The Hidden Mathematics of Attention: Why Transformer Models Are Secretly Solving Differential Equations
Have you ever wondered what's really happening inside those massive transformer models that power ChatGPT and other AI systems? Recent research reveals something fascinating: attention mechanisms are implicitly solving differential equations—and this connection might be the key to the next generation of AI. I've been diving into a series of groundbreaking papers that establish a profound link between self-attention and continuous dynamical systems. Here's what I discovered: The Continuous Nature of Attention When we stack multiple attention layers in a transformer, something remarkable happens. As the number of layers approaches infinity, the discrete attention updates converge to a continuous flow described by an ordinary differential equation (ODE):
