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第305行： − = 参考文献 = − − # Dinh L., Sohl-Dickstein J., Bengio S. Density Estimation Using Real NVP. International Conference on Learning Representations (ICLR), 2017. https://arxiv.org/abs/1605.08803 − # Chen S. S., Gopinath R. A. Gaussianization. Advances in Neural Information Processing Systems (NIPS), 2000. − # Tabak E. G., Vanden-Eijnden E. Density Estimation by Dual Ascent of the Log-Likelihood. Communications in Mathematical Sciences, 2010, 8(1): 217-233. − # Dinh L., Krueger D., Bengio Y. NICE: Non-linear Independent Components Estimation. ICLR 2015 Workshop, 2014. https://arxiv.org/abs/1410.8516 − # Draxler F., Wahl S., Schnörr C., Köthe U. On the Universality of Volume-Preserving and Coupling-Based Normalizing Flows. Proceedings of the 41st International Conference on Machine Learning (ICML), PMLR 235, 2024. − # Ho J., Chen X., Srinivas A., Duan Y., Abbeel P. Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design. ICML, 2019. − # Kingma D. P., Dhariwal P. Glow: Generative Flow with Invertible 1×1 Convolutions. NeurIPS, 2018. − # Rezende D. J., Mohamed S. Variational Inference with Normalizing Flows. ICML, 2015. − # Papamakarios G., Pavlakou T., Murray I. Masked Autoregressive Flow for Density Estimation. NIPS, 2017. − # Grathwohl W., Chen R. T. Q., Bettencourt J., Sutskever I., Duvenaud D. FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models. ICLR, 2019. − # Chen R. T. Q., Behrmann J., Duvenaud D., Jacobsen J.-H. Residual Flows for Invertible Generative Modeling. NeurIPS, 2019. − # Papamakarios G., Nalisnick E., Rezende D. J., Mohamed S., Lakshminarayanan B. Normalizing Flows for Probabilistic Modeling and Inference. Journal of Machine Learning Research, 2021, 22(57): 1-64. − # Zhang J., Liu K. Neural Information Squeezer for [[Causal Emergence]]. [[Entropy]], 2022, 25(1): 26. − # Yang M., Wang Z., Liu K., Rong Y., Yuan B., Zhang J. Finding Emergence in Data by Maximizing [[Effective Information]]. National Science Review, 2025, 12(1): nwae279.
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消融实验表明，若将 RealNVP 替换为普通前馈网络或 VAE，多步预测误差显著上升；在分布外泛化测试中，仅基于 RealNVP 的 NIS/NIS+ 保持了低误差。论文指出：'''可逆神经网络作为编码器和解码器是必需的'''。在 NIS+ 中，RealNVP 继续承担编码–解码功能，而 EI 最大化等改进发生在投影后的宏观动力学空间上，不改动 INN 模块本身<ref name="NISPlus2025">{{cite journal|author1=Yang M.|author2=Wang Z.|author3=Liu K.|author4=Rong Y.|author5=Yuan B.|author6=Zhang J.|title=Finding Emergence in Data by Maximizing Effective Information|journal=National Science Review|year=2025|volume=12|issue=1|page=nwae279}}</ref>。
消融实验表明，若将 RealNVP 替换为普通前馈网络或 VAE，多步预测误差显著上升；在分布外泛化测试中，仅基于 RealNVP 的 NIS/NIS+ 保持了低误差。论文指出：'''可逆神经网络作为编码器和解码器是必需的'''。在 NIS+ 中，RealNVP 继续承担编码–解码功能，而 EI 最大化等改进发生在投影后的宏观动力学空间上，不改动 INN 模块本身<ref name="NISPlus2025">{{cite journal|author1=Yang M.|author2=Wang Z.|author3=Liu K.|author4=Rong Y.|author5=Yuan B.|author6=Zhang J.|title=Finding Emergence in Data by Maximizing Effective Information|journal=National Science Review|year=2025|volume=12|issue=1|page=nwae279}}</ref>。
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