Setting the Record Straight on Transformer Oversmoothing

Transformer-based models have recently become wildly successful across a diverse set of domains. At the same time, recent work has shown that Transformers are inherently low-pass filters that gradually oversmooth the inputs, reducing the expressivity of their representations. A natural question is: How can Transformers achieve these successes given this shortcoming? In this work we show that in fact Transformers are not inherently low-pass filters. Instead, whether Transformers oversmooth or not depends on the eigenspectrum of their update equations. Our analysis extends prior work in oversmoothing and in the closely-related phenomenon of rank collapse. We show that many successful Transformer models have attention and weights which satisfy conditions that avoid oversmoothing. Based on this analysis, we derive a simple way to parameterize the weights of the Transformer update equations that allows for control over its spectrum, ensuring that oversmoothing does not occur. Compared to a recent solution for oversmoothing, our approach improves generalization, even when training with more layers, fewer datapoints, and data that is corrupted.