Differentiable Implicit Layers

In this paper, we introduce an efficient backpropagation scheme for non-constrained implicit functions. These functions are parametrized by a set of learnable weights and may optionally depend on some input; making them perfectly suitable as a learnable layer in a neural network. We demonstrate our scheme on different applications: (i) neural ODEs with the implicit Euler method, and (ii) system identification in model predictive control.