  In the context of lossy compression, Blau & Michaeli (2019) adopt a
mathematical notion of perceptual quality and define the information
rate-distortion-perception function, generalizing the classical rate-distortion
tradeoff. We consider the notion of universal representations in which one may
fix an encoder and vary the decoder to achieve any point within a collection of
distortion and perception constraints. We prove that the corresponding
information-theoretic universal rate-distortion-perception function is
operationally achievable in an approximate sense. Under MSE distortion, we show
that the entire distortion-perception tradeoff of a Gaussian source can be
achieved by a single encoder of the same rate asymptotically. We then
characterize the achievable distortion-perception region for a fixed
representation in the case of arbitrary distributions, identify conditions
under which the aforementioned results continue to hold approximately, and
study the case when the rate is not fixed in advance. This motivates the study
of practical constructions that are approximately universal across the RDP
tradeoff, thereby alleviating the need to design a new encoder for each
objective. We provide experimental results on MNIST and SVHN suggesting that on
image compression tasks, the operational tradeoffs achieved by machine learning
models with a fixed encoder suffer only a small penalty when compared to their
variable encoder counterparts.
