On the number of spurious memories in the Hopfield model

The outer-product method for programming the Hopfield model is discussed. The method can result in many spurious stable states-exponential in the number of vectors that are to be stored-even in the case when the vectors are orthogonal

The number of metastable states in the generalized random orthogonal model

We calculate the number of metastable states in the generalized random orthogonal model. The results obtained are verified by exact numerical enumeration for small systems sizes but taking into account finite size effects. These results are compared with those for Hopfield model in order to examine the effect of strict orthonormality of neural network patterns on the number of metastable states.Comment: 12 pages, 4 EPS figure

Harmonic analysis of neural networks

Neural networks models have attracted a lot of interest in recent years mainly because there were perceived as a new idea for computing. These models can be described as a network in which every node computes a linear threshold function. One of the main difficulties in analyzing the properties of these networks is the fact that they consist of nonlinear elements. I will present a novel approach, based on harmonic analysis of Boolean functions, to analyze neural networks. In particular I will show how this technique can be applied to answer the following two fundamental questions (i) what is the computational power of a polynomial threshold element with respect to linear threshold elements? (ii) Is it possible to get exponentially many spurious memories when we use the outer-product method for programming the Hopfield model

Medical imaging analysis with artificial neural networks

Given that neural networks have been widely reported in the research community of medical imaging, we provide a focused literature survey on recent neural network developments in computer-aided diagnosis, medical image segmentation and edge detection towards visual content analysis, and medical image registration for its pre-processing and post-processing, with the aims of increasing awareness of how neural networks can be applied to these areas and to provide a foundation for further research and practical development. Representative techniques and algorithms are explained in detail to provide inspiring examples illustrating: (i) how a known neural network with fixed structure and training procedure could be applied to resolve a medical imaging problem; (ii) how medical images could be analysed, processed, and characterised by neural networks; and (iii) how neural networks could be expanded further to resolve problems relevant to medical imaging. In the concluding section, a highlight of comparisons among many neural network applications is included to provide a global view on computational intelligence with neural networks in medical imaging