Tootfinder

On the pancyclicity of $2$-connected $[5,3]$-graphs
Feng Liu, Hongxi Liu
https://arxiv.org/abs/2509.20038 https://arxiv.org/pdf/2509.20038

On the pancyclicity of $2$-connected $[5,3]$-graphs
A graph $G$ is called an $[s,t]$-graph if any induced subgraph of $G$ of order $s$ has size at least $t$. In 2024, Zhan conjectured that every $2$-connected $[p + 2, p]$-graph of order at least $2p + 3$ and with minimum degree at least $p$ is pancyclic, where $p$ is an integer with $3 \leq p \leq 5$. In this paper, we confirm the conjecture for the case $p=3$, thereby taking the first step toward a complete resolution of the conjecture.

Consistency of tug-of-war type operators on random data clouds
Jeongmin Han, Huajie Liu
https://arxiv.org/abs/2507.18383 https://arxiv.org/pdf/2507.18383…

Consistency of tug-of-war type operators on random data clouds
In this paper, we study a tug-of-war type operator on geometric graphs and its associated Dirichlet problem on a random data cloud. Specifically, we analyze the convergence of the value functions as the number of data points increases and the step size of the game shrinks. This analysis reveals the connection between our tug-of-war type operator and the corresponding model problem. A key ingredient in establishing this result is the consistency of the operator.

Relaxing Direct Ptychography Sampling Requirements via Parallax Imaging Insights
Georgios Varnavides, Julie Marie Bekkevold, Stephanie M Ribet, Mary C Scott, Lewys Jones, Colin Ophus
https://arxiv.org/abs/2507.18610

Relaxing Direct Ptychography Sampling Requirements via Parallax Imaging Insights
Direct ptychography enables the retrieval of information encoded in the phase of an electron wave passing through a thin sample by deconvolving the interference effect of a converged probe with known aberrations. Under the weak phase object approximation, this permits the optimal transfer of information using non-iterative techniques. However, the achievable resolution of the technique is traditionally limited by the probe step size -- setting stringent Nyquist sampling requirements. At the sam…

Revisiting the Geometrically Decaying Step Size: Linear Convergence for Smooth or Non-Smooth Functions
Jihun Kim
https://arxiv.org/abs/2508.13569 https://a…

Revisiting the Geometrically Decaying Step Size: Linear Convergence for Smooth or Non-Smooth Functions
We revisit the geometrically decaying step size given a positive condition number, under which a locally Lipschitz function shows linear convergence. The positivity does not require the function to satisfy convexity, weak convexity, quasar convexity, or sharpness, but instead amounts to a property strictly weaker than the assumptions used in existing works. We propose a clean and simple subgradient descent algorithm that requires minimal knowledge of problem constants, applicable to either smoo…

Colossal Effect of Nanopore Surface Ionic Charge on the Dynamics of Confined Water
Armin Mozhdehei (IPR), Philip Lenz (UHH), Stella Gries (TUHH), Sophia-Marie Meinert (UHH), Ronan Lefort (IPR), Jean-Marc Zanotti (LLB - UMR 12, MMB), Quentin Berrod (STEP), Markus Appel (ILL), Mark Busch (TUHH), Patrick Huber (TUHH), Michael Fr\"oba (UHH), Denis Morineau (IPR)

Colossal Effect of Nanopore Surface Ionic Charge on the Dynamics of Confined Water
Interfacial interactions significantly alter the fundamental properties of water confined in mesoporous structures, with crucial implications for geological, physicochemical, and biological processes. Herein, we focused on the effect of changing the surface ionic charge of nanopores with comparable pore size (3.5-3.8 nm) on the dynamics of confined liquid water. The control of the pore surface ionicity was achieved by using two periodic mesoporous organosilicas (PMOs) containing either neutral …

NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information
Wei-Ting Tang, Akshay Kudva, Joel A. Paulson
https://arxiv.org/abs/2510.05516

NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information
Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a local BO method that targets the Newton step by jointly learning gradient and Hessian information with Gaussian process surrogates, and selecting evaluations via a one-step lookahead bound on Newton-step error. We show that this bound (and hence the step error) contracts with batch size, so NeST-BO directly inherits inexact-Newton convergence: global progres…

Sparse Polyak: an adaptive step size rule for high-dimensional M-estimation
Tianqi Qiao, Marie Maros
https://arxiv.org/abs/2509.09802 https://arxiv.org/pdf…

