Analysis of Neural Networks in Terms of Domain Functions

Despite their success-story, artificial neural networks have one major disadvantage compared to other techniques: the inability to explain comprehensively how a trained neural network reaches its output; neural networks are not only (incorrectly) seen as a "magic tool" but possibly even more as a mysterious "black box". Although much research has already been done to "open the box," there is a notable hiatus in known publications on analysis of neural networks. So far, mainly sensitivity analysis and rule extraction methods have been used to analyze neural networks. However, these can only be applied in a limited subset of the problem domains where neural network solutions are encountered. In this paper we propose a wider applicable method which, for a given problem domain, involves identifying basic functions with which users in that domain are already familiar, and describing trained neural networks, or parts thereof, in terms of those basic functions. This will provide a comprehensible description of the neural network's function and, depending on the chosen base functions, it may also provide an insight into the neural network' s inner "reasoning." It could further be used to optimize neural network systems. An analysis in terms of base functions may even make clear how to (re)construct a superior system using those base functions, thus using the neural network as a construction advisor

Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

A characterization of the Edge of Criticality in Binary Echo State Networks

Echo State Networks (ESNs) are simplified recurrent neural network models composed of a reservoir and a linear, trainable readout layer. The reservoir is tunable by some hyper-parameters that control the network behaviour. ESNs are known to be effective in solving tasks when configured on a region in (hyper-)parameter space called \emph{Edge of Criticality} (EoC), where the system is maximally sensitive to perturbations hence affecting its behaviour. In this paper, we propose binary ESNs, which are architecturally equivalent to standard ESNs but consider binary activation functions and binary recurrent weights. For these networks, we derive a closed-form expression for the EoC in the autonomous case and perform simulations in order to assess their behavior in the case of noisy neurons and in the presence of a signal. We propose a theoretical explanation for the fact that the variance of the input plays a major role in characterizing the EoC

Cognitive networks: brains, internet, and civilizations

In this short essay, we discuss some basic features of cognitive activity at several different space-time scales: from neural networks in the brain to civilizations. One motivation for such comparative study is its heuristic value. Attempts to better understand the functioning of "wetware" involved in cognitive activities of central nervous system by comparing it with a computing device have a long tradition. We suggest that comparison with Internet might be more adequate. We briefly touch upon such subjects as encoding, compression, and Saussurean trichotomy langue/langage/parole in various environments.Comment: 16 page