Transcription of Neural Ordinary Differential Equations
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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.}
an implicit method, it has better guarantees than explicit methods such as Runge-Kutta but requires solving a nonlinear optimization problem at every step. This setup makes direct backpropagation through the integrator difficult. We implement the adjoint sensitivity method in Python’s autograd framework (Maclaurin et al.,2015).
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