symmetry-discovery-questionnaire_skill

Overview

This skill helps ML engineers and researchers discover and document symmetries in their data through a structured questionnaire and guided tests. It turns informal domain knowledge into concrete symmetry candidates (invariance or equivariance) and actionable next steps for model design. Use it to improve sample efficiency, generalization, and model inductive bias.

How this skill works

The skill walks you through six steps: domain classification, coordinate-system analysis, candidate transformation testing, physical-constraint analysis, output-behavior determination, and documentation. For each candidate transformation you answer targeted ‘‘If I transform the input, should the output change?’’ questions to label symmetries as invariances, equivariances, or non-symmetries and assign confidence. It produces a concise summary of identified, uncertain, and ruled-out transformations plus recommended validation and architectural actions.

When to use it

• You suspect invariances or equivariances would help model performance but aren’t sure which ones.
• Designing architectures (CNN, equivariant NN, GNN) and need the right inductive bias.
• Preparing dataset augmentation strategies and want principled transformations.
• Working on physics-based models where conservation laws may imply symmetries.
• Evaluating which transformations must be preserved for correct outputs.

Best practices

• Start by classifying the primary data type (image, point cloud, graph, time series, etc.) and document reasoning.
• Answer coordinate-system questions explicitly: origin, orientation, handedness, scale, and ordering.
• For each candidate transformation run a pragmatic test: invariance (output unchanged), equivariance (output changes predictably), or none.
• Record confidence and mark uncertain cases for empirical validation with controlled experiments.
• Map confirmed symmetries to group structures and adapt architecture or data augmentation accordingly.

Example use cases

• Image classification: determine whether translation, rotation, or reflection are invariances to reduce required data and select suitable convolutions or augmentation.
• 3D perception: identify SE(3)/E(3) vs. SO(3) needs for point-cloud models and choose rotation-equivariant layers.
• Molecular property prediction: check rotation, translation, reflection and atom-permutation symmetries to use E(3)-equivariant networks.
• Time series forecasting: test time-translation or periodicity to choose invariant pooling or cyclic features.
• Graph tasks: verify node-permutation invariance to justify message-passing GNN architectures.