Resistor-diode circuits realize ReLU monotone operator equilibrium networks, and their exact gradient can be computed in the same hardware by linearizing the diodes.
Symmetry in linear physical systems
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abstract
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is studied from an input-output as well as from a state point of view. Geometrically, it turns out that they both define Lagrangian subspaces with corresponding generating functionals. Furthermore, the relations with time reversibility are analyzed. The system classes under consideration are expected to admit scalable control laws, and to be important building blocks in design.
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Circuit realization and hardware linearization of monotone operator equilibrium networks
Resistor-diode circuits realize ReLU monotone operator equilibrium networks, and their exact gradient can be computed in the same hardware by linearizing the diodes.