symmetry-discovery-questionnaire

SKILL.md

This skill helps you discover hidden symmetries in your data through a structured collaborative process. Symmetries are transformations that leave important properties unchanged - and building them into neural networks dramatically improves performance (better sample efficiency, faster convergence, improved generalization).

You don't need to know group theory. This skill guides you through domain-specific questions to uncover what symmetries might be present.

Ask user what their primary data type is. Use this table to identify likely symmetries and guide further questions. Images (2D grids) → likely translation, rotation, reflection. 3D data (point clouds, meshes) → likely SE(3), E(3). Molecules → E(3) + permutation + point groups. Graphs/Networks → permutation. Sets → permutation. Time series → time-translation, periodicity. Tabular → rarely symmetric. Physical system...

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