Michele Nardin, James W Phillips, William F Podlaski, Sander W KeeminkPlease use the format "First name initials family name" as in "Marie S. Curie, Niels H. D. Bohr, Albert Einstein, John R. R. Tolkien, Donna T. Strickland"
<p>The brain efficiently performs nonlinear computations through its intricate networks<br>of spiking neurons, but how this is done remains elusive. While nonlinear computations<br>can be implemented successfully in spiking neural networks, this requires supervised<br>training and the resulting connectivity can be hard to interpret. In contrast, the<br>required connectivity for any computation in the form of a linear dynamical system can<br>be directly derived and understood with the spike coding network (SCN) framework.<br>These networks also have biologically realistic activity patterns and are highly robust to<br>cell death. Here we extend the SCN framework to directly implement any polynomial<br>dynamical system, without the need for training. This results in networks requiring<br>a mix of synapse types (fast, slow, and multiplicative), which we term multiplicative<br>spike coding networks (mSCNs). Using mSCNs, we demonstrate how to directly derive<br>the required connectivity for several nonlinear dynamical systems. We also show how<br>to carry out higher-order polynomials with coupled networks that use only pair-wise<br>multiplicative synapses, and provide expected numbers of connections for each synapse<br>type. Overall, our work demonstrates a novel method for implementing nonlinear<br>computations in spiking neural networks, while keeping the attractive features of<br>standard SCNs (robustness, realistic activity patterns, and interpretable connectivity).<br>Finally, we discuss the biological plausibility of our approach, and how the high accuracy<br>and robustness of the approach may be of interest for neuromorphic computing.</p>
nonlinear computation, spiking neural network, robustness, multiplicative synapses