Sparse Polyak: an adaptive step size rule for high-dimensional M-estimation
We propose and study Sparse Polyak, a variant of Polyak's adaptive step size, designed to solve high-dimensional statistical estimation problems where the problem dimension is allowed to grow much faster than the sample size. In such settings, the standard Polyak step size performs poorly, requiring an increasing number of iterations to achieve optimal statistical precision-even when, the problem remains well conditioned and/or the achievable precision itself does not degrade with problem size.…

On the maximal displacement of subcritical branching random walks with or without killing
Haojie Hou, Shuxiong Zhang
https://arxiv.org/abs/2508.15156 https://

On the maximal displacement of subcritical branching random walks with or without killing
Consider a subcritical branching random walk $\{Z_k\}_{k\geq 0}$ with offspring distribution $\{p_k\}_{k\geq 0}$ and step size $X$. Let $M_n$ denote the rightmost position reached by $\{Z_k\}_{k\geq 0}$ up to generation $n$, and define $M := \sup_{n\geq 0} M_n$. In this paper we give asymptotics of tail probability of $M$ under optimal assumptions $\sum^{\infty}_{k=1}(k\log k) p_k<\infty$ and $\mathbb{E}[Xe^{γX}]<\infty$, where $γ>0$ is a constant such that $\mathbb{E}[e^{γX}]=\frac{1}{m}$ a…

Grounding Rule-Based Argumentation Using Datalog
Martin Diller, Sarah Alice Gaggl, Philipp Hanisch, Giuseppina Monterosso, Fritz Rauschenbach
https://arxiv.org/abs/2508.10976 ht…

Grounding Rule-Based Argumentation Using Datalog
ASPIC+ is one of the main general frameworks for rule-based argumentation for AI. Although first-order rules are commonly used in ASPIC+ examples, most existing approaches to reason over rule-based argumentation only support propositional rules. To enable reasoning over first-order instances, a preliminary grounding step is required. As groundings can lead to an exponential increase in the size of the input theories, intelligent procedures are needed. However, there is a lack of dedicated solut…

Graph-Aware Learning Rates for Decentralized Optimization
Aaron Fainman, Stefan Vlaski
https://arxiv.org/abs/2509.14854 https://arxiv.org/pdf/2509.14854

Graph-Aware Learning Rates for Decentralized Optimization
We propose an adaptive step-size rule for decentralized optimization. Choosing a step-size that balances convergence and stability is challenging. This is amplified in the decentralized setting as agents observe only local (possibly stochastic) gradients and global information (like smoothness) is unavailable. We derive a step-size rule from first principles. The resulting formulation reduces to the well-known Polyak's rule in the single-agent setting, and is suitable for use with stochastic gr…

Scalable Training for Vector-Quantized Networks with 100% Codebook Utilization
Yifan Chang, Jie Qin, Limeng Qiao, Xiaofeng Wang, Zheng Zhu, Lin Ma, Xingang Wang
https://arxiv.org/abs/2509.10140

Scalable Training for Vector-Quantized Networks with 100% Codebook Utilization
Vector quantization (VQ) is a key component in discrete tokenizers for image generation, but its training is often unstable due to straight-through estimation bias, one-step-behind updates, and sparse codebook gradients, which lead to suboptimal reconstruction performance and low codebook usage. In this work, we analyze these fundamental challenges and provide a simple yet effective solution. To maintain high codebook usage in VQ networks (VQN) during learning annealing and codebook size expans…

Alive, awake. slept OK-ish despite definitely still being sick, and taking another look at the latest version of the Ceres board by @… .
Initial visual inspection looks pretty solid, she's fixed a bunch of the things I complained about.
Next step is to export gerbers from KiCAD, use KLayout to trim them down to size and convert to DXF, …

Contraction and entropy production in continuous-time Sinkhorn dynamics
Anand Srinivasan, Jean-Jacques Slotine
https://arxiv.org/abs/2510.12639 https://arx…

Contraction and entropy production in continuous-time Sinkhorn dynamics
Recently, the vanishing-step-size limit of the Sinkhorn algorithm at finite regularization parameter $\varepsilon$ was shown to be a mirror descent in the space of probability measures. We give $L^2$ contraction criteria in two time-dependent metrics induced by the mirror Hessian, which reduce to the coercivity of certain conditional expectation operators. We then give an exact identity for the entropy production rate of the Sinkhorn flow, which was previously known only to be nonpositive. Exam…

