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→为什么使用可逆神经网络？
解码器可以被视为条件概率 <math>Pr(\hat{\mathbf{x}}_{t+1} | \mathbf{y}(t+1))</math> 的生成模型<ref name=":3">Li, S.H.; Wang, L. Neural Network Renormalization Group. Phys. Rev. Lett. 2018, 121, 260601.</ref><ref name=":4">Hu,H.; Wu,D.; You, Y.Z.; Olshausen, B.; Chen, Y. RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse prior. Mach. Learn. Sci. Technol. 2022, 3, 035009.</ref>，而编码器执行重整化过程。
解码器可以被视为条件概率 <math>Pr(\hat{\mathbf{x}}_{t+1} | \mathbf{y}(t+1))</math> 的生成模型<ref name=":3">Li, S.H.; Wang, L. Neural Network Renormalization Group. Phys. Rev. Lett. 2018, 121, 260601.</ref><ref name=":4">Hu,H.; Wu,D.; You, Y.Z.; Olshausen, B.; Chen, Y. RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse prior. Mach. Learn. Sci. Technol. 2022, 3, 035009.</ref>，而编码器执行重整化过程。
==为什么使用可逆神经网络？==
==使用可逆神经网络的原因==
[[文件:Pasted image 20240519112728.png|居中|600px|'''图2.''' 双射器基本模块的 RealNVP 神经网络 <math> (\psi) </math> 实现。]]
[[文件:Pasted image 20240519112728.png|居中|600px|'''图2.''' 双射器基本模块的 RealNVP 神经网络 <math> (\psi) </math> 实现。]]
有多种方法可以实现可逆神经网络<ref>Teshima, T.; Ishikawa, I.; Tojo, K.; Oono, K.; Ikeda, M.; Sugiyama, M. Coupling-based invertible neural networks are universal diffeomorphism approximators. Adv. Neural Inf. Process. Syst. 2020, 33, 3362–3373.</ref><ref>Teshima, T.; Tojo, K.; Ikeda, M.; Ishikawa, I.; Oono, K. Universal approximation property of neural ordinary differential equations. arXiv 2017, arXiv:2012.02414.</ref>。这里选择如图2所示的RealNVP模块<ref name=":0">Dinh, L.; Sohl-Dickstein, J.; Bengio, S. Density estimation using real nvp. arXiv 2016, arXiv:1605.08803.</ref>来具体实现可逆计算。
有多种方法可以实现可逆神经网络<ref>Teshima, T.; Ishikawa, I.; Tojo, K.; Oono, K.; Ikeda, M.; Sugiyama, M. Coupling-based invertible neural networks are universal diffeomorphism approximators. Adv. Neural Inf. Process. Syst. 2020, 33, 3362–3373.</ref><ref>Teshima, T.; Tojo, K.; Ikeda, M.; Ishikawa, I.; Oono, K. Universal approximation property of neural ordinary differential equations. arXiv 2017, arXiv:2012.02414.</ref>。这里选择如图2所示的RealNVP模块<ref name=":0">Dinh, L.; Sohl-Dickstein, J.; Bengio, S. Density estimation using real nvp. arXiv 2016, arXiv:1605.08803.</ref>来具体实现可逆计算。