Guaranteeing Error Bounds with Preservation of Derived Quantities in Compressive Autoencoders

Scientists conduct large-scale simulations to compute derived quantities from primary data. Thus, it is crucial that data compression techniques maintain bounded errors on these derived quantities or quantities of interest (QoI). Despite the notable performance of recent learned image/video compression approaches using neural networks, they do not guarantee reconstruction errors and cannot manage QoI. This work introduces the Guaranteed Autoencoder with Preserved QoI (GAEQ), which utilizes the interpretation that neural networks with piecewise linear units (PLUs) can be interpreted as a set of linear operators [1]. Although the operators are instance-specific, many instances share the same operator if they fall into the same region of the tessellation formed by PLUs.