Towards Reliable Benchmarking: A Contamination Free, Controllable Evaluation Framework for Multi-step LLM Function Calling
Seiji Maekawa, Jackson Hassell, Pouya Pezeshkpour, Tom Mitchell, Estevam Hruschka
https://arxiv.org/abs/2509.26553

Towards Reliable Benchmarking: A Contamination Free, Controllable Evaluation Framework for Multi-step LLM Function Calling
As language models gain access to external tools via structured function calls, they become increasingly more capable of solving complex, multi-step tasks. However, existing benchmarks for tool-augmented language models (TaLMs) provide insufficient control over factors such as the number of functions accessible, task complexity, and input size, and remain vulnerable to data contamination. We present FuncBenchGen, a unified, contamination-free framework that evaluates TaLMs by generating synthet…

Kahan's Automatic Step-Size Control for Unconstrained Optimization
Yifeng Meng, Chungen Shen, Linuo Xue, Lei-Hong Zhang
https://arxiv.org/abs/2508.06002 https://

Kahan's Automatic Step-Size Control for Unconstrained Optimization
The Barzilai and Borwein (BB) gradient method is one of the most widely-used line-search gradient methods. It computes the step-size for the current iterate by using the information carried in the previous iteration. Recently, William Kahan [Kahan, Automatic Step-Size Control for Minimization Iterations, Technical report, University of California, Berkeley CA, USA, 2019] proposed new Gradient Descent (KGD) step-size strategies which iterate the step-size itself by effectively utilizing the info…

On the optimization dynamics of RLVR: Gradient gap and step size thresholds
Joe Suk, Yaqi Duan
https://arxiv.org/abs/2510.08539 https://arxiv.org/pdf/2510.…

On the optimization dynamics of RLVR: Gradient gap and step size thresholds
Reinforcement Learning with Verifiable Rewards (RLVR), which uses simple binary feedback to post-train large language models, has shown significant empirical success. However, a principled understanding of why it works has been lacking. This paper builds a theoretical foundation for RLVR by analyzing its training process at both the full-response (trajectory) and token levels. Central to our analysis is a quantity called the Gradient Gap, which formalizes the direction of improvement from low-r…

Lossless Derandomization for Undirected Single-Source Shortest Paths and Approximate Distance Oracles
Shuyi Yan
https://arxiv.org/abs/2510.12598 https://ar…

Lossless Derandomization for Undirected Single-Source Shortest Paths and Approximate Distance Oracles
A common step in algorithms related to shortest paths in undirected graphs is that, we select a subset of vertices as centers, then grow a ball around each vertex until a center is reached. We want the balls to be as small as possible. A randomized algorithm can uniformly sample $r$ centers to achieve the optimal (expected) ball size of $Θ(n/r)$. A folklore derandomization is to use the $O(\log n)$ approximation for the set cover problem in the hitting set version where we want to hit all the …

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids
Will Dolphin, Peter J. Dukes
https://arxiv.org/abs/2509.13589 https://arxiv.org/pdf/2…

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids
We improve the status of the problem of determining minimum-sized percolating sets in $a \times b \times c$ grids under the $3$-neighbour process. Using several new constructions, we show that optimal percolating sets exist whenever $\min(a,b,c) \ge 7$. As an important step toward this, we also show that all grids with $\min(a,b,c) \ge 4$ have a percolating set whose size exactly achieves the lower bound $(ab+ac+bc)/3$ whenever this value is an integer.

Reach together: How populations win repeated games
Nathalie Bertrand, Patricia Bouyer, Luc Lapointe, Corto Mascle
https://arxiv.org/abs/2510.02984 https://…

Reach together: How populations win repeated games
In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective. The problem is whether there exists a uniform coalition strategy for the players so that they are sure to win independently of the population size. We use algebraic tools to show that the problem can be solved in polynomial space. First we exhibit a finite s…

Condition number for finite element discretisation of nonlocal PDE systems with applications to biology
Olusegun E. Adebayo, Raluca Eftimie, Dumitru Trucu
https://arxiv.org/abs/2508.09781

Condition number for finite element discretisation of nonlocal PDE systems with applications to biology
In this work, we investigate the condition number for a system of coupled non-local reaction-diffusion-advection equations developed in the context of modelling normal and abnormal wound healing. Following a finite element discretisation of the coupled non-local system, we establish bounds for this condition number. We further discuss how model parameter choices affect the conditioning of the system. Finally, we discuss how the step size of the chosen time-stepping scheme and the spatial gr…

