Permutation-Equivariant Neural Networks

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11 papers3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Degree Bounds for Separating Polynomial and Neural Invariants for Point Clouds
Oct 19, 2026Snir Hordan, Harm Derksen, Mircea Petrache +1Point Cloud Learning Equivariant Neural Networks
Technion – Israel Institute of Technology · Northeastern University · Pontificia Universidad Católica de Chile
Interfaces and Modules: A Scalable Representation for Weight-Space Learning across Architectures
Oct 15, 2026Michał Kozyra, Michael BronsteinWeight-Space Learning Weight-Space Analysis
University of Oxford · AITHYRA
CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope
Oct 9, 2026Gautier MartiPermutation-Equivariant Neural Networks Constrained Generative Modeling
Abu Dhabi Investment Authority (ADIA), Abu Dhabi, United Arab Emirates
Permutation-Equivariant Flow Matching for Alignment-Free Neural Weight Generation
Sep 26, 2026Arkadi Piven, Yam Eitan, Guy Bar-Shalom +5Permutation-Equivariant Neural Networks Flow Matching
Technion – Israel Institute of Technology · Technical University of Munich · Munich Center for Machine Learning +1
Universality and Approximation Rates of Graph Neural Networks with Random Features
Jul 29, 2026Lukas Gonon, Thilo Meyer-Brandis, Niklas WeberGraph Neural Networks Equivariant Neural Networks
School of Computer Science University of St. Gallen St. Gallen, 9000, Switzerland · Department of Mathematics LMU Munich Munich, 80333, Germany
EquiFusion: Kinematics-Agnostic Human Motion Prediction via Equivariant Latent Diffusion
Jul 13, 2026Cecilia Curreli, Florian Hofherr, Dominik Muhle +3Equivariant Neural Networks Human Motion Prediction
Technical University of Munich, Munich, Germany · Munich Center for Machine Learning, Munich, Germany
V2I Work Zone Geometry Reconstruction with Pose-Conditioned UWB Range Denoising
May 28, 2026Jiaxi Liu, Hangyu Li, Yang Cheng +73D Reconstruction Wireless Communications
Department of Civil & Environmental Engineering, University of Wisconsin-Madison, Madison, 53706, Wisconsin, United States
Permutation-preserving Functions and Neural Vecchia Covariance Kernels
May 6, 2026Jian Cao, Nian Liu, Ying LinGaussian Processes Kernel Methods
Department of Mathematics University of Houston Houston, TX 77047 · Department of Industrial and Systems Engineering University of Houston Houston, TX 77047
Any-Subgroup Equivariant Networks via Symmetry Breaking
Mar 19, 2026Abhinav Goel, Derek Lim, Hannah Lawrence +2Equivariant Neural Networks Equivariant GNNs
MIT · TUM · Flatiron Institute
Symbol-Equivariant Recurrent Reasoning Models
Mar 2, 2026Richard Freinschlag, Timo Bertram, Erich Kobler +2Permutation-Equivariant Neural Networks Sudoku Solving
ELLIS Unit Linz, LIT AI Lab & Institute for Machine Learning, Johannes Kepler University Linz, Austria · Clinical Research Institute for Medical AI, Johannes Kepler University Linz, Austria
Quantitative Approximation Rates for Group Equivariant Learning
Feb 23, 2026Jonathan W. Siegel, Snir Hordan, Hannah Lawrence +2Permutation-Equivariant Neural Networks Equivariant Neural Networks
Department of Mathematics, Texas A&M University, College Station, TX, 77840, USA · Faculty of Mathematics, Technion- Israel Institute of Technology, Haifa, 3200003, Israel · Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02139 USA

Oct 19, 2026J/K move · Enter open · S save

Degree Bounds for Separating Polynomial and Neural Invariants for Point Clouds

Snir Hordan, Harm Derksen, Mircea Petrache, Nadav Dym

Technion – Israel Institute of Technology · Northeastern University · Pontificia Universidad Católica de Chile

Point Cloud Learning Equivariant Neural Networks Permutation-Equivariant Neural Networks Message Passing Neural Networks

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Neural networks that respect the symmetries of point clouds commonly compute high-order representations of the rotation group to improve their expressivity. Such models are known to be universal, and thus able to separate any pair of point clouds, when using representations of sufficiently high order, yet no precise bound on this order, as a function of the number of points, was previously known. We establish the first quadratic lower and upper degree bounds for polynomials that separate point clouds of n points up to rotations and permutations. By showing Tensor Field Networks and MACE can express all invariant polynomials of a given degree with sufficient representation order, we additionally derive the first explicit, quadratic bound on the representation order sufficient for these architectures to be complete, replacing previous existence results with concrete guarantees. We further show that, under local regularity assumptions, point cloud separation can be achieved with a message-passing-based model using invariants whose degree depends only on the size of a local neighborhood, rather than on the size of the full point cloud. Finally, we provide counterexamples showing MACE must compute high order irreducible representations to separate locally regular point clouds.