Formal Validation of Neural Networks as Timed Automata

Abstract

We propose a formalisation of spiking neural networks based on timed automata networks. Neurons are modelled as timed automata waiting for inputs on a number of different channels (synapses), for a given amount of time (the accumulation period). When this period is over, the current potential value is computed taking into account the current inputs and the previous decayed potential value. If the current potential overcomes a given threshold, the automaton emits a broadcast signal over its output channel, otherwise it restarts another accumulation period. After each emission, the automaton is constrained to remain inactive for a fixed refractory period. Spiking neural networks are formalised as sets of automata, one for each neuron, running in parallel and sharing channels according to the structure of the network. The model is then validated against some crucial properties defined via proper temporal logic formulae.