Reservoir computing with large valid prediction time for the Lorenz system
Lauren A Hurley, Sean E Shaheen
https://arxiv.org/abs/2508.06730 https://arxiv.o…

Reservoir computing with large valid prediction time for the Lorenz system
We study the dependence of the Valid Prediction Time (VPT) of Reservoir Computers (RCs) on hyperparameters including the regularization coefficient, reservoir size, and spectral radius. Under carefully chosen conditions, the RC can achieve approximately 70% of a benchmark performance, based on the output of a single prediction step used as initial conditions for the Lorenz equations. We report high VPT values (>30 Lyapunov times), as we are predicting a noiseless system where overfitting can be…

Generalized eigenvalue stabilization for immersed explicit dynamics
Tim B\"urchner, Lars Radtke, Sascha Eisentr\"ager, Alexander D\"uster, Ernst Rank, Stefan Kollmannsberger, Philipp Kopp
https://arxiv.org/abs/2509.07632

Generalized eigenvalue stabilization for immersed explicit dynamics
Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass matrices of cut elements to cure their adverse impact on the critical time step size of the global system. We use spectral basis functions, specifically $C^0$ continuous Lagrangian interpolation polynomials defined on Gauss-Lobatto-Legendre (GLL) points, which…

Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximation
Bogdan Butyrin, Eric Moulines, Alexey Naumov, Sergey Samsonov, Qi-Man Shao, Zhuo-Song Zhang
https://arxiv.org/abs/2510.12375

Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximation
In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA) algorithm with decreasing step size. We consider the normal approximation by the Gaussian distribution with covariance matrix predicted by the Polyak-Juditsky central limit theorem and establish the rate up to order $n^{-1/3}$ in convex distance, where $n$ is the number of samples used in the algorithm. We also prov…

Online Learning for Vibration Suppression in Physical Robot Interaction using Power Tools
Gokhan Solak, Arash Ajoudani
https://arxiv.org/abs/2508.03559 https://

Online Learning for Vibration Suppression in Physical Robot Interaction using Power Tools
Vibration suppression is an important capability for collaborative robots deployed in challenging environments such as construction sites. We study the active suppression of vibration caused by external sources such as power tools. We adopt the band-limited multiple Fourier linear combiner (BMFLC) algorithm to learn the vibration online and counter it by feedforward force control. We propose the damped BMFLC method, extending BMFLC with a novel adaptive step-size approach that improves the conv…

Scalings and simulation requirements in two-phase flows
Luis H. Hatashita, Pranav Nathan, Suhas S. Jain
https://arxiv.org/abs/2510.07727 https://arxiv.org/…

Scalings and simulation requirements in two-phase flows
In this work, important two-phase flow scalings are derived, which enable the quantification of grid-point and time-step requirements as functions of Re, We, and Ca numbers. The adequate grid resolution is determined in the inertia-dominated regime with the aid of high-fidelity simulations of stationary two-phase homogeneous isotropic turbulence by evaluating convergence of total interfacial area, size distribution, SMD, and curvature distribution. Although standards for DNS for single-phase tu…

Unbiased Binning: Fairness-aware Attribute Representation
Abolfazl Asudeh (Mila), Zeinab (Mila), Asoodeh, Bita Asoodeh, Omid Asudeh
https://arxiv.org/abs/2509.21785 https://…

Unbiased Binning: Fairness-aware Attribute Representation
Discretizing raw features into bucketized attribute representations is a popular step before sharing a dataset. It is, however, evident that this step can cause significant bias in data and amplify unfairness in downstream tasks. In this paper, we address this issue by introducing the unbiased binning problem that, given an attribute to bucketize, finds its closest discretization to equal-size binning that satisfies group parity across different buckets. Defining a small set of boundary candi…

Digital quantum simulation of many-body localization crossover in a disordered kicked Ising model
Tomoya Hayata, Kazuhiro Seki, Seiji Yunoki
https://arxiv.org/abs/2510.01983 htt…

Digital quantum simulation of many-body localization crossover in a disordered kicked Ising model
Simulating nonequilibrium dynamics of quantum many-body systems is one of the most promising applications of quantum computers. However, a faithful digital quantum simulation of the Hamiltonian evolution is very challenging in the present noisy quantum devices. Instead, nonequilibrium dynamics under the Floquet evolution realized by the Trotter decomposition of the Hamiltonian evolution with a large Trotter step size is considered to be a suitable problem for simulating in the present or near-t…

