Deep feedforward functionality by equilibrium-point control in a shallow recurrent network.

Celestine Preetham Lawrence

Keywords: recurrent physical network, combinational logic, equilibrium-point control, piecewise-linear, parity function

Abstract: Recurrent neural network based machine learning systems are typically employed for their sequential functionality in handling time-varying signals, such as for speech processing. However, neurobiologists find recurrent connections in the vision system and debate about equilibrium-point control in the motor system. Thus, we need a deeper understanding of how recurrent dynamics can be exploited to attain combinational stable-input stable-output functionality. Here, we study how a simplified Cohen-Grossberg neural network model can realize combinational multi-input Boolean functionality. We place our problem within the discipline of algebraic geometry, and solve a special case of it using piecewise-linear algebra. We demonstrate a connectance-efficient realization of the parity function as a proof-of-concept. Small-scale systems of this kind can be easily built, say for hobby robotics, as a network of two-terminal devices of resistors and tunnel diodes. Large-scale systems may be energy-efficiently built as an interconnected network of multi-electrode nanoclusters with non-monotonic transport mechanisms.