Escaping the Gradient Vanishing: Periodic Alternatives of Softmax in Attention Mechanism

• URL: http://arxiv.org/abs/2108.07153v1
• Date: Mon, 16 Aug 2021 15:26:31 GMT
• Title: Escaping the Gradient Vanishing: Periodic Alternatives of Softmax in Attention Mechanism
• Authors: Shulun Wang, Bin Liu and Feng Liu
• Abstract summary: Softmax is widely used in neural networks for multiclass classification, gate structure and attention mechanisms. In this work, we suggest that replacing the exponential function by periodic functions, and we delve into some potential periodic alternatives of Softmax. Our method is proved to be able to alleviate the gradient problem and yield substantial improvements compared to Softmax and its variants.
• Score: 8.007523868483085
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Softmax is widely used in neural networks for multiclass classification, gate structure and attention mechanisms. The statistical assumption that the input is normal distributed supports the gradient stability of Softmax. However, when used in attention mechanisms such as transformers, since the correlation scores between embeddings are often not normally distributed, the gradient vanishing problem appears, and we prove this point through experimental confirmation. In this work, we suggest that replacing the exponential function by periodic functions, and we delve into some potential periodic alternatives of Softmax from the view of value and gradient. Through experiments on a simply designed demo referenced to LeViT, our method is proved to be able to alleviate the gradient problem and yield substantial improvements compared to Softmax and its variants. Further, we analyze the impact of pre-normalization for Softmax and our methods through mathematics and experiments. Lastly, we increase the depth of the demo and prove the applicability of our method in deep structures.

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