PowerBin: Fast Adaptive Data Binning with Centroidal Power Diagrams
Michele Cappellari (University of Oxford)
https://arxiv.org/abs/2509.06903 https://arxi…

PowerBin: Fast Adaptive Data Binning with Centroidal Power Diagrams
Adaptive binning is a crucial step in the analysis of large astronomical datasets, such as those from integral-field spectroscopy, to ensure a sufficient signal-to-noise ratio (S/N) for reliable model fitting. However, the widely used Voronoi-binning method and its variants suffer from two key limitations: they scale poorly with data size, often as O(N^2), creating a computational bottleneck for modern surveys, and they can produce undesirable non-convex or disconnected bins. I introduce PowerB…

Adaptive Conditional Gradient Descent
Abbas Khademi, Antonio Silveti-Falls
https://arxiv.org/abs/2510.11440 https://arxiv.org/pdf/2510.11440

Adaptive Conditional Gradient Descent
Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on linear minimization oracles, as used in the Conditional Gradient or non-Euclidean Normalized Steepest Descent algorithms. Using a simple heuristic to estimate a local Lipschitz constant for the gradient, we can determine step-sizes that guarantee sufficient …

A Distributed Gradient-Based Deployment Strategy for a Network of Sensors with a Probabilistic Sensing Model
Hesam Mosalli, Amir G. Aghdam
https://arxiv.org/abs/2509.02869 https…

A Distributed Gradient-Based Deployment Strategy for a Network of Sensors with a Probabilistic Sensing Model
This paper presents a distributed gradient-based deployment strategy to maximize coverage in hybrid wireless sensor networks (WSNs) with probabilistic sensing. Leveraging Voronoi partitioning, the overall coverage is reformulated as a sum of local contributions, enabling mobile sensors to optimize their positions using only local information. The strategy adopts the Elfes model to capture detection uncertainty and introduces a dynamic step size based on the gradient of the local coverage, ensur…

Crosslisted article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
- Sparse Polyak: an adaptive step size rule for high-dimensional M-estimation
Tianqi Qiao, Marie Maros

MicroDetect-Net (MDN): Leveraging Deep Learning to Detect Microplastics in Clam Blood, a Step Towards Human Blood Analysis
Riju Marwah, Riya Arora, Navneet Yadav, Himank Arora
https://arxiv.org/abs/2508.19021

MicroDetect-Net (MDN): Leveraging Deep Learning to Detect Microplastics in Clam Blood, a Step Towards Human Blood Analysis
With the prevalence of plastics exceeding 368 million tons yearly, microplastic pollution has grown to an extent where air, water, soil, and living organisms have all tested positive for microplastic presence. These particles, which are smaller than 5 millimeters in size, are no less harmful to humans than to the environment. Toxicity research on microplastics has shown that exposure may cause liver infection, intestinal injuries, and gut flora imbalance, leading to numerous potential health ha…

On the Estimation of Multinomial Logit and Nested Logit Models: A Conic Optimization Approach
Hoang Giang Pham, Tien Mai, Minh Ha Hoang
https://arxiv.org/abs/2509.01562 https://…

On the Estimation of Multinomial Logit and Nested Logit Models: A Conic Optimization Approach
In this paper, we revisit parameter estimation for multinomial logit (MNL), nested logit (NL), and tree-nested logit (TNL) models through the framework of convex conic optimization. Traditional approaches typically solve the maximum likelihood estimation (MLE) problem using gradient-based methods, which are sensitive to step-size selection and initialization, and may therefore suffer from slow or unstable convergence. In contrast, we propose a novel estimation strategy that reformulates these m…

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis
Matias D. Cattaneo, Boris Shigida
https://arxiv.org/abs/2509.08483 https://arxiv.org/pdf/…

Modified Loss of Momentum Gradient Descent: Fine-Grained Analysis
We analyze gradient descent with Polyak heavy-ball momentum (HB) whose fixed momentum parameter $β\in (0, 1)$ provides exponential decay of memory. Building on Kovachki and Stuart (2021), we prove that on an exponentially attractive invariant manifold the algorithm is exactly plain gradient descent with a modified loss, provided that the step size $h$ is small enough. Although the modified loss does not admit a closed-form expression, we describe it with arbitrary precision and prove global (f…

A Relaxed Step-Ratio Constraint for Time-Fractional Cahn--Hilliard Equations: Analysis and Computation
Shipeng Li, Hengfei Ding
https://arxiv.org/abs/2508.17178 https://

