Here I mean function in the mathematical sense: a mapping from inputs X to outputs Y. Solutions that minimize hidden activity and readout-weight norms (constraints that can be viewed as proxies for energetic costs) are maximally noise-robust and guaranteed to have identifiable geometry

I absolutely think so! We have previously shown analytically that function and representation are fundamentally dissociable, but that robustness to parameter noise can force the representations of networks implementing the same function to converge: openreview.net/pdf?id=YucuA...

Fun! You may enjoy our recent analytical work showing that function and representation are fundamentally dissociable; but that representational alignment can emerge under additional constraints such as robustness to parameter noise:

openreview.net/pdf?id=YucuA...