  We present a novel information-theoretic framework, termed as TURBO, designed
to systematically analyse and generalise auto-encoding methods. We start by
examining the principles of information bottleneck and bottleneck-based
networks in the auto-encoding setting and identifying their inherent
limitations, which become more prominent for data with multiple relevant,
physics-related representations. The TURBO framework is then introduced,
providing a comprehensive derivation of its core concept consisting of the
maximisation of mutual information between various data representations
expressed in two directions reflecting the information flows. We illustrate
that numerous prevalent neural network models are encompassed within this
framework. The paper underscores the insufficiency of the information
bottleneck concept in elucidating all such models, thereby establishing TURBO
as a preferable theoretical reference. The introduction of TURBO contributes to
a richer understanding of data representation and the structure of neural
network models, enabling more efficient and versatile applications.