A Relaxed Step-Ratio Constraint for Time-Fractional Cahn--Hilliard Equations: Analysis and Computation
Numerical solutions of time-fractional differential equations encounter significant challenges arising from solution singularities at the initial time. To address this issue, the construction of nonuniform temporal meshes satisfying $τ_k/τ_{k-1} \geq 1$ has emerged as an effective strategy, where $τ_k$ represents the $k$-th time-step size. For the time-fractional Cahn-Hilliard equation, Liao et al.~[\textit{IMA J. Numer. Anal.}, \textbf{45} (2025), 1425--1454] developed an analytical framewo…

Comparing and Scaling fMRI Features for Brain-Behavior Prediction
Mikkel Sch\"ottner Sieler, Thomas A. W. Bolton, Jagruti Patel, Patric Hagmann
https://arxiv.org/abs/2507.20601

Comparing and Scaling fMRI Features for Brain-Behavior Prediction
Predicting behavioral variables from neuroimaging modalities such as magnetic resonance imaging (MRI) has the potential to allow the development of neuroimaging biomarkers of mental and neurological disorders. A crucial processing step to this aim is the extraction of suitable features. These can differ in how well they predict the target of interest, and how this prediction scales with sample size and scan time. Here, we compare nine feature subtypes extracted from resting-state functional MRI…

Axisymmetric Gyrokinetic Simulation of ASDEX-Upgrade Scrape-off Layer Using a Conservative Implicit BGK Collision Operator
D. Liu, J. Juno, G. W. Hammett, A. Hakim, A. Shukla, M. Francisquez
https://arxiv.org/abs/2507.22821

Axisymmetric Gyrokinetic Simulation of ASDEX-Upgrade Scrape-off Layer Using a Conservative Implicit BGK Collision Operator
Collisions play an important role in turbulence and transport of fusion plasmas. For kinetic simulations, as the collisionality increases in the domain of interest, the size of the time step to resolve the collisional physics can become overly restrictive in an explicit time integration scheme, leading to high computational cost. With the aim of overcoming such restriction, we have implemented an implicit Bhatnagar-Gross-Krook (BGK) collision operator for use in the discontinuous Galerkin (DG) …

A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
Xiaokai Chang, Junfeng Yang, Jianchao Bai, Jianxiong Cao
https://arxiv.org/abs/2510.00437

A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
The primal-dual splitting algorithm (PDSA) by Chambolle and Pock is efficient for solving structured convex optimization problems. It adopts an extrapolation step and achieves convergence under certain step size condition. Chang and Yang recently proposed a modified PDSA for bilinear saddle point problems, integrating a convex combination step to enable convergence with extended step sizes. In this paper, we focus on composite monotone inclusion problems (CMIPs), a generalization of convex opti…

The Root Finding Problem Revisited: Beyond the Robbins-Monro procedure
Yue Yu, Moulinath Banerjee, Ya'acov Ritov
https://arxiv.org/abs/2508.17591 https://

The Root Finding Problem Revisited: Beyond the Robbins-Monro procedure
We introduce Sequential Probability Ratio Bisection (SPRB), a novel stochastic approximation algorithm that adapts to the local behavior of the (regression) function of interest around its root. We establish theoretical guarantees for SPRB's asymptotic performance, showing that it achieves the optimal convergence rate and minimal asymptotic variance even when the target function's derivative at the root is small (at most half the step size), a regime where the classical Robbins-Monro procedure …

Central limit theorem and Cram\'{e}r-type moderate deviations for Milstein scheme
Peng Chen, Hui Jiang, Jing Wang
https://arxiv.org/abs/2510.03053 https://

Central limit theorem and Cramér-type moderate deviations for Milstein scheme
In this paper, we investigate the Milstein numerical scheme with step size $η$ for a stochastic differential equation driven by multiplicative Brownian motion. Under some appropriate coefficient conditions, the continuous-time system and its discrete Milstein scheme approximation each possess unique invariant measures, which we denote by $π$ and $π_η$ respectively. We first establish a central limit theorem for the empirical measure $Π_η$, a statistical consistent estimator of $π_η$. Su…

Implicit Updates for Average-Reward Temporal Difference Learning
Hwanwoo Kim, Dongkyu Derek Cho, Eric Laber
https://arxiv.org/abs/2510.06149 https://arxiv.…

