussian measures in higher dimensions.

Parametric convergence rate of a non-parametric estimator in multivariate mixtures of power series distributions under conditional independence
Fadoua Balabdaoui, Harald Besdziek, Yong Wang
https://arxiv.org/abs/2509.05452

Parametric convergence rate of a non-parametric estimator in multivariate mixtures of power series distributions under conditional independence
The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with infinite support, to which belong Poisson, Geometric or Negative Binomial mixtures. We show that for all these mixtures, the non-parametric maximum likelihood estimator converges to the truth at the rate $(\log (nd))^{1+d/2} n^{-1/2}$ in the Hellinger distance,…

Nonlinearly Preconditioned Gradient Methods: Momentum and Stochastic Analysis
Konstantinos Oikonomidis, Jan Quan, Panagiotis Patrinos
https://arxiv.org/abs/2510.11312 https://…

Nonlinearly Preconditioned Gradient Methods: Momentum and Stochastic Analysis
We study nonlinearly preconditioned gradient methods for smooth nonconvex optimization problems, focusing on sigmoid preconditioners that inherently perform a form of gradient clipping akin to the widely used gradient clipping technique. Building upon this idea, we introduce a novel heavy ball-type algorithm and provide convergence guarantees under a generalized smoothness condition that is less restrictive than traditional Lipschitz smoothness, thus covering a broader class of functions. Addit…

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence
Yuxing Liu, Yuze Ge, Rui Pan, An Kang, Tong Zhang
https://arxiv.org/abs/2509.07972 https://

Theoretical Analysis on how Learning Rate Warmup Accelerates Convergence
Learning rate warmup is a popular and practical technique in training large-scale deep neural networks. Despite the huge success in practice, the theoretical advantages of this strategy of gradually increasing the learning rate at the beginning of the training process have not been fully understood. To resolve this gap between theory and practice, we first propose a novel family of generalized smoothness assumptions, and validate its applicability both theoretically and empirically. Under the n…

Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
Xun Li, Fan Wu, Xin Zhang
https://arxiv.org/abs/2509.09358 h…

Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
This paper investigates the long-time behavior of zero-sum stochastic linear-quadratic (SLQ) differential games within Markov regime-switching diffusion systems and establishes the turnpike property of the optimal triple. By verifying the convergence of the associated coupled differential Riccati equations (CDREs) along with their convergence rate, we show that, for a sufficiently large time horizon, the equilibrium strategy in the finite-horizon problem can be closely approximated by that of t…

Strong convergence of fully discrete finite element schemes for the stochastic semilinear generalized Benjamin-Bona-Mahony equation driven by additive Wiener noise
Suprio Bhar, Mrinmay Biswas, Mangala Prasad
https://arxiv.org/abs/2509.08453

Strong convergence of fully discrete finite element schemes for the stochastic semilinear generalized Benjamin-Bona-Mahony equation driven by additive Wiener noise
In this article, we have analyzed semi-discrete finite element approximation and full discretization of the Stochastic semilinear generalized Benjamin-Bona-Mahony equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for spatial discretization and the semi-implicit method for time discretization and derive a strong convergence rate with respect to both parameters (spatial and temporal). Numerical experiments have also been performed to s…

Quantum Machine Learning, Quantitative Trading, Reinforcement Learning, Deep Learning
Jun-Hao Chen, Yu-Chien Huang, Yun-Cheng Tsai, Samuel Yen-Chi Chen
https://arxiv.org/abs/2509.09176

Quantum Machine Learning, Quantitative Trading, Reinforcement Learning, Deep Learning
The convergence of quantum-inspired neural networks and deep reinforcement learning offers a promising avenue for financial trading. We implemented a trading agent for USD/TWD by integrating Quantum Long Short-Term Memory (QLSTM) for short-term trend prediction with Quantum Asynchronous Advantage Actor-Critic (QA3C), a quantum-enhanced variant of the classical A3C. Trained on data from 2000-01-01 to 2025-04-30 (80\% training, 20\% testing), the long-only agent achieves 11.87\% return over aroun…

A $\sqrt{2}$-accelerated FISTA for composite strongly convex problems
Kansei Ushiyama
https://arxiv.org/abs/2509.09295 https://arxiv.org/pdf/2509.09295

A $\sqrt{2}$-accelerated FISTA for composite strongly convex problems
In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing convex composite functions, written as the sum of a smooth function and a (possibly) nonsmooth function. When the objective function is strongly convex, the method attains, to the best of our knowledge, the fastest known convergence rate, yielding a simultaneous linear and sublinear nonasymptotic bound. Our convergence analysis remains valid even when one of the two terms is only weakly convex (whi…

Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model
Emmanuel Coffie
https://arxiv.org/abs/2510.04092 https://

Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model
We examine a delayed stochastic interest rate model with super-linearly growing coefficients and develop several new mathematical tools to establish the properties of its true and truncated EM solutions. Moreover, we show that the true solution converges to the truncated EM solutions in probability as the step size tends to zero. Further, we support the convergence result with some illustrative numerical examples and justify the convergence result for the Monte Carlo evaluation of some financia…

Convergence analysis for the Barrett-Garcke-Nurnberg method of transport type
Genming Bai, Harald Garcke, Shravan Veerapaneni
https://arxiv.org/abs/2509.07834 https://

Convergence analysis for the Barrett-Garcke-Nurnberg method of transport type
In this paper, we propose a Barrett-Garcke-Nurnberg (BGN) method for evolving geometries under general flows and present the corresponding convergence analysis. Specifically, we examine the scenario where a closed curve evolves according to a prescribed background velocity field. Unlike mean curvature flow and surface diffusion, where the evolution velocities inherently exhibit parabolicity, this case is dominated by transport which poses a significant difficulty in establishing convergence pro…

An Efficient Solution Method for Solving Convex Separable Quadratic Optimization Problems
Shaoze Li, Junhao Wu, Cheng Lu, Zhibin Deng, Shu-Cherng Fang
https://arxiv.org/abs/2510.11554

An Efficient Solution Method for Solving Convex Separable Quadratic Optimization Problems
Convex separable quadratic optimization problems occur in many practical applications. In this paper, based on an iterative resolution scheme of the KKT system, we develop an efficient method for solving a quadratic programming problem with a convex separable objective function subject to multiple convex separable constraints. We show that the proposed approach leads to a dual coordinate ascent algorithm and provide a convergence proof. Numerical experiments support the superior performance of …

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[2/5]:
- Convergence Analysis of Asynchronous Federated Learning with Gradient Compression for Non-Convex ...
Diying Yang, Yingwei Hou, Weigang Wu

Parareal in time and spectral in space fast L1 quasilinear subdiffusion solver
Josefa Caballero, {\L}ukasz P{\l}ociniczak, Kishin Sadarangani
https://arxiv.org/abs/2510.11023 ht…

Parareal in time and spectral in space fast L1 quasilinear subdiffusion solver
We consider the initial-boundary value problem for a quasilinear time-fractional diffusion equation, and develop a fully discrete solver combining the parareal algorithm in time with a L1 finite-difference approximation of the Caputo derivative and a spectral Galerkin discretization in space. Our main contribution is the first rigorous convergence proof for the parareal-L1 scheme in this nonlinear subdiffusive setting. By constructing suitable energy norms and exploiting the orthogonality of th…

Precise convergence rate of spectral radius of product of complex Ginibre
Yutao Ma, Xujia Meng
https://arxiv.org/abs/2510.07942 https://arxiv.org/pdf/2510.…

Precise convergence rate of spectral radius of product of complex Ginibre
Let $Z_1, \cdots, Z_n$ denote the eigenvalues of the product $\prod_{j=1}^{k_n} \boldsymbol{A}_j$, where $\{\boldsymbol{A}_j\}_{1 \le j \le k_n}$ are independent $n\times n$ complex Ginibre matrices. Define $α= \lim\limits_{n \to \infty} \frac{n}{k_n}$. We prove that $X_n,$ a suitably rescaled version of $\max_{1 \le j \le n} |Z_j|^2,$ converges weakly as follows: to a non-trivial distribution $Φ_α$ for $α\in (0, +\infty)$, to the Gumbel distribution when $α= +\infty$, and to the…

A GPU-Accelerated Matrix-Free FAS Multigrid Solver for Navier-Stokes Equations with Memory-Efficient Implementations
Jiale Meng, Shuqi Tang, Steven M. Wise, Zhenlin Guo
https://arxiv.org/abs/2510.11152

A GPU-Accelerated Matrix-Free FAS Multigrid Solver for Navier-Stokes Equations with Memory-Efficient Implementations
We develop a matrix-free Full Approximation Storage (FAS) multigrid solver based on staggered finite differences and implemented on GPU in MATLAB. To enhance performance, intermediate variables are reused, and an X-shape Multi-Color Gauss-Seidel (X-MCGS) smoother is introduced, which eliminates conditional branching by partitioning the grid into four submatrices. Restriction and prolongation operators are also GPU-accelerated. Convergence tests verify robustness and accuracy, while benchmarks s…

Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
Alberto Gonz\'alez-Sanz, Marcel Nutz, Andr\'es Riveros Valdevenito
https://arxiv.org/abs/2509.08547

Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Here quadratic regularization means that transport couplings are penalized by the squared $L^2$ norm, or equivalently the $χ^2$ divergence. While a number of computational approaches have been shown to work in practice, quadratic regularization is analytically less tractable than entropic, and we are not aware of a previous theoretica…

Gamma Convergence of Partially Segregated Elliptic Systems
Farid Bozorgnia, Avetik Arakelyan
https://arxiv.org/abs/2510.03794 https://arxiv.org/pdf/2510.03…

Gamma Convergence of Partially Segregated Elliptic Systems
We study partially segregated elliptic systems through the use of penalized energy functionals. These systems arise from the minimization of Gross-Pitaevskii-type energies that capture the behavior of multi-component ultracold gas mixtures and other systems involving multiple interacting fluid or gas species. In the case when the domain is planar, i.e., in $\mathbb{R}^2$, our main result is the Gamma convergence of penalized energy to the constrained Dirichlet energy with strict segregation. Th…

DE-Sinc approximation for unilateral rapidly decreasing functions and its computational error bound
Tomoaki Okayama
https://arxiv.org/abs/2510.11411 https://

DE-Sinc approximation for unilateral rapidly decreasing functions and its computational error bound
The Sinc approximation is known to be a highly efficient approximation formula for rapidly decreasing functions. For unilateral rapidly decreasing functions, which rapidly decrease as $x\to\infty$ but does not as $x\to-\infty$, an appropriate variable transformation makes the functions rapidly decreasing. As such a variable transformation, Stenger proposed $t = \sinh(\log(\operatorname{arsinh}(\exp x)))$, which enables the Sinc approximation to achieve root-exponential convergence. Recently, an…

Structure-preserving finite element approximations of a hybrid relativistic cold fluid-particle model
Tileuzhan Mukhamet, Katharina Kormann
https://arxiv.org/abs/2510.11500 http…

Structure-preserving finite element approximations of a hybrid relativistic cold fluid-particle model
We derive mixed finite element discretizations of a cold relativistics fluid model from approximations of the Poisson bracket that preserve mass, energy and the divergence constraints. For time-discretization we derive an implicit energy-conserving average-vector field method or apply an explicit strong-stability preserving Runge-Kutta scheme. We also consider a coupling of the fluid model to relativistic particles. We perform a numerical study of the scheme which shows convergence and conserva…

Rates of convergence in long time asymptotics of an alignment model with symmetry breaking
Alexandre Surin
https://arxiv.org/abs/2509.06765 https://arxiv.o…

Rates of convergence in long time asymptotics of an alignment model with symmetry breaking
We consider a nonlinear Fokker-Planck equation derived from a Cucker-Smale model for flocking with noise. There is a known phase transition depending on the noise between a regime with a unique stationary solution which is isotropic (symmetry) and a regime with a continuum of polarized stationary solutions (symmetry breaking). If the value of the noise is larger than the threshold value, the solution of the evolution equation converges to the unique radial stationary solution. This solution is …

Staggered time discretization in finitely-strained heterogeneous visco-elastodynamics with damage or diffusion in the Eulerian frame
Tom\'a\v{s} Roub\'i\v{c}ek
https://arxiv.org/abs/2510.10355 …

Staggered time discretization in finitely-strained heterogeneous visco-elastodynamics with damage or diffusion in the Eulerian frame
The semi-implicit (partly decoupled, also called staggered or fraction-step) time discretization is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e.\ in the actual deforming configuration, formulated fully in terms of rates. The Kelvin-Voigt rheology and also, in the deviatoric part, the Jeffreys rheology are considered. The numerical stability and, considering the Stokes-type viscosity multipolar of the 2nd-grade, also convergence towa…

Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes
Yinhao Wu, Ping He
https://arxiv.org/abs/2509.09105 https://arxiv.…

Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes
This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H < 1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We pr…

On Convergence Rates of General $N$-Player Stackelberg Games to their Mean Field Limits
Alain Bensoussan, Ziyu Huang, Sheng Wang, Sheung Chi Phillip Yam
https://arxiv.org/abs/2510.02380

On Convergence Rates of General $N$-Player Stackelberg Games to their Mean Field Limits
In this article, we establish precise convergence rates of a general class of $N$-Player Stackelberg games to their mean field limits, which allows the response time delay of information, empirical distribution based interactions, and the control-dependent diffusion coefficients. All these features makes our problem nonstandard, barely been touched in the literature, and they complicate the analysis and therefore reduce the convergence rate. We first justify the same convergence rate for both t…

Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks
Bangti Jin, Longjun Wu
https://arxiv.org/abs/2508.21571 https://

Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks
Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore, the convergence guarantee of stochastic gradient descent is of fundamental importance. In this work, we establish the linear convergence of stochastic gradient descent / flow in training over-parameterized two layer PINNs for a general class of activation fu…

Learning to accelerate distributed ADMM using graph neural networks
Henri Doerks, Paul H\"ausner, Daniel Hern\'andez Escobar, Jens Sj\"olund
https://arxiv.org/abs/2509.05288

Learning to accelerate distributed ADMM using graph neural networks
Distributed optimization is fundamental in large-scale machine learning and control applications. Among existing methods, the Alternating Direction Method of Multipliers (ADMM) has gained popularity due to its strong convergence guarantees and suitability for decentralized computation. However, ADMM often suffers from slow convergence and sensitivity to hyperparameter choices. In this work, we show that distributed ADMM iterations can be naturally represented within the message-passing framewor…

Multivariate CLT for L\'evy processes: convergence rates without moment assumptions
Jorge Gonz\'alez C\'azares, David Kramer-Bang, Aleksandar Mijatovi\'c
https://arxiv.org/abs/2510.06891

Multivariate CLT for Lévy processes: convergence rates without moment assumptions
We prove that the norm of a $d$-dimensional Lévy process possesses a finite second moment if and only if the convex distance between an appropriately rescaled process at time $t$ and a standard Gaussian vector is integrable in time with respect to the scale-invariant measure $t^{-1} dt$ on $[1,\infty)$. We further prove that under the standard $\sqrt{t}$-scaling, the corresponding convex distance is integrable if and only if the norm of the Lévy process has a finite $(2+\log)$-moment. Both eq…

From Nash to Cournot--Nash via $\Gamma$-convergence
Jo{\~a}o Miguel Machado (LMCRC), Guilherme Mazanti (L2S, DISCO), Laurent Pfeiffer (L2S, DISCO)
https://arxiv.org/abs/2509.02205

From Nash to Cournot--Nash via $Γ$-convergence
This work addresses the issue of the convergence of an $N$-player game towards a limit model involving a continuum of players, as the number of agents $N$ goes to infinity. More precisely, we investigate the convergence of Nash equilibria to a Cournot--Nash equilibrium of the limit model. When the cost function of the players is the first variation of some potential function, equilibria can be characterized by a stationarity condition, satisfied in particular by the minimizers of the potential.…

Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential
Yuping Zheng, Andrew Lamperski
https://arxiv.org/abs/2510.02735

Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential
Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large body of work has examined the convergence properties of projected SGD for non-convex losses in asymptotic and non-asymptotic settings. Strong quantitative guarantees are available for convergence measured via Moreau envelopes. However, these results cannot be…

Convergence of the Immersed Boundary Method for an Elastically Bound Particle Immersed in a 2D Navier-Stokes Fluid Fluid
Alexandre X. Milewski (Courant Institute of Mathematical Sciences, New York, NY), Charles S. Peskin (Courant Institute of Mathematical Sciences, New York, NY)
https://arxiv.org/abs/2510.06586

Convergence of the Immersed Boundary Method for an Elastically Bound Particle Immersed in a 2D Navier-Stokes Fluid Fluid
The immersed boundary (IB) method has been used as a means to simulate fluid-membrane interactions in a wide variety of biological and engineering applications. Although the numerical convergence of the method has been empirically verified, it is theoretically unproved because of the singular forcing terms present in the governing equations. This paper is motivated by a specific variant of the IB method, in which the fluid is 2 dimensions greater than the dimension of the immersed structure. In…

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Jeremy Bertoncini, Alberto De Marchi, Matthias Gerdts, Simon Gottschalk
https://arxiv.org/abs/2509.07404

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow tail-convergence typical of first-order schemes, thus requiring many iterations to achieve high-accuracy solutions. Moreover, hyperparameter tuning significantly impacts on the solver performance but how to find an appropriate parameter configuration remains an elusive …

Extending Linear Convergence of the Proximal Point Algorithm: The Quasar-Convex Case
Jos\'e de Brito, Felipe Lara, Di Liu
https://arxiv.org/abs/2509.04375 https://

