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Neural Ordinary Differential Equations

Neural Ordinary Differential Equations Ricky T. Q. Chen*, Yulia Rubanova*, Jesse Bettencourt*, David Duvenaud University of Toronto, Vector Institute {rtqichen, rubanova, jessebett, [ ] 15 Jan 2019. Abstract We introduce a new family of deep Neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a Neural network. The output of the network is computed using a black- box Differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed.}

directly through a Runge-Kutta integrator, re-ferred to as RK-Net. Table1shows test error, number of parameters, and memory cost. Ldenotes the number of layers in the ResNet, and L~ is the number of function evaluations that the ODE solver requests in a single forward pass, which can be interpreted as an implicit number of layers. We find

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