Implicit Updates for Average-Reward Temporal Difference Learning
Temporal difference (TD) learning is a cornerstone of reinforcement learning. In the average-reward setting, standard TD($λ$) is highly sensitive to the choice of step-size and thus requires careful tuning to maintain numerical stability. We introduce average-reward implicit TD($λ$), which employs an implicit fixed point update to provide data-adaptive stabilization while preserving the per iteration computational complexity of standard average-reward TD($λ$). In contrast to prior finite-tim…

High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation
Ilya Levin, Alexey Naumov, Sergey Samsonov
https://arxiv.org/abs/2508.05570 https://

High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation
In this paper, we study the bias and high-order error bounds of the Linear Stochastic Approximation (LSA) algorithm with Polyak-Ruppert (PR) averaging under Markovian noise. We focus on the version of the algorithm with constant step size $α$ and propose a novel decomposition of the bias via a linearization technique. We analyze the structure of the bias and show that the leading-order term is linear in $α$ and cannot be eliminated by PR averaging. To address this, we apply the Richardson-Rom…

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…

The adaptive EM schemes for McKean-Vlasov SDEs with common noise in finite and infinite horizons
Hu Liu, Shuaibin Gao, Junhao Hu
https://arxiv.org/abs/2509.00521 https://…

The adaptive EM schemes for McKean-Vlasov SDEs with common noise in finite and infinite horizons
This paper is dedicated to investigating the adaptive Euler-Maruyama (EM) schemes for the approximation of McKean-Vlasov stochastic differential equations (SDEs) with common noise. When the drift and diffusion coefficients both satisfy the superlinear growth conditions, the $L^p$ convergence rates in finite and infinite horizons are revealed, which reacts to the particle number and step size. Subsequently, there is an illustration of the theory results by means of two numerical examples.

Multireference equation-of-motion driven similarity renormalization group for X-ray photoelectron spectra
Shuhang Li, Zijun Zhao, Francesco A. Evangelista
https://arxiv.org/abs/2509.21646

Multireference equation-of-motion driven similarity renormalization group for X-ray photoelectron spectra
We formulate and implement the core-valence separated multireference equation-of-motion driven similarity renormalization group method (CVS-IP-EOM-DSRG) for simulating X-ray photoelectron spectra (XPS) of strongly correlated molecular systems. This method is numerically robust and computationally efficient, delivering accurate core-ionization energies with O(N^4) scaling relative to basis set size N in the EOM step. To ensure rigorous core intensivity, we propose a simple modification of the gr…

Zero blocking numbers of graphs with complexity results
Hau-Yi Lin, Wu-Hsiung Lin, Gerard Jennhwa Chang
https://arxiv.org/abs/2508.17785 https://arxiv.org/…

Zero blocking numbers of graphs with complexity results
For a graph $G$ in which vertices are either black or white, a zero forcing process is an iterative vertex color changing process such that the only white neighbor of a black vertex becomes black in the next time step. A zero forcing set is an initial subset of black vertices in a zero forcing process ultimately expands to include all vertices of the graph; otherwise we call its complement a zero blocking set. The zero blocking number $B(G)$ of $G$ is the minimum size of a zero blocking set. Th…

ANO : Faster is Better in Noisy Landscape
Adrien Kegreisz
https://arxiv.org/abs/2508.18258 https://arxiv.org/pdf/2508.18258

ANO : Faster is Better in Noisy Landscape
Stochastic optimizers are central to deep learning, yet widely used methods such as Adam and Adan can degrade in non-stationary or noisy environments, partly due to their reliance on momentum-based magnitude estimates. We introduce Ano, a novel optimizer that decouples direction and magnitude: momentum is used for directional smoothing, while instantaneous gradient magnitudes determine step size. This design improves robustness to gradient noise while retaining the simplicity and efficiency of …

Covariance-Adaptive Bouncy Particle Samplers via Split Lagrangian Dynamics
Augustin Chevallier, Erik Raab
https://arxiv.org/abs/2509.24847 https://arxiv.or…

Covariance-Adaptive Bouncy Particle Samplers via Split Lagrangian Dynamics
Piecewise Deterministic Markov Processes (PDMPs) provide a powerful framework for continuous-time Monte Carlo, with the Bouncy Particle Sampler (BPS) as a prominent example. Recent advances through the Metropolised PDMP framework allow local adaptivity in step size and effective path length, the latter acting as a refreshment rate. However, current PDMP samplers cannot adapt to local changes in the covariance structure of the target distribution. We extend BPS by introducing a position-depend…

On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape
Lei Qin, Ye Pu
https://arxiv.org/abs/2508.06922 https://…

