[Python] Enum class with function values ends up with empty members list [duplicate]

It is my understanding that Python Enum values can be any Python object. However, when I run the following

from enum import Enum

def f():
pass

def g():
pass

def h():
pass

class LossType(Enum):
MSE = f
MAE = g
CROSS_ENTROPY = h

print(list(LossType.__members__.keys()))


the output is [].

The same does not happen when we use integer values:

class LossType(Enum):
MSE = 1
MAE = 2
CROSS_ENTROPY = 3
print(list(LossType.__members__.keys()))


produces ['MSE', 'MAE', 'CROSS_ENTROPY']. Why?

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