Generative Flows with Matrix Exponential

Changyi Xiao, Ligang Liu
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:10452-10461, 2020.

Abstract

Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix exponential is a map from matrices to invertible matrices, this property is suitable for generative flows. Based on matrix exponential, we propose matrix exponential coupling layers that are a general case of affine coupling layers and matrix exponential invertible 1 x 1 convolutions that do not collapse during training. And we modify the networks architecture to make training stable and significantly speed up the training process. Our experiments show that our model achieves great performance on density estimation amongst generative flows models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-xiao20a, title = {Generative Flows with Matrix Exponential}, author = {Xiao, Changyi and Liu, Ligang}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {10452--10461}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/xiao20a/xiao20a.pdf}, url = {https://proceedings.mlr.press/v119/xiao20a.html}, abstract = {Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix exponential is a map from matrices to invertible matrices, this property is suitable for generative flows. Based on matrix exponential, we propose matrix exponential coupling layers that are a general case of affine coupling layers and matrix exponential invertible 1 x 1 convolutions that do not collapse during training. And we modify the networks architecture to make training stable and significantly speed up the training process. Our experiments show that our model achieves great performance on density estimation amongst generative flows models.} }
Endnote
%0 Conference Paper %T Generative Flows with Matrix Exponential %A Changyi Xiao %A Ligang Liu %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-xiao20a %I PMLR %P 10452--10461 %U https://proceedings.mlr.press/v119/xiao20a.html %V 119 %X Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix exponential is a map from matrices to invertible matrices, this property is suitable for generative flows. Based on matrix exponential, we propose matrix exponential coupling layers that are a general case of affine coupling layers and matrix exponential invertible 1 x 1 convolutions that do not collapse during training. And we modify the networks architecture to make training stable and significantly speed up the training process. Our experiments show that our model achieves great performance on density estimation amongst generative flows models.
APA
Xiao, C. & Liu, L.. (2020). Generative Flows with Matrix Exponential. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:10452-10461 Available from https://proceedings.mlr.press/v119/xiao20a.html.

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