Universality criteria for broken-isomorphism physical neural networks

Identify the necessary and sufficient architectural and dynamical features that enable universal computation or universal function approximation in broken-isomorphism physical neural networks, i.e., analog systems trained directly in their native physics without enforcing operation-by-operation mathematical isomorphism to digital neural networks.

Background

Broken-isomorphism physical neural networks (PNNs) depart from strict, operation-by-operation emulation of digital neural networks and instead train the native physical transformations of the underlying hardware. This paradigm has the potential to deliver major gains in speed and energy efficiency by leveraging the natural dynamics of physical systems.

A central theoretical gap is understanding what properties of such physical systems are required to approximate arbitrary functions or to perform universal computation. Clarifying these requirements would guide the design of scalable, high-performance PNN hardware and training strategies.