To make sure I understand your notation, f1 is some set of weights, right? If it’s a set of multiple weights I don’t know what you mean when you write ∂y∂f1.

There should also exist at least some f1,f2 where C(f_1,f_1)≠C(f_2,f_2), since otherwise C no longer depends on the pair of redundant networks at all

(I don’t yet understand the purpose of this claim, but it seems to me wrong. If C(f1,f1)=C(f2,f2) for every f1,f2, why is it true that C(f1,f2) does not depend on f1 and f2 when f1≠f2?)

When I put it in a partial derivative, f1 represents the output of that subnetwork.

I mean to say that it means it no longer depends on the outputs of f1 and f2 when they’re equal, which is problematic if the purpose of this scheme is to provide stability for different possible functions.

As I said here, the idea here does not involve having some “dedicated” piece of logic C that makes the model fail if the outputs of the two malicious pieces of logic don’t satisfy some condition.

To make sure I understand your notation, f1 is some set of weights, right? If it’s a set of multiple weights I don’t know what you mean when you write ∂y∂f1.

(I don’t yet understand the purpose of this claim, but it seems to me wrong. If C(f1,f1)=C(f2,f2) for every f1,f2, why is it true that C(f1,f2) does not depend on f1 and f2 when f1≠f2?)

When I put it in a partial derivative, f1 represents the output of that subnetwork.

I mean to say that it means it no longer depends on the outputs of f1 and f2 when they’re equal, which is problematic if the purpose of this scheme is to provide stability for different possible functions.

As I said here, the idea here does not involve having some “dedicated” piece of logic C that makes the model fail if the outputs of the two malicious pieces of logic don’t satisfy some condition.