human
2. Define annealing distributions
Here we'll be annealing between two unnormalized Gaussian distributions with geometric mean intermediates.
They have the same variances, so they should have the same normalizing constants.
assistant
#Here is the Python program you requested.
num_intermediates = 25
betas = np.linspace(0,1,num_intermediates+2)
dim=1

def initial_density(x):
    return np.exp(-((x)**2).sum()/2)

def draw_from_initial():
    return npr.randn(dim)

def target_density(x):
    return np.exp(-((x-4)**2).sum()/2)
    
class GeometricMean():
    def __init__(self,initial,target,beta):
        self.initial = initial
        self.target = target
        self.beta = beta
    
    def __call__(self,x):
        f1_x = self.initial(x)
        fT_x = self.target(x)
        return f1_x**(1-self.beta) * fT_x**self.beta

annealing_distributions = [GeometricMean(initial_density,target_density,beta) for beta in betas]