DipDNN: Preserving Inverse Consistency and Approximation Efficiency for Invertible Learning

Consistent bi-directional inferences are the key for many machine learning applications. Without consistency, inverse learning-based inferences can cause fuzzy images, erroneous control signals, and cascading failure in SCADA systems. Since standard deep neural networks (DNNs) are not inherently invertible to offer consistency, some past methods reconstruct DNN architecture analytically for one-to-one correspondence but compromise key features such as universal approximation. Other work maintains the capability of universal approximation in DNNs via iterative numerical approximation. However, these methods limit their applications significantly due to Lipschitz conditions and issues of numerical convergence. The dilemma of the analytical and numerical methods is the incompatibility between nonlinear layer compositions and bijective function construction for inverse modeling. Based on the observation, we propose decomposed-invertible-pathway DNNs (DipDNN). It relaxes the redundant reconstruction of nested DNN in the former methods and eases the Lipschitz constraint. As a result, we strictly guarantee the consistency of global inverse modeling without harming DNN's capability for universal approximation. As numerical stability and generalizability are keys for controlling critical infrastructures, we integrate contractive property with a parallel structure for inductive biases, leading to stable performance. Numerical results show that DipDNN performs significantly better than past methods, thanks to its enforcement of inverse consistency, numerical stability, and physical regularization.