Implicit Deep Learning

We define a new class of "implicit" deep learning prediction rules that generalize the recursive rules of feedforward neural networks. These models are based on the solution of a fixed-point equation involving a single a vector of hidden features, which is thus only implicitly defined. The new framework greatly simplifies the notation of deep learning, and opens up new possibilities, in terms of novel architectures and algorithms, robustness analysis and design, interpretability, sparsity, and network architecture optimization.