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Register a new userEscaping the Gradient Vanishing: Periodic Alternatives of Softmax in Attention Mechanism
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Added by
Shulun Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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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The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalize the Gumbel-Softmax trick to combinatorial spaces. Our framework is a unified perspective on existing relaxed estimators for perturbation models, and it contains many novel relaxations. We design structured relaxations for subset selection, spanning trees, arborescences, and others. When compared to less structured baselines, we find that stochastic softmax tricks can be used to train latent variable models that perform better and discover more latent structure.
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Fast arbitrary neural style transfer has attracted widespread attention from academic, industrial and art communities due to its flexibility in enabling various applications. Existing solutions either attentively fuse deep style feature into deep content feature without considering feature distributions, or adaptively normalize deep content feature according to the style such that their global statistics are matched. Although effective, leaving shallow feature unexplored and without locally considering feature statistics, they are prone to unnatural output with unpleasing local distortions. To alleviate this problem, in this paper, we propose a novel attention and normalization module, named Adaptive Attention Normalization (AdaAttN), to adaptively perform attentive normalization on per-point basis. Specifically, spatial attention score is learnt from both shallow and deep features of content and style images. Then per-point weighted statistics are calculated by regarding a style feature point as a distribution of attention-weighted output of all style feature points. Finally, the content feature is normalized so that they demonstrate the same local feature statistics as the calculated per-point weighted style feature statistics. Besides, a novel local feature loss is derived based on AdaAttN to enhance local visual quality. We also extend AdaAttN to be ready for video style transfer with slight modifications. Experiments demonstrate that our method achieves state-of-the-art arbitrary image/video style transfer. Codes and models are available.
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