Limitations of Normalization in Attention Mechanism
Authors: name: Timur Mudarisov, name: Mikhail Burtsev, name: Tatiana Petrova, name: Radu State

This paper investigates the limitations of the normalization in attention
mechanisms. We begin with a theoretical framework that enables the
identification of the model's selective ability and the geometric separation
involved in token selection. Our analysis includes explicit bounds on distances
and separation criteria for token vectors under softmax scaling. Through
experiments with pre-trained GPT-2 model, we empirically validate our
theoretical results and analyze key behaviors of the attention mechanism.
Notably, we demonstrate that as the number of selected tokens increases, the
model's ability to distinguish informative tokens declines, often converging
toward a uniform selection pattern. We also show that gradient sensitivity
under softmax normalization presents challenges during training, especially at
low temperature settings. These findings advance current understanding of
softmax-based attention mechanism and motivate the need for more robust
normalization and selection strategies in future attention architectures.