It’s usually much easier to prove a theorem with necessary conditions (a => b) but good on them to be able to provide necessary and sufficient conditions (a <=> b). It just shows how difficult it is to get theoretical results to fully explain today’s very complex large deep neural networks.
The converse is what makes it strategically interesting too. Proving only the forward direction would just say Gaussian worlds are learnable. Proving uniqueness draws a fence: outside Gaussian, no guarantee, and the field is already probing that boundary. And yes, the assumptions are still miles from real networks, which is why I read the brittleness benchmark as the honest companion piece: theory names the target, the benchmark measures the miss.
It’s usually much easier to prove a theorem with necessary conditions (a => b) but good on them to be able to provide necessary and sufficient conditions (a <=> b). It just shows how difficult it is to get theoretical results to fully explain today’s very complex large deep neural networks.
The converse is what makes it strategically interesting too. Proving only the forward direction would just say Gaussian worlds are learnable. Proving uniqueness draws a fence: outside Gaussian, no guarantee, and the field is already probing that boundary. And yes, the assumptions are still miles from real networks, which is why I read the brittleness benchmark as the honest companion piece: theory names the target, the benchmark measures the miss.