I’m sorry to hear that you think the argumentation is weaker now.
the reader has to do the work to realize that indifference over functions is inappropriate
I don’t think that indifference over functions in particular is inappropriate. I think indifference reasoning in general is inappropriate.
I’m very happy with running counting arguments over the actual neural network parameter space
I wouldn’t call the correct version of this a counting argument. The correct version uses the actual distribution used to initialize the parameters as a measure, and not e.g. the Lebesgue measure. This isn’t appealing to the indifference principle at all, and so in my book it’s not a counting argument. But this could be terminological.
I’m sorry to hear that you think the argumentation is weaker now.
I don’t think that indifference over functions in particular is inappropriate. I think indifference reasoning in general is inappropriate.
I wouldn’t call the correct version of this a counting argument. The correct version uses the actual distribution used to initialize the parameters as a measure, and not e.g. the Lebesgue measure. This isn’t appealing to the indifference principle at all, and so in my book it’s not a counting argument. But this could be terminological.