On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape
This paper considers a class of distributed resource allocation problems where each agent privately holds a smooth, potentially non-convex local objective, subject to a globally coupled equality constraint. Built upon the existing method, Laplacian-weighted Gradient Descent, we propose to add random perturbations to the gradient iteration to enable efficient escape from saddle points and achieve second-order convergence guarantees. We show that, with a sufficiently small fixed step size, the it…

Riemannian Change Point Detection on Manifolds with Robust Centroid Estimation
Xiuheng Wang, Ricardo Borsoi, Arnaud Breloy, C\'edric Richard
https://arxiv.org/abs/2508.18045

Riemannian Change Point Detection on Manifolds with Robust Centroid Estimation
Non-parametric change-point detection in streaming time series data is a long-standing challenge in signal processing. Recent advancements in statistics and machine learning have increasingly addressed this problem for data residing on Riemannian manifolds. One prominent strategy involves monitoring abrupt changes in the center of mass of the time series. Implemented in a streaming fashion, this strategy, however, requires careful step size tuning when computing the updates of the center of mas…

$K$-Branching Random Walk with Noisy Selection: Large Population Limits and Phase Transitions
Colin Desmarais, Emmanuel Schertzer, Zs\'ofia Talyig\'as
https://arxiv.org/abs/2509.26254

$K$-Branching Random Walk with Noisy Selection: Large Population Limits and Phase Transitions
We analyze a variant of the Noisy $K$-Branching Random Walk, a population model that evolves according to the following procedure. At each time step, each individual produces a large number of offspring that inherit the fitness of their parents up to independent and identically distributed fluctuations. The next generation consists of a random sample of all the offspring so that the population size remains fixed, where the sampling is made according to a parameterized Gibbs measure of the fitne…

On Generalized Forward-Reflected-Backward Method for Monotone Inclusion Problems
Santanu Soe, V. Vetrivel, Jen-Chih Yao
https://arxiv.org/abs/2509.02005 https://

On Generalized Forward-Reflected-Backward Method for Monotone Inclusion Problems
In this article, we analyze the generalized forward-reflected-backward (GFRB) method, which is an extension of the forward-reflected-backward (FRB) method due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. In particular, we study GFRB with an increasing step-size update that does not require prior knowledge of the Lipschitz constant to run the algorithm. In this sequel, we propose an extended version of the primal-dual twice-reflected algorithm (PDTR), whic…

Popov Mirror-Prox Method for Variational Inequalities
Abhishek Chakraborty, Angelia Nedi\'c
https://arxiv.org/abs/2507.23395 https://arxiv.org/pdf/2507…

Popov Mirror-Prox Method for Variational Inequalities
This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing methods that require prior knowledge of problem-specific parameters, we propose step-size schemes that are entirely parameter-free in both constant and diminishing forms. For stochastic and deterministic monotone VIs, we establish optimal convergence rates in term…

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{…

Loss-Transformation Invariance in the Damped Newton Method
Alexander Shestakov, Sushil Bohara, Samuel Horv\'ath, Martin Tak\'a\v{c}, Slavom\'ir Hanzely
https://arxiv.org/abs/2509.25782

Loss-Transformation Invariance in the Damped Newton Method
The Newton method is a powerful optimization algorithm, valued for its rapid local convergence and elegant geometric properties. However, its theoretical guarantees are usually limited to convex problems. In this work, we ask whether convexity is truly necessary. We introduce the concept of loss-transformation invariance, showing that damped Newton methods are unaffected by monotone transformations of the loss - apart from a simple rescaling of the step size. This insight allows difficult losse…

A Riemannian Variational and Spectral Framework for High-Dimensional Sphere Packing: Barrier-Dynamics Reconciliation, Periodic Rigidity, and Discrete-Time Guarantees
Faruk Alpay, Hamdi Alakkad
https://arxiv.org/abs/2509.21066

A Riemannian Variational and Spectral Framework for High-Dimensional Sphere Packing: Barrier-Dynamics Reconciliation, Periodic Rigidity, and Discrete-Time Guarantees
We develop a unified framework that reconciles a barrier based geometric model of periodic sphere packings with a provably convergent discrete time dynamics. First, we introduce a C2 interior barrier U_nu that is compatible with a strict feasibility safeguard and has a Lipschitz gradient on the iterates domain. Second, we correct and formalize the discrete update and give explicit step size and damping rules. Third, we prove barrier to KKT consistency and state an interior variant clarifying th…