code: def norm_preserving_s(g, norm):
      """
      Find the value of s = ||x|| \sigma that corresponds to the value of
      \sigma that preserves the expected squared norm
      """
      sigma = sigma_star(g, norm)
      return sigma * norm
  
file_path: elu-gelu-kernels/code/dynamics/dynamics.py
imports: from ..kernels.nn_kernel_elu import NNKernelElu
  from ..kernels.nn_kernel_gelu import NNKernelGelu
  from ..kernels.nn_kernel_relu import NNKernelRelu
  import matplotlib
  import matplotlib.pyplot
  from matplotlib import rc
  import numpy
  import scipy.optimize
  from scipy.stats import multivariate_normal
label_desc: Use image node_id 3 for calling a global function with example usage: norm_preserving_s(g, norm) and returns: unknown