MIT Solved a Century-old Equation to Break the Computational Bottleneck Caused by ‘Liquid AI f.

In a Tuesday press release, Daniela Rus, MIT professor and CSAIL Director, stated that the new machine learning models they call ‘CfC’s [closed-form Continuous time] replace the differential equation defining computation of the neuron with a close form approximation. This preserves the beautiful properties of liquid networks without the necessity for numerical integration.” CFC models can be trained and predicted quickly and easily because they are compact, explicable, causal, and easy to train. 

They are a gateway to trusted machine learning for safety-critical purposes.

For those who don’t have a Ph.D. in Really Hard Math, differential equations can be used to describe the state of a system at different points or steps during the process. If you have a robot arm that moves from point A to point B, you can use differential equations to determine where it is at each step of the process. These equations can be very time-consuming to solve for each step. MIT’s “closed-form” solution solves this problem by functionally modeling every system description in a single computational step. As the MIT team explains,

Imagine if you have an end-to-end neural network that receives driving input from a camera mounted on a car. The network is trained to generate outputs, like the car’s steering angle. In 2020, the team solved this by using liquid neural networks with 19 nodes, so 19 neurons plus a small perception module could drive a car. A differential equation describes each node of that system. With the closed-form solution, if you replace it inside this network, it would give you the exact behavior, as it’s a good approximation of the actual dynamics of the system. They can thus solve the problem with an even lower number of neurons, which means it would be faster and less computationally expensive.

The team hopes to be able to construct models of the human mind that can measure in the millions, by solving the equation at the neuron level. This is not possible right now. This CfC model may be able to use the visual training it has received in one environment to adapt it to a completely new setting without any additional work. It’s called distribution generalization. This is something that current-gen models cannot do, but it would be a major step toward generalized AI systems.