Supervised Learning in Multilayer Spiking Neural Networks

The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.Comment: 38 pages, 4 figure

The Power of Linear Recurrent Neural Networks

Recurrent neural networks are a powerful means to cope with time series. We show how a type of linearly activated recurrent neural networks, which we call predictive neural networks, can approximate any time-dependent function f(t) given by a number of function values. The approximation can effectively be learned by simply solving a linear equation system; no backpropagation or similar methods are needed. Furthermore, the network size can be reduced by taking only most relevant components. Thus, in contrast to others, our approach not only learns network weights but also the network architecture. The networks have interesting properties: They end up in ellipse trajectories in the long run and allow the prediction of further values and compact representations of functions. We demonstrate this by several experiments, among them multiple superimposed oscillators (MSO), robotic soccer, and predicting stock prices. Predictive neural networks outperform the previous state-of-the-art for the MSO task with a minimal number of units.Comment: 22 pages, 14 figures and tables, revised implementatio

Comparative performance of some popular ANN algorithms on benchmark and function approximation problems

We report an inter-comparison of some popular algorithms within the artificial neural network domain (viz., Local search algorithms, global search algorithms, higher order algorithms and the hybrid algorithms) by applying them to the standard benchmarking problems like the IRIS data, XOR/N-Bit parity and Two Spiral. Apart from giving a brief description of these algorithms, the results obtained for the above benchmark problems are presented in the paper. The results suggest that while Levenberg-Marquardt algorithm yields the lowest RMS error for the N-bit Parity and the Two Spiral problems, Higher Order Neurons algorithm gives the best results for the IRIS data problem. The best results for the XOR problem are obtained with the Neuro Fuzzy algorithm. The above algorithms were also applied for solving several regression problems such as cos(x) and a few special functions like the Gamma function, the complimentary Error function and the upper tail cumulative $\chi^2$-distribution function. The results of these regression problems indicate that, among all the ANN algorithms used in the present study, Levenberg-Marquardt algorithm yields the best results. Keeping in view the highly non-linear behaviour and the wide dynamic range of these functions, it is suggested that these functions can be also considered as standard benchmark problems for function approximation using artificial neural networks.Comment: 18 pages 5 figures. Accepted in Pramana- Journal of Physic