# Spike-based symbolic computations on bit strings and numbers

**C. Kraisnikovic, W. Maass, and R. Legenstein**

### Abstract:

The brain uses recurrent spiking neural networks for higher cognitive functions
such as symbolic computations, in particular, mathematical computations. We
review the current state of research on spike-based symbolic computations of
this type. In addition, we present new results which show that surprisingly
small spiking neural networks can perform symbolic computations on bit
sequences and numbers and even learn such computations using a biologically
plausible learning rule. The resulting networks operate in a rather low
firing rate regime, where they could not simply emulate artificial neural
networks by encoding continuous values through firing rates. Thus, we propose
here a new paradigm for symbolic computation in neural networks that provides
concrete hypotheses about the organization of symbolic computations in the
brain. The employed spike-based network models are the basis for drastically
more energy-efficient computer hardware – neuromorphic hardware. Hence, our
results can be seen as creating a bridge from symbolic artificial
intelligence to energy-efficient implementation in spike-based neuromorphic
hardware.

**Reference:** C. Kraisnikovic, W. Maass, and R. Legenstein.
Spike-based symbolic computations on bit strings and numbers.
*bioRxiv*, 2021.