Models of Neural Information Squeezer (NIS) for causal emergence

Approximated calculation program for various EI (Dimensionally averaged EI, Eff, and EI) and related 
Quantities on Gaussian neural network
input variables：
input_size: the dimension of input to the func (neural network) (x_dim)
output_size: the dimension of the output of the func (neural network) (y_dim)
sigma_matrix: the inverse of the covariance matrix of the gaussian distribution on Y: dim: y_dim * y_dim
func: any function, can be a neural network
L the linear size of the box of x on one side (-L,L)
num_samples: the number of samples of the monte carlo integration on x

output variables：
d_EI： dimensionally averaged EI
eff： EI coefficient （EI/H_max)
EI: EI, effective information (common)
term1: - Shannon Entropy
term2: EI+Shannon Entropy (determinant of Jacobian)
-np.log(rho): - ln(\rho), where \rho=(2L)^{-output_size} is the density of uniform distribution

Code for calculating mutual information

Experimental code for Spring Oscillator with measurement noise

Experimental code for NIS work on Boolean Network, a networked system on which each node follows a discrete micro mechanism

Experimental code for NIS work on discrete markov chain

The experimental data of three groups of models, of which the vector diagram can be viewed in the folder 'plot'
The vector maps can correspond to the figures in the paper