Transformer Training Instability of Softmax and Lipschitz-Kernel Attentions

JongHyun Hong, Sungyoon Lee

Keywords: Transformer, linear attention, self-attention, optimization, training stability, entropy collapse

Abstract: Transformers have been making significant progress across various domains, and recently, with scaling up of models like LLMs, they have achieved even greater success. Recent findings have shown that the softmax function in the self-attention used to re-weight the attention logits into probability vectors causes \emph{attention entropy collapse}, where the attention is concentrated on a single token, and it leads to unstable training. In this work, we first demonstrate that the (non-Lipschitz) softmax-based attention leads to the attention entropy collapse but the \emph{Lipschitz-kernel}-based attention does not. We show that the Lipschitzness of the attention plays an important role in keeping the attention entropy stable regardless of the variance of the attention logits. Moreover, we argue that the underlying reason why the attention entropy collapse leads to the training instability is that as the attention probabilities become more concentrated, it causes the attention matrix to gradually increase, leading to gradient exploding.

Primary Area: optimization

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Submission Number: 6813