Symmetry

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Period ending 2026-09-21

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Equivariant Neural Networks

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Exact Equivariance

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Equivariance

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241 papers

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Planar Symmetric Pattern Generation
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The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space
Jun 1, 2026Bing-Cheng Chuang, I-Hsuan Chu, Bor-Jiun Lin +3Exact Equivariance Tangent Space
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Extreme dynamic symmetry enables omnidirectional and multifunctional robots
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Mapping Uncharted Symmetries: Machine Discovery in Combinatorics
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Physics-Aligned Canonical Equivariant Fourier Neural Operator under Symmetry-Induced Shifts
May 18, 2026Jiaxiao Xu, Changhong Mou, Yeyu Zhang +1Fourier Neural Operators Symmetry
The Symmetries of Three-Layer ReLU Networks
May 18, 2026Johanna Marie Gegenfurtner, Moritz Grillo, Guido MontúfarRectified Linear Unit Networks Symmetry
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Uncovering Symmetry Transfer in Large Language Models via Layer-Peeled Optimization
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Generating Symmetric Materials using Latent Flow Matching
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Universal Feature Selection with Noisy Observations and Weak Symmetry Conditions
May 10, 2026Dier Tang, Guangyue HanFeature Selection Symmetry
Compact SO(3) Equivariant Atomistic Foundation Models via Structural Pruning
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Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
May 8, 2026Yuxiang Luo, Andrew PerraultNeural Ordinary Differential Equations Velocity Field
Embedding Dimension Lower Bounds for Universality of Deep Sets and Janossy Pooling
May 8, 2026Ali Syed, Aditya Nambiar, Jonathan W. SiegelEmbedding Dimension Equivariant Neural Networks
Broken-symmetry shape discrimination on a driven Duffing ring
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SLayerGen: a Crystal Generative Model for all Space and Layer Groups
May 7, 2026Rees Chang, Andrew Novick, Ryan P Adams +1Crystal Structure Crystal
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May 7, 2026Yang Luo, Yan Gong, Yongsheng Gao +3Category-Level Object Pose Estimation Feed-Forward Visual Geometry Estimation
A Generalized Singular Value Theory for Neural Networks
May 7, 2026Brian Charles Brown, Robert Bridges, David Grimsman +2Singular Value Decomposition Equivariant Neural Networks
Geometric Kolmogorov--Arnold Network (GeoKAN)
May 7, 2026Abhijit Sen, Bikram Keshari Parida, Giridas Maiti +2Kolmogorov-Arnold Networks Geometry-Aware

Jun 1, 2026 · cs.LGJ/K move · Enter open · S save

Planar Symmetric Pattern Generation

Ning Lin, Luxi Chen, Huaguan Chen, Jiacheng Cen+3

Generating objects with specific symmetries is essential in various real-world scenarios. However, adapting existing 2D continuous representations to enforce planar group symmetry remains a challenge, as the transformation of non-reflective group elements may disrupt continuity. To overcome this limitation, we propose a symmetrization framework for arbitrary planar groups. Our method transforms any 2D continuous representation into a symmetric one while preserving continuity. We provide the mathematical formulation of this representation, demonstrate its approximation capability for symmetric functions, and detail the construction methodology. We validate our approach through three visual design tasks (pattern design, paper-cutting design and stylized topology design) and one material design task. Experiments confirm that our representation enables effective symmetry control and demonstrate its broader applicability.

Symmetry Representation Space

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