symmetry-discovery-questionnaire

# Symmetry Discovery Questionnaire

## What Is It?

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.

## Workflow

Copy this checklist and track your progress:

```
Symmetry Discovery Progress:
- [ ] Step 1: Classify your domain and data type
- [ ] Step 2: Analyze coordinate system choices
- [ ] Step 3: Test candidate transformations
- [ ] Step 4: Analyze physical constraints
- [ ] Step 5: Determine output behavior under transformations
- [ ] Step 6: Document symmetry candidates
```

**Step 1: Classify your domain and data type**

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 systems → conservation laws imply symmetries. For detailed worked examples by domain, consult [Domain Examples](./resources/domain-examples.md).

**Step 2: Analyze coordinate system choices**

Guide user through coordinate analysis questions: Is there a preferred origin? (NO → translation invariance). Is there a preferred orientation? (NO → rotation invariance). Is there a preferred handedness? (NO → reflection invariance). Is there a preferred scale? (NO → scale invariance). Is element ordering meaningful? (NO → permutation invariance). Document each answer with reasoning.

**Step 3: Test candidate transformations**

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