Perceptrons and localization of attention's mean-field landscape
This work addresses theoretical understanding of attention mechanisms in Transformers for researchers in machine learning and mathematical modeling.
The paper investigates the effect of perceptron blocks in Transformers viewed as interacting particle systems, showing that critical points in the mean-field limit are typically atomic and localized on subsets of the sphere.
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 explicit energy, and one can make sense of the infinite context length (mean-field) limit thanks to Wasserstein gradient flows. In this paper we study the effect of the perceptron block in this setting, and show that critical points are generically atomic and localized on subsets of the sphere.