We study two strange phenomena in auto-regressive Transformers: (1) the dominance of the first token in attention heads; (2) the occurrence of large outlier activations in the hidden states. We find that popular large language models, such as Llama attend maximally to the first token in 98% of attention heads, a behaviour we attribute to the softmax function. To mitigate this issue, we propose a reformulation of softmax to softmax-1. Furthermore, we identify adaptive optimisers, e.g. Adam, as the primary contributor to the large outlier activations and introduce OrthoAdam, a novel optimiser that utilises orthogonal matrices to transform gradients, to address this issue. Finally, not only do our methods prevent these phenomena from occurring, but additionally, they enable Transformers to sustain their performance when quantised using basic algorithms, something that standard methods are unable to do. In summary, our methods reduce the attention proportion on the first token from 65% to 3.3%, the activation kurtosis in the hidden states from 1657 to 3.1, and perplexity penalty under 4-bit weight quantisation from 3565 to 0.3.

Low-precision fine-tuning of language models has gained prominence as a cost-effective and energy-efficient approach to deploying large-scale models in various applications. However, this approach is susceptible to the existence of outlier values in activation. The outlier values in the activation can negatively affect the performance of fine-tuning language models in the low-precision regime since they affect the scaling factor and thus make representing smaller values harder. This paper investigates techniques for mitigating outlier activation in low-precision integer fine-tuning of the language models. Our proposed novel approach enables us to represent the outlier activation values in 8-bit integers instead of floating-point (FP16) values. The benefit of using integers for outlier values is that it enables us to use operator tiling to avoid performing 16-bit integer matrix multiplication to address this problem effectively. We provide theoretical analysis and supporting experiments to demonstrate the effectiveness of our approach in improving the robustness and performance of low-precision fine-tuned language models.