New acceleration technique for the backpropagation algorithm

Artificial neural networks have been studied for many years in the hope of achieving human like performance in the area of pattern recognition, speech synthesis and higher level of cognitive process. In the connectionist model there are several interconnected processing elements called the neurons that have limited processing capability. Even though the rate of information transmitted between these elements is limited, the complex interconnection and the cooperative interaction between these elements results in a vastly increased computing power; The neural network models are specified by an organized network topology of interconnected neurons. These networks have to be trained in order them to be used for a specific purpose. Backpropagation is one of the popular methods of training the neural networks. There has been a lot of improvement over the speed of convergence of standard backpropagation algorithm in the recent past. Herein we have presented a new technique for accelerating the existing backpropagation without modifying it. We have used the fourth order interpolation method for the dominant eigen values, by using these we change the slope of the activation function. And by doing so we increase the speed of convergence of the backpropagation algorithm; Our experiments have shown significant improvement in the convergence time for problems widely used in benchmarKing Three to ten fold decrease in convergence time is achieved. Convergence time decreases as the complexity of the problem increases. The technique adjusts the energy state of the system so as to escape from local minima

Multi-objective engineering shape optimization using differential evolution interfaced to the Nimrod/O tool

This paper presents an enhancement of the Nimrod/O optimization tool by interfacing DEMO, an external multiobjective optimization algorithm. DEMO is a variant of differential evolution – an algorithm that has attained much popularity in the research community, and this work represents the first time that true multiobjective optimizations have been performed with Nimrod/O. A modification to the DEMO code enables multiple objectives to be evaluated concurrently. With Nimrod/O’s support for parallelism, this can reduce the wall-clock time significantly for compute intensive objective function evaluations. We describe the usage and implementation of the interface and present two optimizations. The first is a two objective mathematical function in which the Pareto front is successfully found after only 30 generations. The second test case is the three-objective shape optimization of a rib-reinforced wall bracket using the Finite Element software, Code_Aster. The interfacing of the already successful packages of Nimrod/O and DEMO yields a solution that we believe can benefit a wide community, both industrial and academic

A Line of Sight Approach to Cosmic Microwave Background Anisotropies

We present a new method for calculating linear cosmic microwave background (CMB) anisotropy spectra based on integration over sources along the photon past light cone. In this approach the temperature anisotropy is written as a time integral over the product of a geometrical term and a source term. The geometrical term is given by radial eigenfunctions which do not depend on the particular cosmological model. The source term can be expressed in terms of photon, baryon and metric perturbations, all of which can be calculated using a small number of differential equations. This split clearly separates between the dynamical and geometrical effects on the CMB anisotropies. More importantly, it allows to significantly reduce the computational time compared to standard methods. This is achieved because the source term, which depends on the model and is generally the most time consuming part of calculation, is a slowly varying function of wavelength and needs to be evaluated only in a small number of points. The geometrical term, which oscillates much more rapidly than the source term, does not depend on the particular model and can be precomputed in advance. Standard methods that do not separate the two terms and require a much higher number of evaluations. The new method leads to about two orders of magnitude reduction in CPU time when compared to standard methods and typically requires a few minutes on a workstation for a single model. The method should be especially useful for accurate determinations of cosmological parameters from CMB anisotropy and polarization measurements that will become possible with the next generation of experiments. A programm implementing this method can be obtained from the authors.Comment: 20 pages, 5 figures. Fortran code available from the author