Numerical Integration

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24 papers2 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

A Path Integral Surrogate for Multi-Step Gradient Inversion in Federated Learning
Oct 2, 2026Agnivo Ghosh, Saumik BhattacharyaNumerical Integration Gradient Inversion Attacks
Department of Electronics and Electrical Communication Engineering Indian Institute of Technology Kharagpur, India
Subgroup Rank-1 Lattice for Practical High-dimensional Black-box Integral Approximation
Sep 28, 2026Yueming LyuKernel Mean Embeddings Kernel Methods
Centre for Frontier AI Research (CFAR) Agency for Science, Technology and Research (A*STAR) 1 Fusionopolis Way #16-16 Connexis Singapore, 138632
Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration
Sep 3, 2026Lidia J. Gomes Da SilvaDynamical Systems Gravitational-Wave Astronomy
SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN Sezione di Trieste · INFN Sezione di Trieste · IFPU - Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
RAPTOR: RAndom-projection Physics-informed Transient sOlveR
Aug 31, 2026Petros Ellinas, Benjamin Vilmann, Spyros Chatzivasileiadis +1Numerical Integration Power Systems
Department of Wind and Energy Systems, Technical University of Denmark, Lyngby, Denmark
Gauss--Hermite Quadrature for Gaussian-Mixture Entropy with an Action-Space Hermite Surrogate
Aug 21, 2026Jae Wan ShimNumerical Integration Surrogate-Assisted Optimization
Extreme Materials Research Center, Korea Institute of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk, Seoul, 02792, Republic of Korea · Climate and Environmental Research Institute, Korea Institute of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk, Seoul, 02792, Republic of Korea · Division of AI-Robotics, KIST Campus, University of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk, Seoul, 02792, Republic of Korea
Hierarchical Bayesian Quadrature
Jul 12, 2026Tim Weiland, Toni Karvonen, Philipp HennigNumerical Integration Uncertainty Quantification
Tübingen AI Center, University of Tübingen, Tübingen, Germany · School of Engineering Sciences, Lappeenranta–Lahti University of Technology LUT, Lappeenranta, Finland
Asymptotic Preservation and Uniform Accuracy of Diffusion and Flow-Matching Samplers
Jul 5, 2026Shiheng ZhangFlow Matching Diffusion Sampling
University of Washington
Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics
Jun 25, 2026Benedict Leimkuhler, Peter A. WhalleyLangevin Dynamics Posterior Sampling
School of Mathematics, University of Edinburgh, Edinburgh, UK. · Seminar for Statistics, Department of Mathematics, ETH Zürich, Zürich, Switzerland.
Amortized mean-shift interacting particles
Jun 14, 2026Ali SiahkoohiAmortized Inference Bayesian Inverse Problems
Department of Computer Science University of Central Florida
True Self-Avoiding Walk for Accelerating Markov-Chain Monte Carlo Integration
May 28, 2026Qinghua, Ding, Venkat AnantharamMarkov Chain Monte Carlo Numerical Integration
Devon · Department of Electrical Engineering and Computer Sciences University of California at Berkeley Berkeley, CA, United States
A Scalable Nonparametric Continuous-Time Survival Model through Numerical Quadrature
May 15, 2026Chaeyeon Lee, Sehwan Kim, Hyungrok DoNumerical Integration Survival Analysis
Department of Statistics · Ewha Womans University · Seoul, Korea +3
QuadNorm: Resolution-Robust Normalization for Neural Operators
May 8, 2026Bum Jun Kim, Makoto Kawano, Yusuke Iwasawa +1Numerical Integration PDE Operator Learning
The University of Tokyo, Japan
Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization
May 8, 2026Lyra Zhornyak, Eric Forgoston, M. Ani HsiehNeural PDE Solvers PDE Surrogate Modeling
University of Pennsylvania · Montclair State University
Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations
May 6, 2026Zhangyong Liang, Huanhuan GaoNeural PDE Solvers PDE Solving
National Center for Applied Mathematics Tianjin University Tianjin, 300072, China · School of Mechanical and Aerospace Engineering, Jilin University Jilin University Changchun, 130025, China
