Predicting the Computational Performance of Neural Circuits Modeled with Simple Digital Neurons

....................................................................................................................................... v CHAPTER 1: INTRODUCTION ............................................................................................................ 1 1.1 Artificial neural networks ....................................................................................................... 1 1.2 Spiking neural networks ......................................................................................................... 1 1.3 Hardware implementation of neural networks ..................................................................... 2 1.4 Liquid State Machines ............................................................................................................ 4 1.5 Readouts ................................................................................................................................ 7 1.6 Measurable qualities of a neural circuit ................................................................................ 8 1.6.1 Firing rates....................................................................................................................... 9 1.6.2 Lyapunov’s exponent .................................................................................................... 10 1.6.3 Class separation ............................................................................................................ 11 1.6.4 Spectral radius ............................................................................................................... 12 1.6.5 Kernel-quality and VC dimension .................................................................................. 12 1.7 Objective and motivation .................................................................................................... 13 1.8 Thesis outline ....................................................................................................................... 13 CHAPTER 2: PREDICTING THE COMPUTATIONAL PERFORMANCE OF A NEURAL CIRCUIT A MATHEMATICAL BACKGROUND .................................................................................................... 15 2.1 The two defining properties of a neural circuit ................................................................... 15 2.2 Kernel-quality ....................................................................................................................... 15 2.3 Generalization property ....................................................................................................... 16 2.3.1 Shattering a set ............................................................................................................. 17