The most complex model we actually understand

3-Second Blueprint (English)

1. Mechanistic interpretability reverse-engineers small Transformers trained on modular addition (x + y mod 113) to see how they generalize.
2. Instead of memorizing tables, hidden-layer neurons encode numbers as sine and cosine waves across different rotational frequencies.
3. Subsequent layers combine sin(x)sin(y) and cos(x)cos(y) surfaces via trigonometric identities to compute clock-like modular sums.