Quadrature-TreeSHAP: Depth-Independent TreeSHAP and Shapley Interactions
May 6, 2026Ron Wettenstein, Rory Mitchell, Peng YuNumerical Integration SHAP Feature Attribution
Reichman University, Herzliya, Israel · Nvidia Corporation · Shopify
On the Role of Strain and Vorticity in Numerical Integration Error for Flow Matching
Apr 22, 2026Chenxi Tao, Seung-Kyum ChoiFlow Matching Jacobian Regularization
Georgia Institute of Technology
On two ways to use determinantal point processes for Monte Carlo integration
Apr 21, 2026Guillaume Gautier, Rémi Bardenet, Michal ValkoDeterminantal Point Process Variance Reduction
†Univ. Lille, CNRS, Centrale Lille, UMR 9189 – CRIStAL, 59651 Villeneuve d’Ascq, France · *Inria Lille-Nord Europe, 40 avenue Halley 59650 Villeneuve d’Ascq, France · ‡DeepMind Paris, 14 Rue de Londres, 75009 Paris, France +1
From Euler to Dormand-Prince: ODE Solvers for Flow Matching Generative Models
Apr 4, 2026Hao XiaoNumerical Integration Flow Matching
ATLAS AI Lab
Certified and accurate computation of function space norms of deep neural networks
Mar 6, 2026Johannes Gründler, Moritz Maibaum, Philipp PetersenNeural Network Verification Numerical Integration
Faculty of Mathematics, University of Vienna, Kolingasse 14–16, 1090 Vienna, Austria
The Partition Principle Revisited: Non-Equal Volume Designs Achieve Minimal Expected Star Discrepancy
Feb 27, 2026Xiaoda XuNumerical Integration Stratified Sampling
School of Mathematics and Physics, Suqian University
Scalable Kernel-Based Distances for Statistical Inference and Integration
Feb 25, 2026Masha NaslidnykNumerical Integration Maximum Mean Discrepancy
Department of Computer Science University College London
Bayesian Quadrature
Feb 18, 2026Maren Mahsereci, Toni KarvonenNumerical Integration
Yahoo Research · School of Engineering Sciences Lappeenranta–Lahti University of Technology LUT
Quenched large deviations for Monte Carlo integration with Coulomb gases
Aug 2, 2025Martin Rouault, Rémi Bardenet, Mylène MaïdaLarge Deviation Principles Numerical Integration
1Univ. Lille, CNRS, Centrale Lille, UMR 9189 – CRIStAL, 59651 Villeneuve d’Ascq, France · 2Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlev´e, F-59000 Lille, France
Artifacts of Numerical Integration in Learning Dynamical Systems
Jul 19, 2025Bing-Ze Lu, Richard TsaiNumerical Integration Dynamical Systems
National Chung Cheng University, Taiwan · The University of Texas at Austin, USA

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A Path Integral Surrogate for Multi-Step Gradient Inversion in Federated Learning

Agnivo Ghosh, Saumik Bhattacharya

Department of Electronics and Electrical Communication Engineering Indian Institute of Technology Kharagpur, India

Numerical Integration Gradient Inversion Attacks Federated Learning

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Federated learning lets many clients train a shared model together without ever sending their private data to a central server. Each client shares only a model update, and this update should reveal far less about the client than its raw training examples would. This premise is what protects the privacy of the clients. Gradient inversion attacks challenge it directly by trying to reconstruct a client's private input images from the single update it shared. Under FedAvg, a client's update accumulates several local training steps, so the server sees only the two endpoints of a hidden weight trajectory. Recent gradient inversion attacks fit a surrogate model along the path between these two endpoints but they still read its gradient at a single point. We propose the Path-Integral Surrogate Model Extension (PI-SME) which treats the accumulated update as a path integral of the gradient field and approximates it by Gauss--Legendre quadrature over several nodes along a learnable Bézier path. On CIFAR-100 and FEMNIST images across a range of trajectory lengths and class-restricted batches PI-SME reconstructs the private inputs more faithfully than the strongest surrogate baseline on several inversion metrics and the matching loss.