Writing

Nov 15, 2026·13 min read·machine-learning·transformers·research·Blog

Adding a 4th Signal to Transformer Attention

A rigorous ablation of a small idea — what happens when a persistent, gated "purpose" state flows across transformer blocks? A real algorithmic finding with real engineering limits.

Apr 18, 2020·2 min read·biology·math·Blog

The Mathematics of Nature

Why do some cicadas emerge on a 13- or 17-year cycle — and never a 14- or 16-year one? Evolution seems to have a preference for prime numbers.