In 2022 we found the first-ever closed-form solution to the liquid neural network differential equations — a problem open since 1907 — which let us scale from hundreds of neurons to billions without numerical solvers.

18:23liquid neural network kind of interaction of neurons with each other in closed form for the first time. This became a nature machine intelligence paper uh published in November of 2022. This is called the closed form continuous time uh systems you know like this is this liquid neural networks in closed form and uh the closed form I mean it has massive implications. Why? Because now I don't need to use any

18:44numerical solvers to actually run a liquid neural networks. I can now have not only hundreds of neurons but now I have I can have billions of neurons next to each other and I can actually scale these computation still keeping the nonlinearity as part of this thing you know then then in in January of act actually beginning of February of 2023 an article came out of a quantum magazine you know about let's

19:10say me and my co-founder Matias we um it was about a profile about like oh the implications of some having some close form solution finally on on on a on on neuron dynamics you know like and how important this can be for both machine learning and also like for brain science as a whole and then so my inbox was full of VCs you know Silicon Valley started

19:30like talk like everybody wanted to throw like a term sheet at us like to really get started and and really scale this technology because this was fundamentally different than a transformer-based architecture and attentionbased architecture this was grounded in biology like the type of math that we have around the same times we Alternative models are coming out like state space models like you know like like the you know like you've

19:52you've seen like faster iterations of state space models like convolutional neural networks that came out like to be like scalable all of them in a linear form because the scalability of alternative models you have to linearize them and then you can scale them you know and we have something here that is also another category you know like it adds some operators that we learned from biology and from physics as we we grew

20:14the research and we got to the point where we can now become very competitive and uh and and you know like building models like for solving more and more general purpose tasks and when I say more and more general purpose task I'm talking about modeling signals beyond predictive performance modeling signals for language for audio and for vision in a way that human humans understand right like that's the for that's the complex