How does it help with neural network design?

By identifying the specific group, it tells developers which architecture patterns (like G-CNNs) to use to ensure the model respects the symmetries of the data.

What is the main purpose of the Symmetry Group Identifier?

It maps identified physical or geometric symmetries to formal mathematical groups, which is a critical step in designing equivariant or invariant neural network architectures.

Is this skill useful for 3D computer vision?

Absolutely. It specifically addresses 3D rotations (SO(3)) and rigid motions (SE(3)) which are fundamental to 3D vision, robotics, and protein folding tasks.

Which mathematical groups does this skill support?

The skill supports a wide range of groups including Cyclic (Cn), Dihedral (Dn), Symmetric (Sn), and continuous Lie groups like SO(2), SO(3), SE(3), and E(3).

Can it handle complex, combined symmetries?

Yes, it provides guidance on how to combine multiple symmetries using direct products (G × H) or semidirect products (G ⋊ H).

Symmetry Group Identifier

Name: Symmetry Group Identifier
Author: lyndonkl

bylyndonkl

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Data Science & ML

Maps identified symmetries to mathematical groups to formalize requirements for equivariant and invariant neural network architectures.

About

The Symmetry Group Identifier skill bridges the gap between domain-specific symmetry discovery and rigorous mathematical formalization. It provides a structured workflow to classify symmetries into discrete or continuous groups—such as Cyclic, Dihedral, or Lie groups like SO(3) and SE(3)—helping researchers and developers define the precise mathematical constraints needed for geometric deep learning. By identifying group properties like compactness and connectivity, and determining how groups combine via direct or semidirect products, it ensures that your AI architecture is built on a sound group-theoretic foundation.

Key Features

Classifies symmetries into discrete or continuous (Lie) group categories
Generates standardized symmetry group specifications for model architecture
Analyzes complex group combinations using direct and semidirect products
8 GitHub stars
Maps physical transformations to specific groups like Cn, Dn, Sn, SO(3), and SE(3)
Verifies mathematical group properties including compactness and commutativity

Use Cases

Identifying rotation and reflection symmetries for medical imaging AI
Designing equivariant neural networks for molecular dynamics and chemistry
Formalizing permutation invariance for graph and point cloud processing

About

Key Features

Classifies symmetries into discrete or continuous (Lie) group categories
Generates standardized symmetry group specifications for model architecture
Analyzes complex group combinations using direct and semidirect products
8 GitHub stars
Maps physical transformations to specific groups like Cn, Dn, Sn, SO(3), and SE(3)
Verifies mathematical group properties including compactness and commutativity

Use Cases

Identifying rotation and reflection symmetries for medical imaging AI
Designing equivariant neural networks for molecular dynamics and chemistry
Formalizing permutation invariance for graph and point cloud processing