Scaled RBF Attention: Trading Dot Products for Euclidean Distance

If you crack open the architecture of almost any modern Transformer, you will find Scaled Dot-Product Attention (SDPA) sitting at its core. We rarely second-guess it. It is heavily optimized by hardware accelerators, it scales beautifully, and empirically, it runs the world. But if you look closely at the underlying math, treating a dot product as a proxy for "similarity" carries some subtle…