Document that tfp.distributions.MixtureSameFamily uses softmax on the fractions

Hello, it tooks me a whlie to understand this:

my_pdf = tfp.layers.MixtureNormal(3, 1)(np.array([1/3, 0/3, 2/3,
                                 4,  # mean1
                                 5,  # std1
                                 6,  # mean2
                                 7,  # std2
                                 8,  # mean3
                                 9   # std3
                                 ], dtype=float))
print(my_pdf.mixture_distribution.probs_parameter())
print(my_pdf.components_distribution.mean().numpy())
print(my_pdf.components_distribution.variance().numpy())

tf.Tensor([0.3213219  0.23023722 0.44844085], shape=(3,), dtype=float32)
[[4.]
 [6.]
 [8.]]
[[25.067198]
 [49.012764]
 [81.00221 ]]

Where the first three numbers are coming from? Why they are not 1/3, 0/3, 2/3? Then I look to the code and found this

https://github.com/tensorflow/probability/blob/main/tensorflow_probability/python/distributions/mixture_same_family.py#LL343C20-L343C39

Why a softmax is applied to the fractions? E.g.

np.exp(tf.math.log_softmax([1/3, 0/3, 2/3]))

I am not sure why this is done, but please can you document it?
I undestand you want the numbers to sum to 1, but I guess this can be requested.

In addition I have recently discovered that also a softsum is applied to the stds

Start with the linked code in tensorflow_probability/python/distributions/mixture_same_family.py around line 343 and reproduce the issue's MixtureNormal example. Document how the mixture fractions and component scale values are transformed, with wording that explains the observed outputs and makes the expected parameterization clear.