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MechanismVideo · 16:21 — 17:51
In 2022, Liquid AI's team found the first-ever closed-form solution to the differential equations governing liquid neural network dynamics, a problem unsolved since Louis Lapicque's 1907 membrane potential equations, enabling the models to scale from hundreds to billions of neurons without numerical solvers.
Liquid AI solved a century-old open problem in neuronal dynamics equations in closed form, a breakthrough published in Nature Machine Intelligence that let them scale liquid networks from hundreds to billions of parameters. ✦ AI generated
Ramin Hasani · The Cognitive Revolution · 2026-07-04 · original ↗
starts at this moment · 16:21
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“So maybe for starters, how would you tell the kind of broad story of Liquid AI leading up to what you're doing today and what the company's mission is today?”
What if we just solve the whole system in closed form? Turns out the closed form solution for this type of equation hasn't existed since 1907. Around 2022, we solved the liquid neural network kind of interaction of neurons with each other in closed form for the first time. This became a Nature Machine Intelligence paper published in November of 2022.
verbatim transcript · starts at 16:21
Transcript · around this moment
16:21then the problem becomes scalability again you know like you you cannot really get to infinite precision with these numerical solvers. One idea that came to us was that what if we just solve the whole system in closed form you know like literally like just you have a differential equation system with these liquid neural networks each of them representing neural neural dynamics of let's say two cells that are
16:41exchanging information with each other at a certain level of abstraction and we saw that okay let's take this system and try to solve it in closed form turns out the closed form solution for this type of equation has hasn't existed since 1907 you know so 1907 there was a scientist called Louis Laik that actually modeled the membrane potential like how to model mathematically membrane potential kind of in in in in
17:06cells and that format of equation became like a fundamental of channel modeling like how information propagates through ion channels inside uh like inside a cell and then how neurons how neurotransmitters are getting propagated to the other one. So 1907 this was Louis Laik's um kind of you know membrane potential equation that is like an open uh differential equation and then really we've seen like some scientists called
17:33Hutchkin and Huxley they uh they started working on really biological kind of grounding this type of differential equation and adding a little bit more complexity into the model they developed a neuroscience model of one neuron how how actually a neuron reacts to let's say a membrane potential 1953 they started 1963 they won a Nobel Prize for the fact that they actually developed a better and a more accurate
17:58representation for a neural neuronal dynamics right and then from there on so that if in every textbook that you read this type of formats of equations they do not have a known closed form solution you know and this format like liquid neural networks were also part of that type of equations we for the first time we actually solved that and in this was like 2022 Around 2022, we solved the
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