symmetry-validation-suite

# Symmetry Validation Suite

## What Is It?

This skill provides **empirical tests to validate symmetry hypotheses**. Before committing to an equivariant architecture, you should verify that your claimed symmetries actually hold. This skill gives you concrete testing protocols and metrics.

**Why validate?** Wrong symmetry assumptions hurt model performance. Too much symmetry over-constrains; missing symmetry wastes capacity.

## Workflow

Copy this checklist and track your progress:

```
Symmetry Validation Progress:
- [ ] Step 1: List symmetry hypotheses to test
- [ ] Step 2: Design transformation test sets
- [ ] Step 3: Run invariance/equivariance tests
- [ ] Step 4: Verify group structure
- [ ] Step 5: Analyze data distribution under transforms
- [ ] Step 6: Document validation results
```

**Step 1: List symmetry hypotheses to test**

Gather candidate symmetries from previous discovery work. For each, document: the transformation type, whether invariance or equivariance is expected, and confidence level. Prioritize testing low-confidence hypotheses. If no hypotheses exist, work with user through domain analysis to identify candidate symmetries first.

**Step 2: Design transformation test sets**

For each symmetry, create test protocol: Sample representative inputs from data distribution. Define transformation sampling strategy (random rotations, all permutations, etc.). Determine appropriate sample sizes for statistical significance. Consider edge cases and boundary conditions. See [Transformation Sampling](#transformation-sampling) for guidance. For detailed methodology, consult [Methodology Details](./resources/methodology.md).

**Step 3: Run invariance/equivariance tests**

For invariance testing: Apply transformation T to input x, compute outputs f(x) and f(T(x)), measure error ||f(T(x)) - f(x)||. For equivariance testing: Compute f(T(x)) and T'(f(x)) where T' is the output transformation, measure error ||f(T(x)) - T'(f(x))||. Use [Testing Protocols](#testi