Operator-Discretized Representation for Temporal Neural Networks

Yasunao Katayama

Keywords: artificial neural network, spiking neural network, operator algebra, diagrammatic category theory

Abstract: This paper proposes a new representation of artificial neural networks to efficiently track their temporal dynamics as sequences of operator-discretized events. Our approach takes advantage of diagrammatic notions in category theory and operator algebra, which are known mathematical frameworks to abstract and discretize high-dimensional quantum systems, and adjusts the state space for classical signal activation in neural systems. The states for nonstationary neural signals are prepared at presynaptic systems with ingress creation operators and are transformed via synaptic weights to attenuated superpositions. The outcomes at postsynaptic systems are observed as the effects with egress annihilation operators (each adjoint to the corresponding creation operator) for efficient coarse-grained detection. The follow-on signals are generated at neurons via individual activation functions for amplitude and timing. The proposed representation attributes the different generations of neural networks, such as analog neural networks (ANNs) and spiking neural networks (SNNs), to the different choices of operators and signal encoding. As a result, temporally-coded SNNs can be emulated at competitive accuracy and throughput by exploiting proven models and toolchains for ANNs.

TL;DR: Propose a new representation of artificial neural networks to efficiently track their temporal dynamics as sequences of operator-discretized events