Solving the Linearly Inseparable XOR Problem with Spiking Neural Networks

Spiking Neural Networks (SNN) are third generation neural networks and are considered to be the most biologically plausible so far. As a relative newcomer to the field of artificial learning, SNNs are still exploring their own capabilities, as well as dealing with the singular challenges that arise from attempting to be computationally applicable and biologically accurate. This paper explores the possibility of a different approach to solving linearly inseparable problems by using networks of spiking neurons. To this end two experiments were conducted. The first experiment was an attempt in creating a spiking neural network that would mimic the functionality of logic gates. The second experiment relied on the addition of receptive fields in order to filter the input. This paper demonstrates that a network of spiking neurons utilizing receptive fields or routing can successfully solve the XOR linearly inseparable problem

Stochastic resonance and finite resolution in a network of leaky integrate-and-fire neurons.

This thesis is a study of stochastic resonance (SR) in a discrete implementation of a leaky integrate-and-fire (LIF) neuron network. The aim was to determine if SR can be realised in limited precision discrete systems implemented on digital hardware. How neuronal modelling connects with SR is discussed. Analysis techniques for noisy spike trains are described, ranging from rate coding, statistical measures, and signal processing measures like power spectrum and signal-to-noise ratio (SNR). The main problem in computing spike train power spectra is how to get equi-spaced sample amplitudes given the short duration of spikes relative to their frequency. Three different methods of computing the SNR of a spike train given its power spectrum are described. The main problem is how to separate the power at the frequencies of interest from the noise power as the spike train encodes both noise and the signal of interest. Two models of the LIF neuron were developed, one continuous and one discrete, and the results compared. The discrete model allowed variation of the precision of the simulation values allowing investigation of the effect of precision limitation on SR. The main difference between the two models lies in the evolution of the membrane potential. When both models are allowed to decay from a high start value in the absence of input, the discrete model does not completely discharge while the continuous model discharges to almost zero. The results of simulating the discrete model on an FPGA and the continuous model on a PC showed that SR can be realised in discrete low resolution digital systems. SR was found to be sensitive to the precision of the values in the simulations. For a single neuron, we find that SR increases between 10 bits and 12 bits resolution after which it saturates. For a feed-forward network with multiple input neurons and one output neuron, SR is stronger with more than 6 input neurons and it saturates at a higher resolution. We conclude that stochastic resonance can manifest in discrete systems though to a lesser extent compared to continuous systems

Learning Mechanisms to account for the Speed, Selectivity and Invariance of Responses in the visual Cortex

Dans cette thèse je propose plusieurs mécanismes de plasticité synaptique qui pourraient expliquer la rapidité, la sélectivité et l'invariance des réponses neuronales dans le cortex visuel. Leur plausibilité biologique est discutée. J'expose également les résultats d'une expérience de psychophysique pertinente, qui montrent que la familiarité peut accélérer les traitements visuels. Au delà de ces résultats propres au système visuel, les travaux présentés ici créditent l'hypothèse de l'utilisation des dates de spikes pour encoder, décoder, et traiter l'information dans le cerveau - c'est la théorie dite du 'codage temporel'. Dans un tel cadre, la Spike Timing Dependent Plasticity pourrait jouer un rôle clef, en détectant des patterns de spikes répétitifs et en permettant d'y répondre de plus en plus rapidement.In this thesis I propose various activity-driven synaptic plasticity mechanisms that could account for the speed, selectivity and invariance of the neuronal responses in the visual cortex. Their biological plausibility is discussed. I also present the results of a relevant psychophysical experiment demonstrating that familiarity can accelerate visual processing. Beyond these results on the visual system, the studies presented here also credit the hypothesis that the brain uses the spike times to encode, decode, and process information - a theory referred to as 'temporal coding'. In such a framework the Spike Timing Dependent Plasticity may play a key role, by detecting repeating spike patterns and by generating faster and faster responses to those patterns

Temporal Coding and Learning in Spiking Neural Networks

Ph.DDOCTOR OF PHILOSOPH