3 accepted papers
We analyze the hardmax limit of self-attention dynamics for token embeddings in the zero-temperature regime $(\beta \to +\infty)$ and relate it to finite-$\beta$ behavior. In this limit, the update rule can be viewed as a Frank-Wolfe step for a quadratic objective over the convex hull of the current…
The forward pass of a Transformer can be seen as an interacting particle system on the unit sphere: time plays the role of layers, particles that of token embeddings, and the unit sphere idealizes layer normalization. In some weight settings the system can even be seen as a gradient flow for an expl…
Viewing Transformers as interacting particle systems, we describe the geometry of learned representations when the weights are not time-dependent. We show that particles, representing tokens, tend to cluster toward particular limiting objects as time tends to infinity. Using techniques from dynamica…