The Neural Information Squeezer (NIS) is a machine learning framework designed for identifying causal emergence within datasets. Causal emergence represents a theoretical construct that aims to quantify the emergence phenomena within complex systems[1]. Given that the underlying mechanisms of the data are often obscure, and that abundant data can be procured through observation, a machine learning framework is of considerable significance in the study of complex systems, particularly with respect to their emergent characteristics.
It represents the original framework of this series[2]. In the context of multi-scale modeling, we employ an encoder to project micro-data onto a macro latent space, which is composed of an Invertible Neural Network (INN) and a projection mechanism. Subsequently, macro-states are forecasted through a dynamics learner denoted as f. During the decoding phase, we introduce a normal distribution to augment its dimensionality. This enables us to compute the discrepancy between predictions and actual targets at the micro-level.
However, the NIS does not address the optimization of effective information within macro dynamics. Following the demonstration of certain mathematical theories, we have introduced an enhanced framework, denoted as NIS+, designed to identify causal emergence by maximizing the effective information. Given multivariable time series as inputs, it is capable of outputting the degree of causal emergence, the optimal coarse-graining strategy, as well as the macro-dynamics or emergent patterns. Further details can be found in reference[3].
The framework is currently under investigation.
ei: The function files used for calculating effective information and mutual information.
exp: The running code for the four experiments presented in the article. (Currently, only the SIR experiment has been demonstrated. For further information regarding the remaining experiments' code, please contact the author, Mingzhe Yang, at [email protected].)
models_new.py: The core code modules of the neural network.
resources: The image files.
results: Some of the results stored from the experimental runs within the article.
[1]Yuan, B., Zhang, J., Lyu, A., Wu, J., Wang, Z., Yang, M., Liu, K., Mou, M., & Cui, P. (2024). Emergence and Causality in Complex Systems: A Survey of Causal Emergence and Related Quantitative Studies. Entropy, 26(2), 108. https://doi.org/10.3390/e26020108
[2]Zhang, J., & Liu, K. (2022). Neural Information Squeezer for Causal Emergence. Entropy, 25(1), 26. https://doi.org/10.3390/e25010026
[3]Yang, M., Wang, Z., Liu, K., Rong, Y., Yuan, B., & Zhang, J. (2023). Finding emergence in data by maximizing effective information (arXiv:2308.09952). arXiv. http://arxiv.org/abs/2308.09952