惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

J
Java Code Geeks
博客园 - 聂微东
人人都是产品经理
人人都是产品经理
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
博客园_首页
量子位
阮一峰的网络日志
阮一峰的网络日志
酷 壳 – CoolShell
酷 壳 – CoolShell
H
Hackread – Cybersecurity News, Data Breaches, AI and More
云风的 BLOG
云风的 BLOG
D
DataBreaches.Net
B
Blog
L
LangChain Blog
Apple Machine Learning Research
Apple Machine Learning Research
Vercel News
Vercel News
博客园 - 三生石上(FineUI控件)
爱范儿
爱范儿
Microsoft Azure Blog
Microsoft Azure Blog
IT之家
IT之家
aimingoo的专栏
aimingoo的专栏
B
Blog RSS Feed
H
Help Net Security
The Cloudflare Blog
U
Unit 42

stat updates on arXiv.org

A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Operator splitting for exploiting linear-rate closure in ...
[Submitted on 16 May 2026 (v1), last revised 29 Jul 2026 (this v · 2026-05-17 · via stat updates on arXiv.org

View PDF HTML (experimental)

Abstract:We introduce an operator-splitting method for infinite hierarchies of linear ordinary differential equations (ODEs) indexed by nonnegative integers. When the coupling coefficients depend linearly on the count index, an exact transformation closes the equations on finite count-index windows without an upper-boundary value. For more general hierarchies, Strang splitting applies the linear-rate closure during the linear-rate substeps and a conventional capped solver to the remainder. We derive the closure from generating functions and the method of characteristics and extend it to multi-indexed systems. The derivation requires neither positivity nor mass conservation, so it applies to a wider class of systems than the examplar stochastic models presented here. We discuss branching processes, stochastic predator-prey dynamics, the Schlögl chemical kinetics model, and a telegraph model for gene expression. Through numerical experiments and computational cost analyses we demonstrate that our operator splitting method is typically advantageous for solving large scale systems in terms of memory usage and computational time, while retaining accuracy competitive with finite state projection (FSP) methods.

Submission history

From: Joshua Chang [view email]
[v1] Sat, 16 May 2026 22:46:15 UTC (1,157 KB)
[v2] Wed, 29 Jul 2026 13:36:51 UTC (809 KB)