Neural Optimal Control for Representation Learning

The intriguing connections recently established between neural networks and dynamical systems have invited deep learning researchers to tap into the well-explored principles of differential calculus. Notably, the adjoint sensitivity method used in neural ordinary differential equations (Neural ODEs) has cast the training of neural networks as a control problem in which neural modules operate as continuous-time homeomorphic transformations of features. Typically, these methods optimize a single set of parameters governing the dynamical system for the whole data set, forcing the network to learn complex transformations that are functionally limited and computationally heavy. Instead, we propose learning a data-conditioned distribution of \emph{optimal controls} over the network dynamics, emulating a form of input-dependent fast neural plasticity. We describe a general method for training such models as well as convergence proofs assuming mild hypotheses about the ODEs and show empirically that this method leads to simpler dynamics and reduces the computational cost of Neural ODEs. We evaluate this approach for unsupervised image representation learning; our new "functional" auto-encoding model with ODEs, AutoencODE, achieves state-of-the-art image reconstruction quality on CIFAR-10, and exhibits substantial improvements in unsupervised classification over existing auto-encoding models.