Why the quantum analogy shows up (unitarity = stability)

1:29:29cool, >> you know, but it's it's kind of it's kind of insane that like it was such a simple trick. It was just like, oh, just make the matrices like add up to one. >> Like just make sure it doesn't blow up. Like yeah, no, that was the whole point of ResNet and they just like did it again. [laughter] But it's not in the same way but like >> still you know the the the concept is very similar and it's it's very physics intuition as well because you know in quantum mechanics for this this reminded me a lot of quantum mechanics because um in quantum mechanics you have for example quantum states and then you have something called operators that operate on these quantum states like a time evolution operator would take your quantum state now and tell you what happens sometime later and sometime later and sometime later right Um,

1:30:12and these operators have a condition that they have to be unitary, meaning the probability has to add up to one. >> Okay. >> Okay. Cuz all of the outcomes need to be all of the outcomes. You can't have an operator that expands probability so that the sum of all probabilities is two. >> But there's a very central physical insight, right? It's like conservation of probability. You also have conservation of energy. In this case, they have like conservation of norm or something like that, you know? It's it's like a very simple insight. >> This is and and this goes back to the way you kind of always talk about and see the world which is like you can apply the the the >> the mental model that we have as physicists into other domains. >> Yeah. And it gives you it's like a way

1:30:54of thinking about stuff and systems. Yeah. And you know, order and progress and and it >> because it's funny that we again did the Princeton neuro story followed up by this one because there there it's like two different types >> types of manifold. Yeah. In this case, the manifold is like constrain it into this size. Yes. >> Right. There it was like a a a giant smooth sort of manifold. Here it's like just make it small. and and the what is and what was driving you know with the sort of deepse story it's it's obviously very much focused on like a commercial

1:31:34outcome uh the insight was >> not particularly uh not it didn't have a huge wow fac had wow factor not the the intuition >> yeah [clears throat] >> whereas I feel like with the the Princeton neuroscience story like the intuition >> intuition yeah was really really cool Um we I know every a lot of the AI community and the sort of tech community