Extending Linear Convergence of the Proximal Point Algorithm: The Quasar-Convex Case
This work investigates the properties of the proximity operator for quasar-convex functions and establishes the convergence of the proximal point algorithm to a global minimizer with a particular focus on its convergence rate. In particular, we demonstrate: (i) the generated sequence is mi\-ni\-mi\-zing and achieves an $\mathcal{O}(\varepsilon^{-1})$ complexity rate for quasar-convex functions; (ii) under strong quasar-convexity, the sequence converges linearly and attains an $\mathcal{O}(\ln(\…

Convergence analysis for pseudo-monotone variational inequality problem involving projections onto a moving ball
Watanjeet Singh, Sumit Chandok
https://arxiv.org/abs/2509.05589 …

Convergence analysis for pseudo-monotone variational inequality problem involving projections onto a moving ball
This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set $\mathfrak{C}$ or onto a half-space containing $\mathfrak{C}$. However, computing projections onto a complicated feasible set can be difficult, and projections onto a half-space may fall outside $\mathfrak{C}$. Keeping this in mind, we aim to develop an iterative scheme t…

Explicit Global Convergence Rates of BFGS without Line Search
Jianjiang Yu, Weiguo Gao, Luo Luo
https://arxiv.org/abs/2509.22508 https://arxiv.org/pdf/2509…

Explicit Global Convergence Rates of BFGS without Line Search
This paper studies the convergence rates of the Broyden--Fletcher--Goldfarb--Shanno~(BFGS) method without line search. We show that the BFGS method with an adaptive step size [Gao and Goldfarb, Optimization Methods and Software, 34(1):194-217, 2019] exhibits a two-phase non-asymptotic global convergence behavior when minimizing a strongly convex function, i.e., a linear convergence rate of $\mathcal{O}((1 - 1 / \varkappa)^{k})$ in the first phase and a superlinear convergence rate of $\mathcal{…

A Geometric Multigrid-Accelerated Compact Gas-Kinetic Scheme for Fast Convergence in High-Speed Flows on GPUs
Hongyu Liu, Xing Ji, Yuan Fu, Kun Xu
https://arxiv.org/abs/2509.06347

A Geometric Multigrid-Accelerated Compact Gas-Kinetic Scheme for Fast Convergence in High-Speed Flows on GPUs
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core challenge lies in preserving the robustness of implicit algorithms in the presence of strong discontinuities, while simultaneously enabling massive thread parallelism under the constraints of limited GPU memory. To address this, we propose a GPU-optimized, geometric…

On the (almost) Global Exponential Convergence of the Overparameterized Policy Optimization for the LQR Problem
Moh Kamalul Wafi, Arthur Castello B. de Oliveira, Eduardo D. Sontag
https://arxiv.org/abs/2510.02140

On the (almost) Global Exponential Convergence of the Overparameterized Policy Optimization for the LQR Problem
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple example that, surprisingly, the gradient flow solution can be exponentially or asymptotically convergent, depending on how the problem is formulated. We then deepen the analysis and show that a policy optimization strategy for the continuous-time linear quadrati…

Global Convergence and Acceleration for Single Observation Gradient Free Optimization
Caio Kalil Lauand, Sean Meyn
https://arxiv.org/abs/2509.04424 https://

Global Convergence and Acceleration for Single Observation Gradient Free Optimization
Simultaneous perturbation stochastic approximation (SPSA) is an approach to gradient-free optimization introduced by Spall as a simplification of the approach of Kiefer and Wolfowitz. In many cases the most attractive option is the single-sample version known as 1SPSA, which is the focus of the present paper, containing two major contributions: a modification of the algorithm designed to ensure convergence from arbitrary initial condition, and a new approach to exploration to dramatically accel…

A High-order Backpropagation Algorithm for Neural Stochastic Differential Equation Model
Daili Sheng, Minghui Song, Xiang Peng, Xuanqi Dong
https://arxiv.org/abs/2509.06292 http…

A High-order Backpropagation Algorithm for Neural Stochastic Differential Equation Model
Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the sample-wise backpropagation algorithm in neural stochastic differential equation model which has been proposed in [Archibald et al., SIAM Journal on Numerical Analysis, 62 (2024), pp. 593-621]. It is necessary to emphasize that, improving the convergence orde…

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method
April Niu, Kai Wang, Juba Ziani
https://arxiv.org/abs/2509.08161 https://ar…

Finding a Multiple Follower Stackelberg Equilibrium: A Fully First-Order Method
In this work, we propose the first fully first-order method to compute an epsilon stationary Stackelberg equilibrium with convergence guarantees. To achieve this, we first reframe the leader follower interaction as single level constrained optimization. Second, we define the Lagrangian and show that it can approximate the leaders gradient in response to the equilibrium reached by followers with only first-order gradient evaluations. These findings suggest a fully first order algorithm that alte…